Model predictive-based reset gain-scheduling dynamic control law for polytopic LPV systems

Abstract

This paper proposes a novel systematic approach for designing a reset gain-scheduling dynamic controller based on a model predictive method for a class of nonlinear systems represented by polytopic linear parameter varying models. The proposed design procedure involves offline and online steps. In the offline step, sufficient conditions of the gain-scheduling dynamic controller design in terms of linear matrix inequalities are derived through a novel D-stability region. Thus, the feedback gain vertices are computed by the convex optimization techniques. Then in the online step, based on a predefined reset set, an affine after reset value function for the controller states is optimally selected by solving a generalized Eigenvalue problem. Also, the temporal regulation technique is utilized to avoid Zeno solution problem. Finally, the merits of the proposed controller are demonstrated by applying it on a nonlinear continuous stirred tank reactor.