Causal state feedback representation for linear quadratic optimal control problems of singular Volterra integral equations

Author:

Han Shuo1,Lin Ping1,Yong Jiongmin2

Affiliation:

1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

2. Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA

Abstract

<p style='text-indent:20px;'>This paper is concerned with a linear quadratic optimal control for a class of singular Volterra integral equations. Our framework covers the problems for fractional differential equations. Under some necessary convexity conditions, an optimal control exists, and can be characterized via Fréchet derivative of the quadratic functional in a Hilbert space or via maximum principle type necessary conditions. However, these (equivalent) characterizations are not causal, meaning that the current value of the optimal control depends on the future values of the optimal state. Practically, this is not feasible. We obtain a causal state feedback representation of the optimal control via a Fredholm integral equation. Finally, a concrete form of our results for fractional differential equations is presented.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Control and Optimization,General Medicine

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