A SCALAR SIGN FUNCTION APPROACH TO DIGITAL CONTROL OF CONTINUOUS-TIME CHAOTIC SYSTEMS WITH STATE CONSTRAINTS

Abstract

In this paper, a scalar sign function-based digital design methodology is presented to develop a digital tracking controller for the continuous-time chaotic systems with absolute value state constraints. A scalar sign function, which is the counterpart of the well-known matrix sign function, is utilized to approximately represent the absolute value state term by a rational function. As a result, the original state constrained nonsmooth nonlinear system becomes a smooth nonlinear system having rational nonlinear terms. Then, an optimal linearization technique is applied to the afore-mentioned nonlinear system for finding an optimal linearization model, which has the exact dynamics of the original nonlinear system at any operating point of interest with minimal modeling error in the vicinity of the operating point on the trajectory. To overcome the effect of modeling errors and to quickly track the desired reference signals, a high-gain optimal analog tracker is designed for the obtained linear model. For practical implementation of the high-gain analog tracker, the prediction-based digital redesign technique is utilized to obtain a low-gain digital tracker for digital control of the sampled-data nonlinear system with constrained states. Chua's chaotic circuits are used to demonstrate the effectiveness of the proposed approach.