A gradient algorithm for optimal control problems with model-reality differences

In this paper, we propose a computational approach to solve amodel-based optimal control problem. Our aim is to obtain the optimal so-lution of the nonlinear optimal control problem. Since the structures of bothproblems are different, only solving the model-based optimal control problemwill not give the optimal solution of the nonlinear optimal control problem.In our approach, the adjusted parameters are added into the model used soas the differences between the real plant and the model can be measured.On this basis, an expanded optimal control problem is introduced, where system optimization and parameter estimation are integrated interactively. TheHamiltonian function, which adjoins the cost function, the state equation andthe additional constraints, is defined. By applying the calculus of variation, aset of the necessary optimality conditions, which defines modified model-basedoptimal control problem, parameter estimation problem and computation ofmodifiers, is then derived. To obtain the optimal solution, the modified model-based optimal control problem is converted in a nonlinear programming prob-lem through the canonical formulation, where the gradient formulation can bemade. During the iterative procedure, the control sequences are generated asthe admissible control law of the model used, together with the correspondingstate sequences. Consequently, the optimal solution is updated repeatedly bythe adjusted parameters. At the end of iteration, the converged solution ap-proaches to the correct optimal solution of the original optimal control problemin spite of model-reality differences. For illustration, two examples are studiedand the results show the effciency of the approach proposed