We consider a joint sensor and controller design problem for linear Gaussian stochastic systems in which a weighted sum of quadratic control cost and the amount of information acquired by the sensor is minimized. This problem formulation is motivated by situations where a control law must be designed in the presence of sensing, communication, and privacy constraints. We show that the optimal joint sensor-controller design is relatively easy when the sensing policy is restricted to be linear. Namely, an explicit form of the optimal linear sensor equation, the Kalman filter, and the certainty equivalence controller that jointly solves the problem can be efficiently found by semidefinite programming (SDP). Whether the linearity assumption in our design is restrictive or not is currently an open problem.
Feedback control over noisy channels has been a popular research topic in the past two decades. Most of the early contributions focus on stabilization of unstable dynamical systems using feeback control over band-limited communication channels. A very partial list of papers in this context is @cite_16 @cite_5 @cite_8 @cite_12 @cite_21 @cite_14 @cite_2 . This research direction naturally leads to trade-off studies between the achievable control performance and the required capacity of the sensor-controller communication channel. If the communication rate is finite, larger block length (achieving high resolution) is not necessarily preferred since the resulting delay leads to the loss of control performance @cite_24 . LQG control performance subject to capacity constraints is considered in @cite_23 , where a certain separation principle" between control design and communication design is reported. The authors of @cite_11 consider a fundamental performance limitation of the finite horizon minimum-variance control (MVC) over noisy communication channels in the LQG regime. More comprehensive literature surveys on control designs over communication channels are available in @cite_19 @cite_25 @cite_7 @cite_22 .
@cite_14 @cite_22 @cite_7 @cite_8 @cite_21 @cite_24 @cite_19 @cite_23 @cite_2 @cite_5 @cite_16 @cite_25 @cite_12 @cite_11
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Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate @math bits sec and the expected cost @math . We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lower-bound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. The bound applies as long as the system noise has a probability density function. It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variable-length vector quantization to prove that the new converse bounds are tight. In this paper, we consider a robust network control problem. We consider linear unstable and uncertain discrete time plants with a network between the sensor and controller and the controller and plant. We investigate the effect of data drop out in the form of packet losses. Four distinct control schemes are explored and sufficient conditions to ensure almost sure stability of the closed loop system are derived for each of them in terms of minimum packet arrival rate and the maximum uncertainty. I. INTRODUCTION In the past decade, networked control systems (NCS) have gained much attention from both the control com- munity and the network and communication community. When compared with classical feedback control system, networked control systems have several advantages. For example, they can reduce the system wiring, make the system easy to operate and maintain and later diagnose in case of malfunctioning, and increase system agility (20). Although NCS have advantages, inserting a network in between the plant and the controller introduces many problems as well. For instance, zero-delayed sensing and actuation, perfect information and synchronization are no longer guaranteed in the new system architecture as only finite bandwidth is available and data packet drops and delays may occur due to network traffic conditions. These must be revisited and analyzed before networked control systems become prevalent. Recently, many researchers have spent effort on these issues and some significant results were obtained and many are in progress. Many of the aforementioned issues are studied separately. Tatikonda (19) and Sahai (13) have presented some interesting results in the area of control under communication constraints. Specifically, Tatikonda gave a necessary and sufficient condition on the channel data rate such that a noiseless LTI system in the closed loop is asymptotically stable. He also gave rate results for stabilizing a noisy LTI system over a digital channel. Sahai proposed the notion of anytime capacity to deal with real time estimation and control for a networked control system. In our paper (17), the authors have considered various rate issues under finite bandwidth, packet drops and finite controls. An optimal bit allocation scheme is given in (16) under the networked setting. The effect of pacekt drops on state estimation was studied by Sinopoli, et. al. in (3). It has further been investigated by many researchers including the present authors in (15) and (6). Abstract The paper considers the problem of robust stabilization of linear uncertain discrete-time systems via limited capacity communication channels. We consider the case when the control input is to be transmitted via communication channel with a bit-rate constraint. A constructive method to design a robustly stabilizing controller is proposed. Wireless vehicle-to-vehicle (V2V) and vehicle-toinfrastructure (V2I) communication holds great promise for significantly reducing the human and financial costs of vehicle collisions. A common characteristic of this communication is the broadcast of a device's core state information at regular intervals (e.g., vehicle speed and location or traffic signal state and timing). Unless controlled, the aggregate of these broadcasts will congest the channel under dense traffic scenarios, reducing the effectiveness of collision avoidance applications that use transmitted information. Active congestion control using distributed techniques is a topic of great interest for establishing the scalability of this technology. This paper defines a new adaptive congestion control algorithm that can be applied to the message rate of devices in this vehicular environment. While other published approaches rely on binary control, the LInear MEssage Rate Integrated Control (LIMERIC) algorithm takes advantage of full-precision control inputs that are available on the wireless channel. The result is provable convergence to fair and efficient channel utilization in the deterministic environment, under simple criteria for setting adaptive parameters. This “perfect” convergence avoids the limit cycle behavior that is inherent to binary control. We also discuss several practical aspects associated with implementing LIMERIC, including guidelines for the choice of system parameters to obtain desired utilization outcomes, a gain saturation technique that maintains robust convergence under all conditions, convergence with asynchronous updates, and using channel load to determine the aggregate message rate that is observable at a receiver. This paper also extends the convergence analysis for two important cases, i.e., measurement noise in the input signal and delay in the update process. This paper illustrates key analytical results using MATLAB numerical results and employs standard NS-2 simulations to demonstrate the performance of LIMERIC in several high-density scenarios.