A duality-based LPV approach to polynomial state feedback design

In this paper, a state feedback design for the class of polynomial control systems is proposed. The proposed design solves the stabilization problem by considering polynomial control systems as linear parameter varying (LPV) control systems. With the help of duality theory and the sum of squares decomposition, a stabilizing state feedback can be computed efficiently, if a certain semidefinite program is feasible. The main advantages of the proposed state feedback design are that no special requirements on the system structure are imposed and that the results are of global nature.

[1]  Ryan Feeley,et al.  Some controls applications of sum of squares programming , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[2]  A. Papachristodoulou,et al.  On the construction of Lyapunov functions using the sum of squares decomposition , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[3]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[4]  Murat Arcak,et al.  Constructive nonlinear control: a historical perspective , 2001, Autom..

[5]  Tingshu Hu,et al.  Dissipativity for dual linear differential inclusions through conjugate storage functions , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[6]  Jeff S. Shamma,et al.  Existence of SDRE stabilizing feedback , 2003, IEEE Trans. Autom. Control..

[7]  F. Allgöwer,et al.  Feedback passivation of an electrostatic microactuator: a semidefinite programming approach , 2004 .

[8]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[9]  P. Parrilo.  Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

[10]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[11]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[12]  A. Papachristodoulou,et al.  Nonlinear control synthesis by sum of squares optimization: a Lyapunov-based approach , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[13]  Bruce Reznick,et al.  Sums of squares of real polynomials , 1995 .