Seminar Details
2018-12-18 (14:00) : Computation of the maximal invariant set of discrete-time systems with quasi-smooth nonlinear constraints
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Zheming Wang (UCLouvain)
Abstract :
Invariant set theory is an important tool for stability analysis and control design of constrained dynamical systems and it has been successfully used to solve various problems in system and control. In this talk, we study the computation of the maximal invariant set of linear systems with a class of nonlinear constraints that has quadratic relaxations. With these quadratic relaxations, we are able to determine a sufficient condition for the maximal invariant set. By using the sufficient condition, we propose an algorithm to compute the exact maximal invariant set. At each iteration, we will solve a set of linear matrix inequalities instead of a nonlinear optimization problem. Thanks to this feature, the proposed algorithm is computationally tractable and efficient in many cases. Under mild assumptions, the proposed algorithm will terminate in finite time. This algorithm can also be extended to a class of nonlinear systems that admit a state feedback linearization. The performance of this algorithm is demonstrated on several numerical examples.