Robust Explicit Control of Complex Hybrid Discrete Processes

Abstract

The paper deals with design of simple end effective robust explicit control of complex hybrid systems. We consider discrete hybrid systems consisting of several discrete state-space models with parametrical uncertainties. The parametric uncertainties are considered in coefficients of state space model (A) and (B). The main goal of the paper is to be proposed and verified the robust explicit hybrid control algorithms such for stable and for unstable complex dynamical systems with respect to parameter model uncertainties. Proposed robust explicit controller method is based on the iterative algorithm’s computation of control law parameters for the known target polytope with respect to parameters uncertainties and constraints on state, control and output variables. For demonstration ability of the proposed methods, we verified the several examples. An example is presented to illustrate the details of the proposed robust hybrid parametric controller design. In this paper we consider hybrid dynamical model consisting of 4 state-space model with 30% uncertainties of matrix (A) coefficients. We compare obtained numerical and graphical results with solution which are obtained from very known MPT toolbox. Our proposed method solution in all cases gives a stable solution while the MPT does not guarantee the stability for tested cases. The proposed method and algorithm is convenient for application for SISO and MIMO processes.