Abstract estimates of the rate of convergence for optimal control problems (Q1363641)

An extended penalty function method for solving constrained optimal control problems is presented. Optimal control problems of this type are among the most difficult problems to solve numerically. The available approaches can be divided into direct and indirect methods. In the direct method the state and control variables are parametrized using piecewise polynomial approximation or global expansion. Inserting these approximations into the cost functional, the dynamic equations, the constraints, and the boundary conditions results in a finite-dimensional parameter optimization problem. Using the penalty function method, the problem is transformed into a sequence of control problems without inequality constraints. The cost functional penalty term assumes large values when the constraints are violated, and small values when the constraints are satisfied. A continuation method for solving the sequence of differential-algebraic boundary value problems arising from the transformed optimal control problems is also presented. The effectiveness of the suggested approach is demonstrated by examples.