Optimal control for the stochastic Fitzhugh-Nagumo model with recovery variable

DOI10.3934/eect.2018027zbMath1408.93148arXiv1705.10227OpenAlexW2963199252WikidataQ129212214 ScholiaQ129212214MaRDI QIDQ1711898

Luca Di Persio, Francesco Giuseppe Cordoni

Publication date: 18 January 2019

Published in: Evolution Equations and Control Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.10227

zbMATH Keywords

stochastic optimal controlstochastic partial differential equationsEkeland's variational principlestochastic Fitzhugh-Nagumo equation

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Set-valued and variational analysis (49J53) Optimal stochastic control (93E20) Variational principles in infinite-dimensional spaces (58E30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Optimality conditions for problems involving randomness (49K45)

Related Items

Optimal control of mean field equations with monotone coefficients and applications in neuroscience ⋮ On a positional control problem for a nonlinear equation with distributed parameters ⋮ Optimal control of the FitzHugh-Nagumo stochastic model with nonlinear diffusion ⋮ Exponential stability for the Schlögl system by Pyragas feedback ⋮ Stabilisation of highly nonlinear hybrid stochastic differential delay equations by delay feedback control ⋮ Deterministic control of stochastic reaction-diffusion equations ⋮ Stochastic port-Hamiltonian systems

Cites Work

• Unnamed Item
• Unnamed Item
• A class of Lévy driven SDEs and their explicit invariant measures
• Approximation and convergence of solutions to semilinear stochastic evolution equations with jumps
• Stochastic reaction-diffusion equations on networks with dynamic time-delayed boundary conditions
• Kolmogorov equations for stochastic PDEs.
• On a random scaled porous media equation
• Small noise asymptotic expansions for stochastic PDE's. I: The case of a dissipative polynomially bounded non linearity
• Stochastic FitzHugh-Nagumo equations on networks with impulsive noise
• Optimal control of population dynamics
• Sparse optimal control of the Schlögl and Fitzhugh-Nagumo systems
• Analysis and control of nonlinear infinite dimensional systems
• On the variational principle
• Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control
• Gaussian estimates on networks with applications to optimal control
• Stochastic Maximum Principle for Optimal Control of a Class of Nonlinear SPDEs with Dissipative Drift
• Optimal control of stochastic FitzHugh–Nagumo equation
• Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions
• Gaussian estimates on networks with dynamic stochastic boundary conditions
• Convexity and Optimization in Banach Spaces
• ANALYSIS OF THE STOCHASTIC FITZHUGH–NAGUMO SYSTEM
• Existence, uniqueness and space regularity of the adapted solutions of a backward spde
• Random perturbations of the reduced Fitzhugh-Nagumo equation
• Ergodicity for Infinite Dimensional Systems
• Stochastic Equations in Infinite Dimensions
• Riccati-Based Feedback Control of the Monodomain Equations With the Fitzhugh--Nagumo Model
• Nonlinear Differential Equations of Monotone Types in Banach Spaces