Decentralized control of complex systems.

*(English)*Zbl 0728.93004
Mathematics in Science and Engineering, 184. Boston, MA etc.: Academic Press, Inc. xiv, 526 p. $ 74.95 (1990).

The monograph consisting of 9 chapters and appendix is the theory of decentralized feedback control design of structured dynamic systems described by ODEs in the time domain. It systematically surveys most of recent knowledge in decentralized control including numerous author’s pioneering results. Chapter 1 (structured systems) provides a graph- theoretic framework for structural modeling of complex systems. Structural controllability, structural observability and structurally fixed modes are considered. Chapter 2 (stabilization) deals with connective stability and connective stabilization via decentralized state feedback. A graph-theoretic algorithm testing decentralized stabilizability in the dependence on the structure of interconnection matrices is derived. Chapter 3 (optimization) deals with the LQ decentralized control. The concept of suboptimality robustness of suboptimal control measured by gain and phase margins, and the solution of inverse optimal problem of decentralized control are considered. Chapter 4 (estimation and control) provides building of decentralized asymptotic observers including the separation property for structured systems and the LQG decentralized control design. Chapter 5 (output control) presents conditions for structured systems always stabilizable by dynamic output feedback and for structured systems connectively stabilizable by static output feedback using digraphs. An adaptive version of decentralized output feedback control is included. In Chapter 6 (hierarchical LBT decompositions) digraph algorithms for partitioning a system into a Lower block triangular (LBT) form and their usage by a sequential optimization of hierarchically structured systems are presented. In Chapter 7 (Nested epsilon decompositions) a digraph algorithm for nested epsilon decompositions is derived. Its control applications for weakly coupled systems and systems with block diagonal dominant matrices are included. Chapter 8 (Overlapping decompositions) presents the inclusion principle and its applications in decentralized control. In Chapter 9 (reliable control) a unified synthesis of robust decentralized control with respect to both the plant and controller failures employing overlapping decompositions is presented. In appendix graph-theoretic algorithms for analyzing structural properties of structured systems are supplied and their complexity is discussed. The results presented in the book essentially contribute to the development of the theory of decentralized control of complex systems.

Reviewer: L.Bakule (Praha)

##### MSC:

93A14 | Decentralized systems |

93B52 | Feedback control |

93C15 | Control/observation systems governed by ordinary differential equations |

93D30 | Lyapunov and storage functions |

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |