Observer-Based Fuzzy PID Control for Nonlinear Systems With Degraded Measurements: Dealing With Randomly Perturbed Sampling Periods

Abstract

This paper addresses the problem of observer-based fuzzy proportional- integral-derivative (PID) control for a class of nonlinear systems subject to degraded measurements and randomly perturbed sampling periods (RPSPs). In the existing results, the degraded measurements and RPSPs are handled separately, where the sampling of different sensors is usually assumed to be synchronous. In our work, a comprehensive model is built to reflect the joint effects of degraded measurements and RPSPs by using a series of stochastic variable sequences and a set of Markov processes. In this model, the sampling periods of each sensor are allowed to be diverse, time-varying and randomly perturbed, thereby fully capturing the environmental effects and device constraints. Different from the existing literature that uses proportional type controllers, an observer-based fuzzy PID controller with a modified structure is proposed which fully utilizes the system information. To overcome the difficulties of the incomplete measurement information, some auxiliary variables related to the sampling periods are introduced under which the measurement output is transformed into a form delayed with stochastic delays. Subsequently, by using the special variable separation and inequality technique, sufficient conditions are derived to ensure the exponentially ultimate boundedness of the closed-loop system in the mean-square sense. The desired gains for the observer and PID controller are obtained through the solution of an optimization problem. Lastly, the effectiveness of the developed approach is demonstrated through simulation examples.