Mojtaba Barkhordari Yazdi

  PhD Defense Presentation

   Abstract:

  In this thesis, the stabilization problem of a class of nonlinear hybrid systems is considered. The complex behavior of hybrid systems originates from the interaction of continuous and discrete event dynamics. Stabilization of switched nonlinear systems with nonlinear subsystems is a challenging problem. The stabilizing controller consists of a switching law and a continuous control law. Moreover, the switching signal has some constraints.

  The new concept of modal state feedback linearization is proposed. The objective is to find a suitable state feedback for each subsystem and a common diffeomorphism state transformation to transform each of the closed-loop subsystems to an equivalent linear one in a way that the resulted switched linear system is controllable. Using this technique we can reduce the complexity of the design procedure by transforming the switched nonlinear system into an equivalent controllable switched linear system.

  The necessary and sufficient conditions for modal state feedback linearizability of single-input affine switched nonlinear systems are given. This result is extended for the general case, namely switched nonlinear systems with arbitrary number of subsystems and dynamical dimension. In order to simplify the verification of conditions, similar results are developed for some special cases. The developed results are based on a differential geometry. Our approach is constructive in nature in the sense that once the conditions are satisfied, the state transformation is obtained and this leads to modal state feedback linearization.

  A method to design stabilizing controller for switched nonlinear systems in partial-linear triangular form is proposed to handle partial modal feedback linearizable systems.

  An approach to design a stabilizing switching law for a class of switched linear systems with constrained switching is developed as the second stage of designing the controller. The existence of solution can be verified using some geometrical properties and graph theory. An algorithm is proposed to generate all of the solutions.

  Date: 29^th August Time: 2 pm

  Place: seminar room