Lubomír Bakule

Decentralized control: An overview ☆

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 largescale 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. # 2008 Elsevier Ltd. All rights reserved.

Structure of Expansion-Contraction Matrices in the Inclusion Principle for Dynamic Systems

This paper characterizes a general structure of complementary matrices involved in the input-state-output inclusion principle for linear time invariant dynamic systems. Aggregations and restrictions are adopted as two practically important classes within this scheme. Further, contractibility conditions for feedback controllers are presented, including the decentralized control design. The identified structure enables the formulation of conditions on the complementary matrices which can be useful for analysis and synthesis of control problems.

Decentralized control and overlapping decomposition of mechanical systems–Part 1. System decomposition

This paper improves a new inclusion concept, called ‘txtension’ to mechanical systems described by matrix second-order equations. Recent work on specialization of the inclusion principle has been generalized to the expansion and contraction of input, state and output spaces, but without the possibility of constructing completely general contractible controllers. In this paper, necessary and sufficient conditions for extensions and contractible feedback controllers are proved. They enable the construction of general contractible controllers without any constraint on the structure of controllers for mechanical systems.

Decentralized control and communication

Abstract In this paper, the past and current issues involved in the design of decentralized networked control systems are reviewed. The basic models of interconnected systems described as continuous-time linear time-invariant systems in the time domain serve as a framework for the inclusion of communication channels in the decentralized feedback loop. The I/O-oriented models and the interaction oriented models with disjoint subsystems and interactions are distinguished. The overview is focused on packet dropouts, transmission delays, and quantization effects which are included in the time-driven design of feedback loop components. Single- and multiple-packet transmissions are considered in this contents. The design of decentralized state feedback gain matrices with delayed feedback uses the methodology of sampled-data feedback design for continuous-time systems, while the decentralized H ∞ quantizer design is based on the static output controller. The Liapunov stability approach results in computationally efficient decentralized control design strategies described by using linear matrix inequalities.

Generalized selection of complementary matrices in the inclusion principle

This paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state LQ optimal control of LTI systems, it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices, the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control design.

Decentralized control: Status and outlook

This paper reviews state of the art in the area of decentralized networked control systems with an emphasis on event-triggered approach. The models or agents with the dynamics of linear continuous-time time-invariant state-space systems are considered. They serve for the framework for network phenomena within two basic structures. The I/O-oriented systems as well as the interaction-oriented systems with disjoint subsystems are distinguished. The focus is laid on the presentation of recent decentralized control design and co-design methods which offer effective tools to overcome specific difficulties caused mainly by network imperfections. Such side-effects include communication constraints, variable sampling, time-varying transmission delays, packet dropouts, and quantizations. Decentralized time-triggered methods are briefly discussed. The review is deals mainly with decentralized event-triggered methods. Particularly, the stabilizing controller–observer event-based controller design as well as the decentralized state controller co-design are presented within the I/O-oriented structures of large scale complex systems. The sampling instants depend in this case only on a local information offered by the local feedback loops. Minimum sampling time conditions are discussed. Special attention is focused on interaction-oriented system architecture. Model-based approach combined with event-based state feedback controller design is presented, where the event thresholds are fully decentralized. Finally, several selected open decentralized control problems are briefly offered as recent research challenges.

Overlapping reliable control for a cable-stayed bridge benchmark

The brief presents a reliable 1-out-2 reduced order control design strategy for a cable-stayed bridge benchmark using two overlapping subsystems and the linear quadratic Gaussian (LQG) design. Reliability with regard to controller failures is considered. Local controllers are designed for reduced order subsystems of expanded system. They are implemented and evaluated on the original overall system model. Two different sets of numerical experiments of reliable control design within 1-out-2 controller failure structure have been systematically tested using a SIMULINK scheme and compared to the benchmark sample centralized LQG design. The performance of the reliable control design has been assessed by means of given benchmark evaluation criteria. The dynamics of the closed-loop benchmark model with this multiple controller exhibits an acceptable behavior though slightly worse than in the centralized case. Thereby, the main result is a practical well working 1-out-2 reliable controller designed for a real world large-scale system. The significance of this new strategy lies in its practical systematic approach for reliable control design for large scale systems.

Robust Overlapping Guaranteed Cost Control of Uncertain State-Delay Discrete-Time Systems

This note presents a new extension of the inclusion principle to cope with the problem of designing robust overlapping controllers for state-delayed discrete-time systems with norm bounded uncertainties using the concept of guaranteed cost control. Expansion-contraction relations for systems and contractibility conditions for output guaranteed cost memoryless controllers are proved, including conditions on the equality of guaranteed performance bounds. The controllers are designed in the expanded space using a linear matrix inequality (LMI) delay independent procedure specifically adapted to this class of problems. The designed controllers are then contracted and implemented into the original system. The results are specialized for the overlapping decentralized control design. The method enables an effective construction of block tridiagonal controllers. A numerical illustrative example is supplied

Preservation of controllability-observability in expanded systems

The result contributed by the article is that controllability-observability of an original continuous-time LTI dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices. This new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases, such as aggregations and restrictions, which enable such preservation only in certain special cases. A complete unrestricted transmission of these qualitative properties from the original controllable-observable system to its expansion is a basic requirement on the expansion/contraction process, mainly when controllers/observers are designed in expanded systems to be consequently contracted for implementation in initially given systems. An original system composed of two overlapped subsystems is adopted as a general prototype ease. A numerical example is supplied.

Complexity-reduced guaranteed cost control design for delayed uncertain symmetrically connected systems

Complexity reduced guaranteed cost control design problem is considered for a class of nonlinear symmetrically connected uncertain state-delayed systems. Nonlinear systems with identical nominal linear both subsystems and symmetric connections are supposed. Point time-delays and norm bounded parametric uncertainties are considered. A reduced-order guaranteed cost control problem is constructed first. The dimension of its state equals to the dimension of a subsystem in the original system. Then, a memoryless guaranteed cost dynamic output feedback controller is designed for the reduced problem using the LMI approach. It is proved that when this controller is implemented into each subsystem of the original system then such decentralized output controller is a guaranteed cost controller for the overall system.