2022•Optimal Control Applications and MethodsOpen access

Time‐optimal L1/L2 norms optimal control for linear time‐invariant systems

H.C.M. Mai, Xuesong Chen, Zhaoyang Yin

Abstract

Abstract The theoretical properties of a novel time‐optimal / norms optimal control for linear time‐invariant systems are investigated. The ‐optimal control (or sparsest control) is converted to the time‐optimal / norms optimal control which can be solved efficiently. The proposed control is obtained via minimization of the time‐optimal / norms optimal control input along with the constraints on the state variable. Subsequently, by using the nonsmooth maximum principle, the uniqueness and continuity of the optimal solution of the time‐optimal / norms optimal control are proved. The superiority of the time‐optimal / norms optimal control is illustrated by numerical examples.

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Key concepts: Optimal control, Uniqueness, Mathematics, Minification, LTI system theory, Linear-quadratic-Gaussian control, Invariant (physics), Control theory (sociology)