Solvability, Controllability and Optimal Control of the Stochastic FitzHugh-Nagumo Equation
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Name:
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Affiliation:
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Country:
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Durga Nagarajan
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Assistant Professor
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India
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Introduction:
| | In this work, we investigate the solvability, controllability and optimal control of the stochastic FHN equation driven by Brownian motion and possible jump processes. First, we establish the existence and uniqueness of solutions under appropriate assumptions using the theory of stochastic differential inclusions. Next, we analyze the controllability of the system by transforming the physical model into a differential inclusion framework, allowing us to explore the feasibility of steering the system towards desired states. Furthermore, we derive an existence condition for optimal control, leveraging linear programming techniques to design control policies that stabilize the system while minimizing energy costs. Finally, we apply our findings to neural activity regulation, demonstrating the implications of control strategies in neuroscience.
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