A design approach of constrained linear time-varying quadratic regulation

A new method for the infinite horizon quadratic regulation of constrained linear time varying systems is addressed. The key idea is to achieve a cost value arbitrarily close (but not equal) to the theoretically minimum one. In a neighborhood of the origin, the controller 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 and an unconstrained Riccati iteration formula. The proposed solver has low computational burden and preserves the feasibility of the original problem iff the min-max LQR exists as a feasible solution. A simulation example validates its stability.