Hybrid decentralized maximum entropy control for large-scale

In the analysis of complex, large-scale dynamical systems it is often essential to decompose the overall dynamical system into a collection of interacting subsystems. Because of implementation constraints, cost, and reliability considerations, a decentralized controller architecture is often required for controlling large-scale interconnected dynamical systems. In this paper, a novel class of fixed-order, energy-based hybrid decentralized controllers is proposed as a means for achieving enhanced energy dissipation in large-scale lossless and dissipative dynamical systems. These dynamic decentralized controllers combine a logical switching architecture with continuous dynamics to guarantee that the system plant energy is strictly decreasing across switchings. The general framework leads to hybrid closed-loop systems described by impulsive differential equations. In addition, we construct hybrid dynamic controllers that guarantee that each subsystem‐subcontroller pair of the hybrid closed-loop system is consistent with basic thermodynamic principles. Special cases of energy-based hybrid controllers involving state-dependent switching are described, and an illustrative combustion control example is given to demonstrate the efficacy of the proposed approach. c 2006 Elsevier Ltd. All rights reserved.

[1]  R. Saeks.  On the decentralized control of interconnected dynamical systems , 1979 .

[2]  D. Baĭnov,et al.  Systems with impulse effect : stability, theory, and applications , 1989 .

[3]  D. Siljak,et al.  Generalized decompositions of dynamic systems and vector Lyapunov functions , 1981 .

[4]  Franck Plestan,et al.  Asymptotically stable walking for biped robots: analysis via systems with impulse effects , 2001, IEEE Trans. Autom. Control..

[5]  N. Viswanadham,et al.  Decentralized control of interconnected dynamical systems , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[6]  Mesut Erol Sezer,et al.  On decentralized stabilization of interconnected systems , 1980, Autom..

[7]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[8]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[9]  S. Bhat,et al.  An invariance principle for nonlinear hybrid and impulsive dynamical systems , 2003 .

[10]  Jan C. Willems,et al.  Dissipative Dynamical Systems , 2007, Eur. J. Control.

[11]  VijaySekhar Chellaboina,et al.  Vector dissipativity theory and stability of feedback interconnections for large-scale non-linear dynamical systems , 2004 .

[12]  Wassim M. Haddad,et al.  Non-linear impulsive dynamical systems. Part I: Stability and dissipativity , 2001 .

[13]  Wassim M. Haddad,et al.  Non-linear impulsive dynamical systems. Part II: Stability of feedback interconnections and optimality , 2001 .

[14]  D. Siljak.  Complex Dynamic Systems: Dimensionality, Structure and Uncertainty , 1983 .

[15]  D. Siljak,et al.  An inclusion principle for dynamic systems , 1984 .

[16]  Edward J. Davison,et al.  Sequential stability and optimization of large scale decentralized systems, , 1979, Autom..

[17]  Drumi D. Bainov,et al.  Impulsive Differential Equations: Asymptotic Properties of the Solutions , 1995, Series on Advances in Mathematics for Applied Sciences.

[18]  Robert S. Germain,et al.  Large Scale Systems , 1996 .

[19]  Fred E. C. Culick,et al.  Nonlinear behavior of acoustic waves in combustion chambers. I, II. [stability in solid propellant rocket engine and T burner , 1976 .

[20]  Wassim M. Haddad,et al.  Energy- and Entropy-Based Stabilization for Lossless Dynamical Systems via Hybrid Controllers , 2007, IEEE Transactions on Automatic Control.

[21]  W. Haddad,et al.  A system-theoretic foundation for thermodynamics: energy flow, energy balance, energy equipartition, entropy, and ectropy , 2004, Proceedings of the 2004 American Control Conference.

[22]  D. Siljak,et al.  Decentralized control with overlapping information sets , 1981 .

[23]  A. Samoilenko,et al.  Impulsive differential equations , 1995 .

[24]  Qing Hui,et al.  Thermodynamic Stabilization via Energy Dissipating Hybrid Controllers , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[25]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[26]  U. Ozguner.  Near-optimal control of composite systems: The multi time-scale approach , 1979 .

[27]  André Titli,et al.  Interconnected dynamical systems : stability, decomposition, and decentralisation , 1982 .

[28]  Sébastien Candel,et al.  Combustion instabilities coupled by pressure waves and their active control , 1992 .

[29]  Qing Hui,et al.  Thermodynamic modeling, energy equipartition, and nonconservation of entropy for discrete-time dynamical systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[30]  A. Linnemann.  Decentralized control of dynamically interconnected systems , 1984 .

[31]  Ikeda,et al.  Overlapping decompositions, expansions, and contractions of dynamic systems , 1979 .

[32]  D. K. Lindner.  On the decentralized control of interconnected systems , 1985 .

[33]  Dragoslav D. Šiljak,et al.  Large-Scale Dynamic Systems: Stability and Structure , 1978 .