Uncertain Nonlinear Receding Horizon Control Systems Subject to Non-Zero Computation Time

In this paper Receding Horizon Control (RHC) of an uncertain nonlinear system is considered where the computation time is non-negligible. In a well-known method, the solution process of the optimal control problem is started one sampling period in advance by using the prediction of the initial conditions, thus giving the controller a reasonable deadline to complete the optimization process. The current work suggests the use of the theory of neighboring extremal paths to improve the performance of the existing method by adding a correction phase to the previous method and therefore recovering the exact solution in the presence of prediction errors. An immediate result would be that the properties of the RHC techniques involving zero computation time would be valid for practical systems in the actual implementation, where a zero computation time is unachievable. The new approach is applied for the control of a mobile robot system which demonstrates significant performance improvements over the existing method.