Model predictive control schemes for linear parameter varying systems

Abstract

This dissertation presents several contributions inherently the control of con- strained Linearly Parameter Varying (LPV) systems. First the basic analysis and synthesis tools needed to deal with the class of LPV systems are carried out and introduced. Some novel results are given, especially for what regards the use of scheduled control laws and stability conditions for LPV with slow parameter variations. Then we moved on the problem of constrained control. Several new constrained stabilization results are proposed here for the first time and improvements in the procedures to build-up time-variant strategies able to deal with constrained LPV system are given. Moreover a new particular kind of control strategy based on the idea of exploiting the prediction set structure is introduced here for the first time in the LPV framework. It has been pointed out in which way those approaches can be arranged within Model Predictive Control (MPC) schemes to more efficiently deal with constrained LPV systems and two new fast-MPC algorithms for LPV system have been proposed. In this thesis some attention has been given to the analysis of LPV systems with slow parameter variations and some preliminary results are reported. Such a class of systems has many potentials but, due to the ”hidden” nonlinearities it introduces, it is still not well understood and would deserves further careful investigations.