A Chebyshev Spectral Method For Optimal Control of the Heat Equation

A Chebyshev Spectral Method For Optimal Control of the Heat Equation

This paper presents a spectral method of solving the optimal control problem for the heat equation. The method is based upon constructing the Mth degree interpolation polynomials, using Chebyshevs nodes, to approximate the state and the control functions. The partial differential equation describing the system dynamics is converted into a linear control problem and the optimum condition is obtained by applying the Pontryaginʹs Maximum Principle.