A differential inclusion algorithm for optimal control problems

The authors describe a conceptual algorithm allowing the computation of optimal control processes for control problems whose data are required to satisfy weak hypotheses on their control dependence. To achieve this goal, a differential inclusion formulation of the control problem is considered and a recursive procedure based on certain necessary conditions of optimality of the Pontryagin type is defined to compute a trajectory minimizing a given cost functional. State variable estimates are updated with information obtained by approximating a solution to the Hamiltonian inclusion of the optimality conditions. Under the hypotheses, this limiting trajectory is locally optimal for the given control problem and its associated control strategy is then computed. Since this procedure of searching for optimality involves only the state and adjoint variables, this algorithm is well suited to deal with the lack of regularity with respect to the control variable usually present in most control problems