Input-derivative-constrained approximate dynamic programming for unknown continuous-time linear systems

In this paper, a model-free approximate dynamic programming (ADP) technique for continuous-time linear systems is proposed to solve the infinite horizon optimal regulator problems with input derivative constraints. By the fact that the input coupling matrix B is not shown in the explicit formula of the solution to the input-derivative-constrained optimal regulator problem, the assumption of the known B matrix is relaxed. And then, partially model-free ADP technique given in [D. Vrabie et al.] is employed to this regulator problem in order to develop the model-free approximate dynamic programming technique. Moreover, using the inherent property of the input-derivative-constrained optimal regulator problem, we extend the proposed model-free ADP technique to the more general linear systems which include constant matching disturbances. The proposed technique can be considered an adaptive optimal controller since it updates the parameters in the controller in a way that the parameters converge to the optimal ones. The simulation is executed to verify the applicability of the proposed method.