Constrained linear time-varying quadratic regulation with guaranteed optimality

Authors:
Baocang Ding;Julia H. Tang
Affiliations:
Hebei University of Technology, School of Electricity and Automation, Tianjin, China;China-Lithium Limited Company, Shanghai, China
Venue:
International Journal of Systems Science
Year:
2007

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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.