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Robust Nonlinear Model Predictive Control

Model Predictive Control (MPC) is one of the few techniques suitable for ro- bust stabilization of uncertain nonlinear systems subject to constraints. A ¯rst method for the design of robust MPC consists in minimizing a nominal per- formance index while imposing the ful¯llment of constraints for each admissible disturbance. This calls for the inclusion in the problem formulation of tighter state and terminal constraints and leads to very conservative solutions. With a signi¯cant increase of the computational burden, an alternative approach con- sists in solving a min-max optimization problem. In particular, in the closed- loop formulation, the performance index is minimized with respect to a vector of feedback control policies for the worst case, i.e. the disturbance sequence over the optimization horizon which maximizes the performance index. In this talk, some of the results we have obtained in the last few years will be presented. In particular, in order to analyze the stability properties of the system in presence of both state dependent and state independent uncertainties/disturbances, the concepts of Input-to-State Stability (ISS) and Input-to-State practical Stabil- ity (ISpS) have been used. Due to the presence of state and input constraints, global results are in general not useful to apply the ISS property to MPC. On the other hand, local results do not allow the analysis of the properties of the predictive control law in terms of region of attraction. Therefore in [2] we have proposed a regional version of the ISS property. Moreover, the power of this tool has been used in order to obtain stabilizing decentralized and cooperative MPC algorithms.

Type of Seminar:
Ph.D. Seminar
Davide M. Raimondo
May 05, 2008   16:00

ETZ J 91
Contact Person:

Melanie Zeilinger
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