Optimally switched linear systems

In this paper we address the problem of optimal switching for switched linear systems. The uniqueness of our approach lies in describing the switching action by multiple control inputs. This allows us to embed the switched system in a larger family of systems and apply Pontryagin's Minimum Principle for solving the optimal control problem. This approach imposes no restriction on the switching sequence or the number of switchings. This is in contrast to search based algorithms where a fixed number of switchings is set a priori. In our approach, the optimal solution can be determined by solving the ensuing two-point boundary value problem. Results of numerical simulations are provided to support the proposed method.

[1]  Panos J. Antsaklis,et al.  Optimal control of switched systems based on parameterization of the switching instants , 2004, IEEE Transactions on Automatic Control.

[2]  William H. Press,et al.  Numerical recipes in C , 2002 .

[3]  Alberto Bemporad,et al.  Synthesis of state-feedback optimal controllers for continuous-time switched linear systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

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

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

[6]  H. Sussmann,et al.  A maximum principle for hybrid optimal control problems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[7]  Raymond A. DeCarlo,et al.  Optimal control of switching systems , 2005, Autom..

[8]  Alberto Bemporad,et al.  A master-slave algorithm for the optimal control of continuous-time switched affine systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  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).

[10]  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).