TRANSITION-TIME OPTIMIZATION FOR SWITCHED SYSTEMS

Abstract This paper proposes an algorithmic framework for optimal mode switches in hybrid dynamical systems. The problem is cast in the setting of optimal control, whose variable parameter consists of the switching times, and whose associated cost criterion is a functional of the state trajectory. The number of switching times (and hence of switching modes) is also a variable which may be unbounded, and therefore the optimization problem is not defined on a single metric space. Rather, it is defined on a sequence of spaces of possibly increasing dimensions. The paper characterizes optimality in terms of sequences of optimality functions and proposes an algorithm that is demonstrably convergent in this context.

[1]  L. Armijo.  Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

[2]  Elijah Polak,et al.  Optimization: Algorithms and Consistent Approximations , 1997 .

[3]  A. Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[4]  Damien Flieller,et al.  General sampled data modeling of power systems supplied by static converter with digital and analog controller , 1998 .

[5]  Ronald C. Arkin,et al.  An Behavior-based Robotics , 1998 .

[6]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

[7]  Alberto Bemporad,et al.  Piecewise linear optimal controllers for hybrid systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[8]  H. Sussmann,et al.  Set-valued differentials and the hybrid maximum principle , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[9]  Christos G. Cassandras,et al.  Optimal control of a class of hybrid systems , 2001, IEEE Trans. Autom. Control..

[10]  A. Giua,et al.  Optimal control of switched autonomous linear systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[11]  Xuping Xu,et al.  Optimal control of switched autonomous systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[12]  Xuping Xu,et al.  Optimal control of switched systems via non-linear optimization based on direct differentiations of value functions , 2002 .

[13]  P. Caines,et al.  On trajectory optimization for hybrid systems: theory and algorithms for fixed schedules , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[14]  Erik I. Verriest.  Regularization method for optimally switched and impulsive systems with biomedical applications , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[15]  Y. Wardi,et al.  Optimal control of switching times in switched dynamical systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[16]  P. Valigi,et al.  A modelling approach for the dynamic scheduling problem of manufacturing systems with non negligible setup times and finite buffers , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[17]  Magnus Egerstedt,et al.  Transition-time optimization for switched-mode dynamical systems , 2006, IEEE Transactions on Automatic Control.