Decentralised control for complex systems - an invited survey <s> Introduction <s> This paper surveys the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems. <s> BIB001 </s> Decentralised control for complex systems - an invited survey <s> Introduction <s> Large scale control systems results of multivariable feedback systems models and structure of interconnected systems decentralized stabilizability the decentralized stabilization and pole assignment optimal decentralized control stability analysis of interconnected systems decentralized design for strongly coupled subsystems decentralized design for weakly coupled systems decentralized PI controllers strongly coupled symmetric composite systems survey of the results and open problems in feedback control of large-scale systems. <s> BIB002 </s> Decentralised control for complex systems - an invited survey <s> Introduction <s> The decentralised load-frequency controller design problem concerned is translated into an equivalent problem of decentralised controller design for a multi-input multi-output (MIMO) control system. It is shown that, subject to a condition based on the structured singular values, each local area load-frequency controller can be designed independently. The stability condition for the overall system can be stated as to achieve a sufficient interaction margin and a sufficient gain and phase margin defined in classical feedback theory during each independent design. It is demonstrated by computer simulations that within this general framework, very simple local controllers can be designed to achieve satisfactory performances for a sample two-area power system and a simplified four-area power system. Under the proposed framework based on the structured singular values, other design methods for local area controllers may also be applied. © IEE, 1998. <s> BIB003 </s> Decentralised control for complex systems - an invited survey <s> Introduction <s> This paper focuses on a class of large-scale interconnected stochastic nonlinear systems. The interconnections are bounded by strong nonlinear functions that contain first order and higher order polynomials as special cases. The problem we address is to design a decentralized controller such that the closed-loop, large-scale, interconnected stochastic nonlinear system is globally asymptotically stable in probability for all admissible interconnections. It is shown that the decentralized global stabilization via both state feedback and output feedback can be solved by a Lyapunov-based recursive design method. <s> BIB004 </s> Decentralised control for complex systems - an invited survey <s> Introduction <s> The problem of decentralized output-feedback tracking with disturbance attenuation is addressed for a new class of large-scale and minimum-phase nonlinear systems. Common assumptions like matching and growth conditions are not required for the underlying decentralized system with a diagonal structure. An observer-based decentralized controller design is presented. The proposed decentralized output-feedback laws achieve asymptotic tracking and internal Lagrange stability when the disturbance inputs disappear, and, guarantee external stability in the presence of disturbance inputs. These external stability properties include Sontag's ISS and iISS conditions and standard L"2-gain property. <s> BIB005 </s> Decentralised control for complex systems - an invited survey <s> Introduction <s> Abstract Despite the closed-loop performance advantages of centralized multivariable controllers, the great majority of industrial process control applications is still based on decentralized controllers. Because of their single loop structure, decentralized controllers cannot suppress the interactions of the plant, which are only taken into account in the controller tuning phase. Therefore, it would be useful in many cases to delimit in some way the undesirable effects of the coupling between inputs and outputs of the closed loop system. A control algorithm to achieve this goal is developed in the paper. The proposal is applicable even to processes with non-minimum phase transmission zeros (provided their off-diagonal transfer functions have their zeros in the left-half-plane). Based on sliding mode attributes, the proposed scheme can be easily added to a previously designed decentralized control system. <s> BIB006 </s> Decentralised control for complex systems - an invited survey <s> Introduction <s> In this paper, the problem of decentralized adaptive output-feedback stabilization is investigated for large-scale stochastic nonlinear systems with three types of uncertainties, including parametric uncertainties, nonlinear uncertain interactions and stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystems are stochastic input-to-state stable, an adaptive output-feedback controller is constructively designed by the backstepping method. It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability. In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin. The contributions of the work are characterized by the following novel features: (1) even for centralized single-input single-output systems, this paper presents a first result in stochastic, nonlinear, adaptive, output-feedback asymptotic stabilization; (2) the methodology previously developed for deterministic large-scale systems is generalized to stochastic ones. At the same time, novel small-gain conditions for small signals are identified in the setting of stochastic systems design; (3) both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states; (4) parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields, which may appear nonlinearly; (5) the concept of stochastic input-to-state stability and the method of changing supply functions are adapted, for the first time, to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control. <s> BIB007 </s> Decentralised control for complex systems - an invited survey <s> Introduction <s> Abstract The paper reviews the past and present results in the area of decentralized control of large scale complex systems. An emphasis is laid on decentralization, decomposition, and robustness. These methodologies serve as effective tools to overcome specific difficulties arising in large scale complex systems such as high dimensionality, information structure constraints, uncertainty, and delays. Several prospective topics for future research are introduced in this contents. The overview is focused on recent decomposition approaches in interconnected dynamic systems due to their potential in providing the extension of decentralized control into networked control systems. <s> BIB008 </s> Decentralised control for complex systems - an invited survey <s> Introduction <s> Decentralized Control and Filtering provides a rigorous framework for examining the analysis, stability and control of large-scale systems, addressing the difficulties that arise because dimensionality, information structure constraints, parametric uncertainty and time-delays. This monograph serves three purposes: it reviews past methods and results from a contemporary perspective; it examines presents trends and approaches and to provide future possibilities; and it investigates robust, reliable and/or resilient decentralized design methods based on a framework of linear matrix inequalities. As well as providing an overview of large-scale systems theories from the past several decades, the author presents key modern concepts and efficient computational methods. Representative numerical examples, end-of-chapter problems, and typical system applications are included, and theoretical developments and practical applications of large-scale dynamical systems are discussed in depth. <s> BIB009 </s> Decentralised control for complex systems - an invited survey <s> Introduction <s> A decentralized adaptive approximation design for the fault tolerant control of a class interconnected feedback linearizable nonlinear systems is considered in this technical note. Multiple faults may occur in the subsystems local dynamics as well as in the interconnections between the subsystems. Linearly parameterized neural networks are used to adaptively approximate the unknown interconnection effects and changes in model dynamics due to failures. A dead-zone modification in the adaptive laws is combined with an adaptive bounding method for addressing stability and robustness issues in the presence of residual approximation errors. Outside the coverage region of the approximators, a decentralized safety control scheme is designed to steer back the trajectory by using a sliding mode approach with adaptive bounds. A simulation example is presented for illustrating the effectiveness of the proposed fault tolerant control methodology. <s> BIB010
In the real world, there are a number of systems which can be modelled as dynamical equations composed of interconnections between a collection of lower-dimensional subsystems. Such classes of systems are called large-scale interconnected systems, which are often widely distributed in space BIB002 BIB009 BIB001 . A fundamental property of an interconnected system is that a perturbation of one subsystem can affect the other subsystems as well as the overall performance of the entire network. The purpose of control and monitoring paradigms from the domain of engineering within a large scale interconnected systems architecture is thus to minimise the effect of any perturbation or uncertainty on the overall system behaviour. Large scale interconnected systems widely exist in society.A typical large scale interconnected system is the multi-machine power system . Other examples of large scale interconnected systems that present a great challenge to both system analysts and control designers include power networks, ecological systems, biological systems and energy systems BIB009  . For interconnected systems, the presupposition of centrality fails to hold due to either the lack of centralised information or the lack of centralised computing capability. When the number of subsystems is large, the computation time increases significantly if centralised control is employed. In the extreme case when information transfer among the subsystems is blocked, centralised control schemes simply cannot be applied. Even with engineered systems, issues such as the economic cost and reliability of communication links, particularly when systems are characterised by geographical separation, limit the appetite to develop centralised systems. From the perspective of economics and reliability, decentralised strategies are very pertinent for large scale interconnected systems. This has motivated the application of decentralised control methodologies to interconnected systems BIB004 BIB005 BIB007 BIB010 . In BIB003 , a decentralised load-frequency controller design problem is translated into an equivalent problem of decentralised control design for a multi-input multi-output (MIMO) control system. A recent survey paper BIB008 has covered several decomposition approaches such as disjoint subsystems, overlapping subsystems, symmetric composite systems, multi-time scale systems and hierarchically structured systems to simplify the analysis and synthesis tasks for large-scale systems to reduce the computation complexity. Decentralised control for large-scale interconnected systems has been studied extensively. The application of decentralised schemes has dominated practice in industry due to the advantages of flexibility in operation, tolerance of failure and simplified design and tuning BIB006 . Research on large-scale interconnected systems analysis and synthesis can be traced back to at least the 1970s, and the survey paper BIB001 clearly shows the development of this topic at that time when almost all of the work was focused on linear cases. With the advancement of technology and increasing requirements for high levels of performance, specifically in recent years, the dynamic systems used to model reality have become more complex involving nonlinearity, uncertainty, time delay and interconnection. Therefore, the study of complex interconnected systems has become increasingly important. The interest in this subject has been revived by new developments in nonlinear systems and control. This paper will review the past and recent results for both linear and nonlinear large-scale interconnected systems: decentralised schemes based on modern control approaches such as variable structure control, adaptive control and backstepping approaches, are covered; decentralised control for a class of interconnected systems with symmetric and similar structures is included; the decentralised control for singular large scale systems is reviewed as well. Some interesting/open issues will be highlighted for future discussion.