Predictive control with added feedback for fast nonlinear systems

A major difficulty arises in predictive control when the prediction of the system evolution becomes unreliable due to the presence of uncertainty. This problem is particularly important for fast nonlinear systems since significant divergence can occur during the time required for optimization. As a solution to this problem, the addition of a linear state feedback controller regulating the prediction error is proposed. Using the neighbouring extremal theory, it is shown that this combination is a first-order approximation to an infinitely-fast receding horizon controller. The effectiveness of this methodology is illustrated via simulation on an inverted pendulum.