Generating Function Approach to Linear Quadratic Optimal Control Problem with Constraints on the State

This paper extends the generating function approach to the state constrained linear quadratic optimal control problem by utilizing penalties. The original constrained problem is approximated by an unconstrained problem with a novel penalty function by which the latter problem can be solved via generating function method based on Taylor series approximation. In view of this, the optimal solution can be given as the state feedback control with explicit boundary conditions and pre-computed coefficients. This structure is useful in the repetitive on-line computation for optimal solutions satisfying a number of different boundary conditions. Examples demonstrate the effectiveness of the developed method.