The authors propose a new conditioning dual-rate observer-based tracker for hybrid chaotic systems with saturating actuators. First, a chaotic system is translated into an appropriate linearization model by using the optimal linearization method. Then, a digitally redesigned observer with a high-gain property is developed to accurately estimate the states of the linearization model.
The design of the tracker is based on advanced digital redesign techniques equipped with a predictive feature and using a slow-rate sampling period for the unconstrained chaotic system. Also, the authors add an inner state compensator based on the fast-rate digital redesign technique to deal with the wind-up phenomenon.
The aim is to change the dynamics of the internal states of the controller when the actuator is saturated, and so the authors feed the difference between the unconstrained input signal of plant \(u(t)\) and this input passed through a saturation limiter \(\bar u(t)\) to the inner-loop compensator. The state compensator has no effect when the actuator is working linearly, but it modifies the state of the controller when the actuator is saturated. It can systematically reduce the wind-up effects and preclude input saturation. The design principle and procedure, together with some necessary analyses, are given, and two illustrative examples are presented to illustrate the effectiveness of the proposed procedure.