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arXiv · 2401.03148

Impulse approximate controllability for stochastic evolution equations and its applications

Yuanhang Liu
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Abstract

This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm problem seeks to identify an optimal impulse control characterized by the minimum norm among all feasible controls, guiding the system's solutions from an initial state within a fixed time interval toward a predetermined target while the minimal time problem is to find an optimal impulse control (among certain control constraint set), which steers the solution of the stochastic equation from a given initial state to a given target set as soon as possible. These problems, to the best of our knowledge, are among the first to discuss in the stochastic case.

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Yuanhang Liu. 2024-01-06. Impulse approximate controllability for stochastic evolution equations and its applications. https://arxiv.org/abs/2401.03148

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