Linear-quadratic control of Volterra integral systems and extensions

2021/01/13 by S. A. Belbas, Belbas, S. A.
Engineering · Mathematics · #45D05 #49K21 #49N10 #Advanced Differential Equations and Dynamical Systems #Aerospace Engineering and Control Systems #Control and Dynamics of Mobile Robots #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2101.04902

openalex publication_date 2021/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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