Simultaneous state estimation and control for nonlinear systems subject to bounded disturbances
In this work, we address the output--feedback control problem for nonlinear systems under bounded disturbances using a moving horizon approach. The controller is posed as an optimisation-based problem that simultaneously estimates the state trajectory and computes future control inputs. It minimises a criterion that involves finite backward and forward horizons with respect to the unknown initial state, measurement noises and control input variables.The main novelty of this work relies on linking the lengths of the forward and backward windows with the closed-loop stability, assuming detectability and decoding sufficient conditions to assure system stabilizability. It leads to a formulation that does not require to be a Control Lyapunov Function for the terminal cost of the controller. Simulation examples are carried out to compare the performance of solving simultaneously and independently the estimation and control problems. Furthermore, the examples show how the controller influences the length of the estimation window through its gain.