Boundary Approximate Controllability under Positivity Constraints of Infinite-Dimensional Control Systems

Yassine El Gantouh ()
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Yassine El Gantouh: Universidad Autónoma de Madrid

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 2, No 1, 449-478

Abstract: Abstract This paper focuses on boundary approximate controllability under positivity constraints of a wide range of infinite-dimensional control systems. We develop frequency-domain controllability criteria. Firstly, we derive a controllability result under positivity constraints on the control for such systems. Then, and more importantly, we provide a necessary and sufficient condition for controllability under positivity constraints on the control and the state. The obtained results are applied to the controllability of transportation and heat conduction networks. In particular, provided that the underlying graph is strongly connected, the controllability under positivity constraints on the control/state of transport network systems is fully characterized by a Kalman-type rank condition. For a system of heat equations with Robin boundary conditions on a path-like network, we establish approximate controllability under positivity state constraint with a single positive input through the starting node. However, we prove the lack of controllability under unilateral control constraint.

Keywords: Infinite-dimensional control systems; Positive semigroups; Controllability under constraints; PDEs on networks; 93C20; 93B05; 35R02 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02200-9

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