CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Japanese Patent Application No. 2019-119171 filed on Jun. 26, 2019, incorporated herein by reference in its entirety.

BACKGROUND

1. Technical Field

The present disclosure relates to a distributed control system in which each of control devices for a plurality of apparatuses is connected to each other via a network and controls the state of its own apparatus based on the state of its own apparatus and the state of other apparatuses. More specifically, the present disclosure relates to a system in which the control devices for the plurality of apparatuses compose a multi-agent system, and the state of each apparatus is controlled according to a control protocol (consensus control, covering control, and distributed optimization control) of the multi-agent system. The apparatus to be controlled and/or managed in the distributed control system may be any apparatus, and may be, for example, an energy source in a distributed energy management system, that is, any machine or apparatus that sends energy through various media or on various carriers (a generator (a synchronous generator, an asynchronous generator, and the like), a solar battery, a windmill (a wind power generator, and the like), a waterwheel (a hydraulic power generator, and the like), a fuel cell, a chemical battery, a storage battery, other power generation apparatuses, a recharger, a charger/discharger, a light emitter, a heater, a cooler, a boiler, an engine, a gas turbine, a steam engine, and the like), a mobile object (a vehicle, an aircraft, a ship, a satellite, and the like), various types of manufacturing machines or processing machines in an industrial plant, and various sensors in a sensor network. Further, the distributed control system may be composed of any apparatus of which the operation is controlled and managed by the IoT technology. In addition, the state to be controlled in the distributed control system may be any measurable physical quantity and/or rate of change or rate of fluctuation thereof, such as output (power), voltage, pressure, temperature, torque, driving force, braking force, electromagnetic force, electromagnetic field, strength, radio field strength, frequency, number of vibration, phase, power factor, time, current, flow rate, flow velocity, volume, charge density, magnetic flux density, enthalpy, energy amount (heat storage amount, charge amount, and the like), position, moving speed, acceleration, rotating speed, operating speed, and rate of change of speed.

2. Description of Related Art

With the development of communication network technology, a technology is proposed and realized in which a plurality of apparatuses, particularly apparatuses located at a distance from each other, are connected to a network system, and the operation or state of the plurality of apparatuses is collectively or remotely controlled and managed through the network system. As one of the systems that control and manage a plurality of apparatuses using such a communication network technology, a distributed control system is used in which apparatuses connected to each other via the network mutually monitor the operation state of each other, and the state of each apparatus is controlled and managed autonomously. As a control protocol of the operation state of each apparatus in such a distributed control system, a control protocol or algorithm of a “multi-agent system” in which each apparatus in the system is controlled by a distributed controller is known, and in relation thereto, various configurations are proposed.

For example, Japanese Unexamined Patent Application Publication No. 2010-146246 proposes a configuration in which, when a plurality of multi-agent systems are independently constructed and operated in one system, an inter-agent communication function can be shared between the multi-agent systems in one terminal computer. Japanese Unexamined Patent Application Publication No. 2009-159808 proposes a distributed power system that includes a plurality of generators and loads, and uses a multi-agent technology in which a section agent arranged in each of sections separated by a section switch in the power system comprehend a tidal current amount in the section, requests a generator agent or a downstream section agent to adjust a tidal current increase/decrease amount, and the generator agent or the downstream section agent autonomously repeats the adjustment in cooperation with other generator agents or downstream section agents, thereby performing a distributed power supply in a section, and a demand-and-supply control in a downstream section. Moreover, Japanese Unexamined Patent Application Publication No. 2016-099955 proposes a configuration in which an information processing device of each user specifies a transmission destination to which division value data indicating a division value based on the maximum power amount and a division value thereof is transmitted, and transmits the division value data, and another information processing device that receives the division value data calculates, from division values, the average value or a standard deviation of the power managed by a plurality of power management devices in order to improve the confidentiality of data on each user while responding to an increase in the number of users who share a statistical value. Further, it has been proposed that a control method of a multi-agent system is effective in controlling the state of an agent, such as a power supply source or an energy source, in a distributed energy management system (“Control of Multi-agent System” in System Control Engineering Series 22, Corona Publishing Co., Ltd. on Sep. 18, 2015, by Shunichi Azuma and five others). In “Average-consensus Problem of Multi-agent Systems with Non-uniform and Asymmetric Time-delays” (Vol. 47, No. 2, 100/109 (2011) in a journal published by The Society of Instrument and Control Engineers, by Kazunori Sakurama and one other), a condition in which a consensus value is obtained in an average consensus problem in multi-agent systems with heterogeneous time-delays in information transfer on a network is analyzed and considered. In addition, in “Average Consensus in Multi-agent Systems with Non-uniform Time-varying Delays and Random Packet Losses” (pages 322 to 326 of paper published at a third IFAC International Conference on Intelligent Control and Automation Science in Chengdu, China, on Sep. 2 to 4, 2013, by Jian Wu, Yang Shi, Bingxian Mu, Huxiong Li, and Wenbai Li), a method of converging the state values of all agents to their consensus value, which is the average value of initial values of the agents, in the average consensus problem in multi-agent systems when the time-delay occurring in information transfer on a network is symmetric has been proposed.

SUMMARY

In a control protocol of a multi-agent system on states of a plurality of apparatuses connected to a communication network in a distributed control system, a state indicator value xirepresenting a state of any apparatus, that is, an agent i, is controlled according to the following equation:
xi[k+1]=xi[k]+Ts·ui[k]  (1)
ui[k]=Σj∈NinF(xj[k],xi[k])  (1a)

Here, xi[k] and xi[k+1] respectively represent a state indicator value of the agent i at a time k and a target value to be taken by the state indicator value one sampling time after the time k. xj[k] represents a state indicator value of an agent j, directly connected to the agent i via the communication network, at the time k. Tsrepresents a sampling period. Moreover, ui[k] in equation (1a) is referred to as a “distributed controller”, and F(xj[k], xi[k]) is a function of xi[k], xj[k]. In addition, the above equation is applied to a case of a discrete-time system. In a case of a continuous-time system, an equation obtained by rewriting a differential equation of the state xito a differential equation is used. Particularly, when the distributed control is consensus control, the distributed controller ui[k] is expressed by the following equation:

ui⁡[k]=∑j∈Nin⁢aij⁡(xj⁡[k]-xi⁡[k])(2)aij={11+max(Ni,Nj⁢:j∈Ni0:j∉Ni(2⁢a)

Here, Niand Njrepresent sets of agents directly connected to agents i and j, respectively, |Ni| and |Nj| represent numbers (degrees) of Niand Nj, respectively. When a configuration of the system is an undirected graph in which all agents are connected and the state of each agent in the system is controlled according to the above equation (2), in theory, the state indicator value xiof each agent converges to an average value of initial values xi[0] of the state indicator values xiof the agents as a consensus value (average consensus control) as follows:

X*=∑i=1n⁢xi⁡[0]n(3)

It has been found (see Japanese Patent Application No. 2019-010040), in a case of the consensus control or other control (covering control, distributed optimization control) of the multi-agent system described above, based on the research so far, under the assumption of simultaneity between agents (a state in which there is no time delay in signal information transfer on the communication network between agents and each agent can refer to the state indicator value of an adjacent agent in real time (immediately)), the state indicator value xiof each agent in the calculation according to the above equation (1) stably converges. However, when the condition of the simultaneity between the agents is not satisfied, that is, when there is a time delay in the signal information transfer in the communication network between the agents, the state indicator value xidoes not converge, or even if it converges, the consensus value deviates from an expected consensus value (for example, the value in the equation (3)) or oscillations occur, and as a result, it has been found (see Japanese Patent Application No. 2019-010040) that it is difficult to stably control the state value of each agent in the control protocol of the multi-agent system as it is. Moreover, particularly, in a case of average consensus control, it is observed that when there is a time delay in the signal information transfer on the communication network between the agents, the average value of the state indicator values xiof all agents is not maintained as an average value of initial values xi[0] of the state indicator values xiof the agents, and even if the state indicator values xiof all agents converge to the consensus value, the consensus value deviates from the average value of the initial values xi[0] of the state indicator values xiof all agents (that is, the value in equation (3)).

On the other hand, in a communication network used in an actual distributed control system, it is impossible to avoid an occurrence of delay in the signal information transfer caused by several factors, such as an application delay [a μ-second order] (a delay that occurs when a transmission-side passes a packet to a TCP/IP layer, a delay that occurs when a reception-side receives and processes a packet and returns a response), a serialization delay [μ to m seconds order] (the period from when the first bit of a packet is transmitted to when the last bit is transmitted, which increases as the network bandwidth decreases, a propagation delay (a delay that occurs when a signal propagates a cable medium), a congestion delay (the time required to store an excess packet in a buffer and retransmit the excess packet when the bandwidth of the line is exceeded). Moreover, particularly, in a large network to which many agents are connected, a signal traffic is congested so that a communication delay occurs due to factors, such as a delay in signal transmission via a communication cable, a delay in transmission via a router, a hub, or the like, a collision due to a concentration of communication, and a delay in transmission during multi-hop communication. Therefore, in order to control, by the control protocol of the multi-agent system in an actual distributed control system, the state of each agent as expected, it is necessary to improve the control protocol according to equation (1).

In this regard, the inventors of the present disclosure have already disclosed in Japanese Patent Application No. 2019-010040 as follows: in the state control of each agent, in case in which the distributed controller calculates a changed amount of the state indicator value of its own (own agent), that is, a control input of the distributed controller (uiin the equation (1)) with reference to the state indicator values of agents (adjacent agents) adjacent to the own agent, when the control device of each apparatus intermittently refers to the state indicator value of the adjacent agents instead of using all of the state indicator values of the adjacent agents sampled in time series, it is possible to compensate for worsening of the state indicator value's convergence to a consensus value, which is caused by time delay in signal information transfer on the communication network between the agents. In addition, in the average consensus control in which it is assumed that two-way time delays between any two agents are equal (that is, the time delays are symmetric), it is possible to match the consensus value to which the state indicating value of each agent converges with the average value of the initial values xi[0] of the state indicator values xiof all agents as expected by using the state indicating value of which the sample time matches that of the referred state indicating value of the adjacent agent, as the state indicating value of the own agent in control input of the distributed controller. As such, it is possible to compensate for convergence of the state indicating value to the consensus value and accuracy thereof.

As a result of further research and development by the inventors of the present disclosure, it has been found that in a control protocol of a multi-agent system in a case in which a meaningful time delay occurs in signal information transfer on the communication network between agents, convergence of the state indicator value of each agent to the consensus value or an equilibrium value depends on a length of delay time (transmission time) in transmission of the state indicator values between adjacent agents, and thus the convergence of the state indicator value of each agent can be further improved by adjusting the contribution of the distributed controller to the target value of the state indicator value of each agent between the adjacent agents according to a length of delay time (communication delay time) in transmission of the state indicator value of each agent. Moreover, it has been found that the above effect can be obtained even when the time delay in signal communication between adjacent agents is not symmetric. This finding is used in the present disclosure.

Thus, one aspect of the present disclosure is a distributed control system configured to control or manage a state of each of a plurality of apparatuses connected to each other via a communication network according to a control protocol of a multi-agent system as described above. The present disclosure provides a system configured to control the state of each apparatus using a new control protocol that can compensate for worsening of convergence of the state indicator value of each agent, which is caused by delay in signal communication even when the delay in the signal communication on the communication network is not symmetric (including when the time delay is symmetric).

The distributed control system according to one aspect of the present disclosure includes a plurality of control devices configured to respectively control the states of the plurality of apparatuses and a communication network composed of a plurality of communication lines that connect the plurality of control devices. A state indicator value indicating a selected state is measured in each of the apparatuses, and is transmitted from a control device of a corresponding one of the apparatuses via the communication line to a control device of an apparatus adjacent to the corresponding apparatus, from among the plurality of apparatuses connected to the communication lines. The control device of each of the apparatuses is configured to control the state of an own apparatus from among the plurality of apparatuses, the own apparatus controlling the selected state by oneself, by referring to the state indicator value of the own apparatus and the state indicator value of the adjacent apparatus, such that the state indicator value of the own apparatus matches a state target value that is determined according to the control protocol of a multi-agent system. Each of the control devices includes a state target value determination unit that determines, according to the control protocol, the state target value of the own apparatus, using the current state indicator value of the own apparatus, and a distributed controller input that is a function of the state indicator value of the adjacent apparatus and the state indicator value of the own apparatus. The state target value determination unit is configured to determine a control gain which adjusts contribution of the distributed controller input to the state target value based on at least one of a communication delay time when the state indicator value of the adjacent apparatus is transmitted from the control device of the adjacent apparatus to each of the plurality of control devices and the communication delay time when the state indicator value of the own apparatus is transmitted from each of the plurality of control devices to the control device of the adjacent apparatus.

In the above configuration, the “apparatus” may be any apparatus of which an operation state is controlled, such as an energy source, a mobile object, various pieces of manufacturing machinery, and various sensors, as described in the “Technical Field”, the “selected state” of the “apparatus” is any measurable physical quantity and/or a rate of change or rate of fluctuation of the physical quantity, as described in the “Technical Field”, and may be an arbitrarily selected state. The “state indicator value” is an actually measured value indicating the selected state, and the “state target value” is a target value of the state to which the state indicator value should match in the state control. The control device may be any form of control device that measures the state indicator value indicating any state of the apparatus and autonomously controls the state, and typically, may appropriately control the state of the apparatus using a computer. The communication line which is connected between the control devices of the apparatuses and transmits a signal indicating the state value of each apparatus may be a line that transmits a signal in any type, such as wired communication, wireless communication, and optical communication. In addition, in the above configuration, “own apparatus” refers to an apparatus of which the state is controlled by its own control device from among the control devices in the system, and the “adjacent apparatus” refers to an apparatus of which the state is controlled by a control device directly connected to the apparatus via the communication line, from among the control devices. (An apparatus of which the state is controlled by another control device further connected via the communication line to a control device connected via the communication line, from among the control devices, refers to the adjacent apparatus of the adjacent apparatus.) The “control protocol of the multi-agent system”, as known in this field, may be any protocol that achieves the consensus control for solving a consensus problem in the multi-agent system, the covering control for solving a covering problem, and the distributed optimization control for solving a distributed optimization problem (hereinafter, referred to as “the consensus control, and the like”). Particularly, the consensus control is a form of control that controls the state of each agent such that the state indicator values of all agents (that is, apparatuses) in the system asymptotically match a certain consensus value. In other words, the consensus control controls the state of each agent such that the state indicator values xi, xjof any agents i, j in the system satisfy the following equation:

limk→∞⁢(xi⁡[k]-xj⁡[k])=0(4)
and such that the state indicator value xiof any agent i converges to a certain constant value α, that is, satisfies the following equation:

limk→∞⁢xi⁡[k]=α(5)

The consensus control to which the present disclosure is applied may be an average consensus control in which the consensus value is the average value of the initial values of the status indicator values of all agents, and a leader and follower consensus control in which the consensus value is the status indicator value of a certain agent in the system, or a consensus control in which the consensus value is a geometric average value, a maximum value, or a minimum value of the initial values of the state indicating values of all agents. Further, when the control protocol is the consensus control, the function of the state indicator value of the adjacent apparatus and the state indicator value of the own apparatus is a difference between the state indicator value of the adjacent apparatus and the state indicator value of the own apparatus. In other control forms, the state of each agent is controlled such that the state indicator value xiof any agent i converges to a certain equilibrium value (hereinafter, the consensus value and the equilibrium value are referred to as “the consensus value, and the like”).

As described above, it has been found by the research so far as follows: in a case in which the control protocol of the above multi-agent system controls the state of each agent by using a differential equation of the above equation (1) as it is, which is generally known for achieving the consensus control, and the like, in theory, when each agent can refer to the state indicating value of the adjacent agent in real time, that is, when there is no time delay when the state indicator value is transmitted from the adjacent agent to each agent via the communication line, the state indicator values of all the agents converge to a certain consensus value, and the like. However, when a meaningful time is required for transmitting the state indicator value between agents via the communication line (when time delay occurs), the state indicator value of each agent does not converge to the consensus value, and the like, or even if it converges, the consensus value deviates, or the like. Therefore, in a distributed control system that uses an actual communication network in which time delay in transmission of the state indicator value via the communication line occurs, an appropriate consensus control, and the like, cannot be achieved by control using the equation (1) as it is. To resolve the above shortcoming, the inventors of the present disclosure have proposed in Japanese Patent Application No. 2019-010040, a configuration for compensating for the influence on the consensus control, which is caused by the delay in the signal communication on the communication network.

The inventors of the present disclosure further searched for a control protocol that can appropriately achieve the consensus control and the like, and particularly a control protocol that can obtain an advantageous effect even when the time delay of the signal communication is not symmetric. As a result, as described above, it has been found that the quality of the convergence of the state indicator value of each agent to the consensus value, and the like, depends on the length of time (the communication delay time) required for communication of the state indicator value between adjacent control devices, and the convergence of the state indicator value of each apparatus can be further improved by adjusting the contribution of the distributed controller to the target value of the state indicator value of each agent according to the length of the communication delay time.

Thus, in the system according to the above aspect of the present disclosure, as described above, the state target value determination unit of the control device of each apparatus determines the state target value of own apparatus of each of the control devices using the current state indicator value of the own apparatus, and the distributed controller input which is a function of the state indicator value of the adjacent apparatus and the state indicator value of the own apparatus. The control gain which adjusts contribution of the distributed controller input to the state target value is determined based on a communication delay time when the state indicator value of the adjacent apparatus is transmitted from the control device of the adjacent apparatus to each control device or a communication delay time when the state indicator value of the own apparatus is transmitted from each control device to the control device of the adjacent apparatus. As such, the convergence of the state indicator value of each agent to the consensus value, and the like, is further improved.

In the system according to the above aspect, the state target value determination unit of each of the plurality of control devices may determine the control gain based on the longer time from among the communication delay time when the state indicator value of the adjacent apparatus is transmitted from the control device of the adjacent apparatus to each of the plurality of control devices and the communication delay time when the state indicator value of the own apparatus is transmitted from each of the plurality of control devices to the control device of the adjacent apparatus. Since the communication delay time (a first communication delay time) when the state indicator value of the adjacent apparatus is transmitted from the control device of the adjacent apparatus to each control device may be different from the communication delay time (a second communication delay time) when the state indicator value of the own apparatus is transmitted from each control device to the control device of the adjacent apparatus when the delay in the signal communication on the communication network is not necessarily symmetric, an influence on the convergence of the state indicator value is larger as the communication delay time is longer. Therefore, in order to curb the influence, the control gain may be determined based on the longer time of the first communication delay time and the second communication delay time.

Further, in the system according to the above aspect, the state target value determination unit of each of the plurality of control devices may reduce the control gain when the communication delay time is long compared to when the communication delay time is short. As the communication delay time between the adjacent apparatuses is longer, the contribution of the function of the state indicator value in the distributed controller of the adjacent apparatus worsens the convergence of the state indicator value. Therefore, in order to reduce the contribution of the function of the state indicator value between the adjacent apparatuses having the long communication delay time, the control gain may be set to be reduced when the communication delay time is long compared to when the communication delay time is short.

Further, in the system according to the above aspect, the state target value determination unit of each of the plurality of control devices may set, when the distributed controller input is the sum of functions of the state indicator values of a plurality of apparatuses adjacent to the own apparatus and the state indicator value of the own apparatus, the control gain for each of functions corresponding to the control devices of the adjacent apparatuses connected to each of the plurality of control devices. The control device of each apparatus may be connected to the control device of at least one adjacent apparatus via the communication network, and the communication delay time is different for each adjacent control device. Therefore, when the distributed controller input is the sum of the functions of the state indicator values of a plurality of adjacent apparatuses and the state indicator value of the own apparatus, the control gain may be determined according to the communication delay time corresponding to each adjacent control device, that is, each function of the state indicator values of the apparatuses adjacent to each other in the distributed controller. In addition, in the case of the average consensus control, at a request for maintaining the average value of the state indicator values of the plurality of apparatuses in the system, the control gains on the functions of the state indicator values of the apparatuses adjacent to each other in each of the distributed controllers of the adjacent apparatuses may be set equal to each other such that the contributions of the difference between the state indicator values in the distributed controllers of the adjacent apparatuses on the state target values of the adjacent apparatuses are equal to each other.

In the above aspect, with the above configuration of the present disclosure, the distributed controller input uiof the equation (1) may be modified, using the control gain as described above, as follows:
ui[k]=Σj∈NinGij·F(xj[kaj],xi[kbi])  (6)

Here, Gijis the control gain set for each of functions F corresponding to the control devices of the adjacent apparatuses connected to each control device, and may be a function of max(Δij, Δji) using the communication delay time (the first communication delay time) Δijwhen the state indicator value of the adjacent apparatus is transmitted from the control device of the adjacent apparatus to each control device and the communication delay time (the second communication delay time) ΔTwhen the state indicator value of the own apparatus is transmitted from each control device to the control device of the adjacent apparatus. kajis a measurement time of the state indicator value of the adjacent apparatus j, which is referred to in calculation by the distributed controller ui, and kbiis a measurement time of the state indicator value of the own apparatus i, which is referred to in calculation by the distributed controller ui(kajand kbido not have to match the current time k, as to be described below). Moreover, the control gain Gijin the distributed controller uimay be set to be equal, for example, to the control gain Gjiin the corresponding distributed controller uj. In the system according to the above aspect, the control gain Gijset for each of the functions corresponding to the control devices of the adjacent apparatuses connected to each of the plurality of control devices may be given as Gij=Γmax(Δij,Δji). . . (7), using an integer F smaller than 1, the communication delay time (the first communication delay time) Δijwhen the state indicator value of the adjacent apparatus is transmitted from the control device of the adjacent apparatus to each of the plurality of control devices, and the communication delay time (the second communication delay time) Δjiwhen the state indicator value of the own apparatus is transmitted from each of the plurality of control devices to the control device of the adjacent apparatus.

In the above configuration of the present disclosure, when the control gain is determined by the communication delay time of the state indicator value, the control device of each apparatus needs to check when the state indicator value referred to in the determination of the state target value has been measured and when the state indicator value referred to has been received at the control device of the transmission destination. Therefore, the measurement time is given as a measurement time stamp to the measured state indicator value of each apparatus in each control device and transmitted to the control device of the adjacent apparatus together with the state indicator value, and the reception time is given as a reception time stamp to the received state indicator value of each control device, such that the communication delay time that is a difference between the measurement time and the reception time may be transmitted to the control device of a transmission source of the state indicator value and referred to in the determination of the control gain.

Further, in the system according to the above aspect of the present disclosure, each control device may include a transmission unit that transmits the state indicator value of the own apparatus to the control device of the adjacent apparatus. The transmission unit may be configured to transmit the latest state indicator value of the own apparatus after the state indicator value of the own apparatus is transmitted and arrives at the control device of the adjacent apparatus. As proposed in Japanese Patent Application No. 2019-010040, in the multi-agent system, in determination of a change amount per cycle in the state target value of each agent (that is, the distributed controller input), when the control device of each apparatus intermittently refers to the state indicator value of the adjacent agent instead of using all of the state indicator values measured in time series in the adjacent agent, and more specifically, refers to the state indicator value of the adjacent agent leaving out the state indicator values of the adjacent agent measured from when one state indicator value is transmitted from the adjacent agent via the communication line to when it arrives at each agent (that is, the value referred to as the state indicator value of the adjacent agent is the value of each time period between when a signal of the state indicator value is transmitted from the adjacent agent to each agent and when the a notification that the signal is reached is transmitted from each agent to the adjacent agent), the convergence of the state indicator value of each agent to the consensus value, and the like is improved. Therefore, in the system of the present disclosure, as described above, the transmission unit that transmits the state indicator value of the own apparatus of the control device of each apparatus to the control device of the adjacent apparatus transmits the state indicator value of the own apparatus once, stands by the transmitted state indicator value of the own apparatus for reaching the control device of the adjacent apparatus, and transmits the latest state indicator value of the own apparatus, such that the control device of each apparatus may intermittently refer to the state indicator value of the adjacent apparatus. As such, the convergence of the state indicator value of each apparatus to one consensus value, and the like may be improved.

Still further, in the system according to the above aspect of the present disclosure, the function used by the state target value determination unit of each control device may be the function of the latest state indicator value of the adjacent apparatus received from the control device of the adjacent apparatus and the latest state indicator value of the own apparatus received by the control device of the adjacent apparatus. Here, “the latest state indicator value of the adjacent apparatus received from the control device of the adjacent apparatus” is the latest value among the state indicator values that is transmitted from the control device of the adjacent apparatus and received by each control device, not the latest state indicator value sequentially measured in the adjacent apparatus. In other words, the state indicator value of the adjacent apparatus referred to in the distributed controller of the multi-agent system of the present disclosure is the latest value among the state indicator values measured in the adjacent apparatus at a time traced back by the amount of the first communication delay time (the time required for transmission of the state indicator value from the control device of the adjacent apparatus to each control device) from the time when each control device has received the state indicator value. Moreover, “the latest state indicator value of the own apparatus received by the control device of the adjacent apparatus” is the latest value among the state indicator values of the own apparatus that is transmitted from the control device of the own apparatus and actually received by the control device of the adjacent apparatus (which is the transmission source of the state indicator value received by the control device of the own apparatus), not the latest state indicator value sequentially measured in the own apparatus. In other words, the state indicator value of the own apparatus referred to in the distributed controller of the multi-agent system of the present disclosure is the latest value among the state indicator values measured in the own apparatus at a time traced back by the amount of the second communication delay time (the amount of time required for transmission of the state indicator value from the control device of each own apparatus to the control device of the adjacent apparatus) from the time when the control device of the adjacent apparatus receives the state indicator value. With the above-described configuration, as to be described in a “DETAILED DESCRIPTION OF EMBODIMENTS” below, during a control operation, the same state indicator value may be referred to as the state indicator value of the adjacent apparatus and the state indicator value of the own apparatus in the distributed controller of each control device (that is, when the apparatus i and the apparatus j exchange the state indicator values xi[kb] and xj[ka], xi[kb], which is the value of the adjacent apparatus for the apparatus j, is referred to as the value of the own apparatus for the apparatus i, and xj[ka], which is the value of the adjacent apparatus for the apparatus i, is referred to as the value of the own apparatus for the apparatus j). Therefore, the average value of the state indicator values of a plurality of apparatuses in the system is maintained, as such it is possible to stabilize the consensus value, and the like, of the state indicator value of each apparatus.

In the above configuration, in response to reception of the state indicator value of the own apparatus transmitted by itself to the control device of the adjacent apparatus, each control device refers to the state indicator value of the own apparatus in the distributed controller. Therefore, each control device may include a state indicator value reception notification unit that notifies the control device of the adjacent apparatus of the transmission source that the control device has received the state indicator value of the adjacent apparatus once it receives the state indicator value of the adjacent apparatus transmitted from the control device of the adjacent apparatus, such that each control device can notice that the state indicator value of the own apparatus transmitted by the control device itself has been received by the control device of the adjacent apparatus. In other words, each control device can transmit, as a reception-side of the state indicator value, a reception notification to the transmission source, using the state indicator value reception notification unit, and thus each control device can notice, as a transmission-side of the state indicator value, that the state indicator value has arrived at a reception-side. As such, the distributed controller refers to the state indicator value same as that received by the control device of the adjacent apparatus. Therefore, the state indicator value of the own apparatus referred to in the distributed controller of the state target value determination unit of each control device may be the latest state indicator value of the own apparatus that receives the notification from the control device of the adjacent apparatus that the state indicator value of the own apparatus has been received by the control device of the adjacent apparatus.

As described above, the transmission unit of the control device of each apparatus may transmit the next (that is, the latest) state indicator value to the control device of the adjacent apparatus in response to the notification from the control device of the adjacent apparatus that the state indicator value of the own apparatus has arrived at the control device of the adjacent apparatus, by including the state indicator value reception notification unit in each control device. In this case, when the transmission unit of the control device of each apparatus does not receive the notification that a signal of the state indicator value of the own apparatus has arrived even after a predetermined time has elapsed from the control device of the adjacent apparatus even after transmitting the state indicator value, the transmission unit may transmit the next state indicator value (time-out processing). Here, the “predetermined time” may be set to any time longer than a time required for transmitting the signal of an assumed state indicator value (the communication delay time). Alternatively, when the communication delay time can be predicted, the transmission unit of the control device of each apparatus may once transmit the state indicator value of the own apparatus, stand by for a time corresponding to the communication delay time, and then transmit the next state indicator value to the control device of the adjacent apparatus.

Further, in the configuration of the above aspect of the present disclosure, the state indicator value of the own apparatus referred to in the distributed controller of each control device is the value received by the control device of the adjacent apparatus. Therefore, as described above, when the transmission unit that transmits the state indicator value of the own apparatus of each control device to the control device of the adjacent apparatus is configured to transmit the latest state indicator value of the own apparatus after the state indicator value of the transmitted state indicator value of the own apparatus arrives at the control device of the adjacent apparatus, for the state indicator value of the own apparatus referred to in the distributed controller of each control device, similar to the state indicator value of the adjacent apparatus, the value intermittently transmitted to the adjacent apparatus from among the state indicator values measured in time series in the own apparatus, instead of all of the state indicator values measured in time series in the own apparatus, is used.

Thus, according to the above aspect of the present disclosure, a configuration is provided in which the state target value of each apparatus is determined by a new control protocol that determines the control gain adjusting the contribution of the distributed controller input to the state target value based on the communication delay time of the state indicator value, in the distributed control system in which each apparatus is connected via the communication network. As described above, in the communication network of the actual distributed control system, an occurrence of the asymmetric time delay caused by various factors is inevitable in signal transmission. With the configuration of the above aspect of the present disclosure, since it is possible to compensate for the influence of such a time delay in transmission of the state indicator value on the control of the multi-agent system, the distributed control system that can appropriately control the state of each apparatus is expected to be more widely distributed.

Further objects and advantageous effects of one aspect of the present disclosure will become apparent from the following description of embodiments of the present disclosure.

