The Optimal Control of an Excitable Neural Fibre
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We consider the optimal control of a neural fibre, described by a nonlinear diffusion equation with a polynomial nonlinearity. An iterative scheme is established to compute a minimum-energy control, in which at each step of the iteration a linear problem is solved by means of measure-theoretical methods and linear programming. The method converges for moderate values of the nonlinear terms. Some numerical results are given.
KeywordsLinear Problem Linear Programming Problem Radon Measure Nonlinear Diffusion Equation Suboptimal Control
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