D. D. Siljak

Decentralized adaptive control: structural conditions for stability

Decentralized adaptive control schemes are presented for a class of large-scale interconnected systems. These schemes have the advantage that in addition to the standard assumption about the uncertainty of the subsystems, the strength of interconnection is assumed unknown. Provided certain structural constraints are satisfied, the adaptation gains automatically adjust to levels that assure stability of the overall system. Simulations of a spring-coupled dual pendulum showed that for high interconnection strengths, the proposed algorithm exhibits better tracking performance than existing algorithms. >

Parameter space methods for robust control design: a guided tour

Recently, there has been a renewed interest in the parameter space approach to control system analysis and design. The original concept has a long history starting in Russia by Vishnegradsky in 1876 and spreading throughout the world by the works of Neimark, Aizerman, Mitrovic, Meerov, Thaler, Seltzer, Ackermann, and many others. The parameter space approach has generally been viewed as an alternative to the classical methods of Routh-Hurwitz, Nyquist, Evans, Bode, and Nichols. When in the sixties the advent of the LQG theory of Kalman decreased the interest in classical design techniques, it almost diminished applications of the parameter methods. A recent widespread interest in robust design of control systems subject to structured perturbations shifted a considerable part of the research activity toward parameter space methods, and, at the same time, enlarged the scope of the approach to include the Liapunovs method as well as frequency domain concepts. The purpose of this paper is to review new and significant developments in the robust control design for structured (parametric) perturbations, which complement the large and well represented effort in robust design of control systems under structured and unstructured perturbations via frequency domain characterizations. A critical comparison of various parameter space concepts and methods is offered and examples are used to illustrate some of the differences between various results available at present. Directions for future research are suggested, which are motivated by applications as well as by utilization of modern computing technology. The paper is organized in three sections as follows.

Reliable control using multiple control systems

Abstract The objective of this paper is to provide a mathematical framework for building reliable control using less reliable controllers. The new ingredient in the design is the multiple control system which provides the necessary redundancy for reliability enhancement in control systems subject to controller failures. The proposed reliability design is based upon the decentralized control schemes used so far for synthesizing reliable control systems subject to perturbations in the plant interconnection structure.

Robust stabilization of nonlinear systems: The LMI approach

This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI). The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable.

Decentralized control with overlapping information sets

A decentralized control scheme is proposed for linear systems composed of overlapping subsystems. By expanding the state space of the system, a higher-dimensional space is formed where the subsystems appear as disjoint. In the expanded space, standard optimization techniques can be used to formulate a suboptimal decentralized control law for the overall system. A suitable contraction of the obtained control law, which is compatible with the information constraints imposed by the overlapping subsystems, can be implemented in the original system. The application of the proposed decentralized control scheme is illustrated using a 19th order model for load-frequency control of a two-area interconnected power system.

Control of Large-Scale Systems: Beyond Decentralized Feedback

In this paper, we present an array of new results that are aimed at broadening the scope of control design under information structure constraints. Both structural and algebraic enhancements of decentralized feedback will be considered, with convex optimization as a common mathematical framework. This approach leads to computationally efficient design strategies that are well suited for large-scale applications. In all cases, the obtained feedback laws guarantee robustness with respect to a wide range of nonlinear uncertainties, both within the subsystems and in the interconnections.

An inclusion principle for dynamic systems

The purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems, which is a suitable mathematical framework for comparing systems with different dimensions. The framework offers immediate results in reduced-order modeling and the overlapping decentralized control of complex systems. The presentation, which is limited to linear constant systems, relies on both the matrix algebra (computations) and the geometric elements (structure) to provide a balanced view of the issues involved in the concept of inclusion. The framework is quite broad, and has been used to consider nonlinear and time-varying systems, as well as systems with hereditary and stochastic effects.

Stability of Large-Scale Systems under Structural Perturbations

A large-scale system is considered as a system constituted of subsystems which may be connected or disconnected from each other during operation. A new concept of connective stability is introduced by which a large-scale system is regarded as stable if it remains stable (in the sense of Lyapunov) under structural perturbations produced by the on-off participation of the subsystems. Algebraic conditions are developed that guarantee exponential connective stability of large-scale systems which may be composed of linear and nonlinear time-varying subsystems coupled by linear or nonlinear connections.

Asymptotic stability and instability of large-scale systems

The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunovs theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations. With minor technical adjustments, the theory is broadened to include considerations of unstable subsystems as well as instability of composite systems.

Structurally fixed modes

A notion of structurally fixed modes is introduced in the framework of decentralized control systems to identify the modes that cannot be shifted by decentralized feedback regardless of the numerical values of system parameters. In this way, a qualitative characterization of decentralized fixed modes is provided, which is suitable for delineating decentrally stabilizable systems. The characterization leads naturally to the notion of fixed modes with respect to arbitrary feedback structure constraints.