Linear-quadratic control of Volterra integral systems and extensions
S. A. Belbas ((1), W. H. Schmidt (2) (1) Mathematics Department,, University of Alabama, Tuscaloosa, AL (retired faculty) (2) Institut f\"ur, Mathematik und Informatik, Universit\"at Greifswald, Germany)
TL;DR
This paper investigates linear-quadratic optimal control problems for Volterra systems, providing necessary and sufficient conditions for linear-quadratic cases and novel solvability results for nonlinear cases.
Contribution
It introduces sharp optimality conditions for linear-quadratic Volterra control and a new form of necessary conditions involving double Volterra equations for nonlinear cases.
Findings
Sharp necessary and sufficient conditions for linear-quadratic Volterra control
Novel necessary conditions involving double Volterra equations
Proof of solvability for the double Volterra equations
Abstract
We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary and sufficient conditions for optimality. For problems that are linear-quadratic in the control only, we obtain a novel form of necessary conditions in the form of double Volterra equation; we prove the solvability of such equations.
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Taxonomy
TopicsControl and Dynamics of Mobile Robots · Aerospace Engineering and Control Systems · Advanced Differential Equations and Dynamical Systems