The quadratic tracking problem for systems with persistent memory in $\zzr^d$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914742094790656 |
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| author | Pandolfi, Luciano |
| author_facet | Pandolfi, Luciano |
| contents | 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 \emph{ 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 \emph{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The quadratic tracking problem for systems with persistent memory in $\zzr^d$ Pandolfi, Luciano Optimization and Control 49J99, 45D05 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 \emph{ 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 \emph{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. |
| title | The quadratic tracking problem for systems with persistent memory in $\zzr^d$ |
| topic | Optimization and Control 49J99, 45D05 |
| url | https://arxiv.org/abs/2404.04117 |