Verification of Optimality and Costate Estimation Using Hilbert Space Projection
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In this paper, we present a direct method for solving optimal control problems based on function approximation using Hilbert space projection. In this approach, the state and control variables are approximated in a finitedimensional Hilbert space, and the state dynamics and the path constraints are imposed using projection. The resulting nonlinear programming problem is analyzed to derive a set of conditions under which the costates of the optimal control problem can be estimated from the associated Karush-Kuhn-Tucker multipliers. It is shown that the estimated costates have the same order of finite-dimensional approximation as the state and control approximations. The numerical results demonstrate that the present method can address a fairly general class of optimal control problems, including problems with state inequality constraints.
