The aim of this thesis is answering to two significant problems in the field of automatic control: the state estimation and the robust model predictive control for uncertain systems in the presence of input and state constraints, based on the set-membership approach, more precisely related to zonotopic sets. Uncertainties acting on the system are modeled via the deterministic approach, and thus they are unknown but bounded by a known set.In this context, the first part of the thesis proposes an estimation method to compute a zonotope containing the real states of the system, which are consistent with the disturbances, the measurement noise and the interval parametric uncertainties. This method is based on the minimization of the P-radius of a zonotope, which is an original criterion to characterize the size of the zonotope, in order to obtain a good trade-off between the complexity and the precision of the estimation. This approach is first developed for single-output systems, and then extended to the case of multi-output systems. The first solution for multi-output systems is a direct extension of the solution for single-output systems (the multi-output system being considered as several single-output systems). Another solution is then proposed, leading to solve a Polynomial Matrix Inequality optimization problem using a relaxation technique. Due to the fact that the previous approaches are just extensions of the solution for a single-output system, and despite their good performance results obtained in simulation, a novel approach dedicated to multi-output systems based on the intersection of a polytope and a zonotope is finally developed and validated.The second part of the thesis deals with the problem of robust output feedback control for uncertain systems. Model predictive control is chosen due to its use in many areas, its ability to deal with constraints and uncertainties. Among the approaches from the literature, the implementation of robust predictive techniques based on tubes of trajectories is developed. The use of a zonotopic set-membership estimation improves the quality of the estimation, as well as the performance of the control, for systems subject to unknown, but bounded disturbances and measurement noise.In the last part, the combination of zonotopic set-membership estimation and robust model predictive control is tested in simulation on a magnetic levitation system. The simulation results reflect a satisfactory behavior validating the developed theoretical techniques.
Robust predictive control by zonotopic set-membership estimation.