A Periodic Dichotomy in Linear Control Theory
Shichao Ye, Xingwu Zeng, Can Zhang
TL;DR
This paper introduces a periodic dichotomy transformation in linear control theory, providing explicit solutions for periodic linear quadratic optimal control problems under certain stability conditions.
Contribution
It constructs a novel periodic dichotomy transformation using solutions of Riccati and Lyapunov equations, enabling explicit characterization of optimal extremals.
Findings
Established a complete characterization of the optimal extremal.
Provided an explicit representation of the optimal extremal.
Utilized solutions of periodic Riccati and Lyapunov equations.
Abstract
In this paper, we construct a periodic dichotomy transformation using solutions of periodic Riccati and Lyapunov equations. As an application of this transformation, we provide an explicit representation of the optimal extremal for periodic linear quadratic optimal control problems. Specifically, we establish a complete characterization of the optimal extremal under suitable exponential stabilizability and detectability assumptions.
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