Constrained linear time-varying quadratic regulation with guaranteed optimality

Abstract

A suboptimal solution to constrained linear time varying quadratic regulation (CLTVQR) is proposed. In a neighborhood of the origin, the problem is formulated as a min-max LQR based on polytopic inclusion of the dynamics in this neighborhood. Outside this neighborhood, the control moves are obtained by solving a constrained finite horizon optimization problem. The main contribution is to obtain a cost value arbitrarily close (but not equal) to that of the optimal CLTVQR. The suboptimal CLTVQR preserves the feasibility of the optimal CLTVQR if and only if the min-max LQR exists feasible solution. By mild modification, this suboptimal method can be applied to nonlinear systems.

Keywords:

• Constrained quadratic regulation
• Polytopic inclusion
• Min-max optimization
• Linear matrix inequality

Acknowledgments

This work is supported by National Nature Science Foundation of China (Grant no. 60504013), Foundation from Educational Office of Hebei Province in China (Grant No. ZH2006008), and Foundation from Science and Technological Office of Hebei Province in China (Grant no. 06213545).