Model predictive control (MPC) for constrained nonlinear systems

This thesis addresses the development of stabilizing model predictive control (MPC) algorithms for nonlinear systems subject to input constraints and in the presence of uncertainty, disturbances and measurement noise.; Our basic MPC scheme consists of a finite horizon MPC technique with the introduction of an additional state constraint which we have denoted contractive constraint. This is a Lyapunov-based approach in which a Lyapunov function chosen a priori is decreased discretely. We will show in this work that the implementation of this additional constraint into the on-line optimization makes it possible to prove strong stability properties of the closed-loop system.; Another important aspect considered in this work is the computational efficiency and implementability of the algorithms proposed. The MPC schemes previously proposed in the literature which are able to guarantee stability of the closed-loop system involve the solution of a nonlinear programming problem (NLP) at each time step.; Due to the difficulties inherent to solving NLPs, it is important that an alternative implementation be found which guarantees that the problem can be solved in a finite number of steps. It is well-known that both linear and quadratic programming (QP) problems satisfy this requirement.; If a standard quadratic objective function is used and the constraints are linear, then the contractive constraint can be implemented in such a way that the optimization problem in the prediction step of the MPC algorithm is reduced to a QP. Having linear input/state constraints means that a linear approximation of the original nonlinear system has to be used in the prediction as well as in the computation of the contractive constraint. Thus, in order to make the algorithm more easily implementable we introduce the difficulty of having to handle the mismatch between the real nonlinear system and its linear approximation used in the control computations. In other words, we now have a robust MPC control problem at hand.; In summary, this thesis is an application of contractive principles to MPC and it is dedicated to robust stability analysis, design and implementation of state and output feedback contractive MPC schemes.