The quadratic tracking problem for systems with persistent memory in \zzr^d

2024/04/05 by Pandolfi, Luciano · 1 citation
#45D05 #49J99 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2404.04117

Abstract

The classical quadratic regulator problem has rarely been studied for systems with persistent memory until recent times. In this paper we study the quadratic tracking problem on a finite time horizon for a system described by a controlled linear Volterra integrodifferential equation in \zzr^d. We use the Fredholm equation approach and we derive the synthesis of the optimal control in terms of a Riccati differential equation, independent of the reference signal, and of two equations which instead depend on the reference signal. In the final section we introduce a representation of the system in a state space of finite memory (as the tracking problem under study) and we show that the equations used in the synthesis can be formulated as a differential system in this space. This fact has to be contrasted with the semigroup approach which requires that the system be recasted in a space of infinite memory.

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