Learning Optimal Control Using Integral Equations

This paper concerns the problem of determining an optimal control action for a dynamic linear system using an adaptive learing algorithm. The control is subjected to inequality constraints. The optimality criterion consists of a finite horison quadratic cost functional with weightings on the state trajectory errors and control action. The optimal control problem is reformulated using variational calculus as an integral equation on the control action and associated Kuhn-Tucker multipliers. The adaptive algorithm simultaneously updates the control action and the associated Kuhn-Tucker multiplier function using a gradient adaptive functional estimation algorithm. It is shown that the function estimates converge asymptotically to the optimal action and associated Kuhn-Tucker multiplier function respectively. The optimisation adaptive algorithm is tested by a computer simulation example.