A Simple LP-Type Formulation of the Positively Invariance Condition for a Convex Polyhedral Set and a Fast Algorithm for Solving a Linear Constrained Regulator Problem.

概要

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Let S be a convex polyhedral set in the state space of a linear continuous-time system. The positive invariance (PI) condition of S is studied in terms of the dual set of S. The PI condition in the dual space is obtained, which yields a set of standard LP-type equations. Moreover, a method for simplifying these equations is presented. It is pointed out that the conventional algebraic PI condition has redundancies in the LP-type formulas. It is also shown that linear state constraints can be expressed by standard LP-type equations using the dual set of S.These results are then applied to a linear constrained regulator problem and a fast algorithm for solving the problem is obtained, where the problem is formulated by a relatively small-sized LP without computing the extreme points of S.Numerical experiments for a 2nd-order system are performed for examining the efficacy of the proposed algorithm.
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