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.