Modelling and optimal output feedback control for discrete-time systems: Multi-model approach

This paper presents a contribution to study and synthesis an optimal output feedback controller for a class of discrete-time nonlinear systems that can be represented by a Takagi-Seguno (T-S) fuzzy models. First, we interest for modelling and identification of the studied systems by using the clustering method. In particular, we use Gustafson-Kessel (GK) clustering algorithm. Second, we address the problem of optimal controller synthesis. The optimality of the proposed control technique reside on the minimization of a quadratic criterion reflecting a compromise between fast convergence of the controlled system and the control law who must be admissible formulated as a quadratic output feedback control. Thus, the gradient technique is applied to the Lagrange function in order to obtain necessary conditions to perform the optimal control matrices. Finally, this methodology is implemented on an inverted pendulum system.