Robust H∞ Fuzzy Observer-Based Fault-Tolerant Tracking Control for Nonlinear Stochastic System: A Sum of Square Approach

Abstract

In this study, the robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy observer-based fault-tolerant tracking control strategy is proposed for the stochastic polynomial fuzzy system (SPFS) under the effect of external disturbance, measurement noise, system/sensor fault signals and continuous/discontinuous internal random fluctuations. At first, the smoothed models of fault signals are constructed to describe their dynamic behavior. Then, by integrating the SPFS with the smoothed models of fault signals as one augmented system, the state/fault signal estimation problem can be transformed to a state estimation problem of augmented system by the proposed polynomial fuzzy observer. With the utilization of estimated state/fault signals and reference trajectory, a fuzzy polynomial fault-tolerant tracking controller can be implemented. To attenuate the effect of undesired external disturbance and measurement noise on the state/fault signal estimation and tracking control performance, the robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy observer-based fault-tolerant tracking control strategy is proposed in this study. By utilizing the homogeneous Lyapunov function and Lipschiz condition, the Itô-Lévy formula is reformulated to relax the compensation terms of stochastic processes during the design. Then, the design conditions are derived in terms of interpolation function-dependent matrix inequality and consequently transformed to a two-step sum of square (SOS) condition design problem for the robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy observer-based fault-tolerant tracking control strategy. A simulation example of double lane maneuvering task for autonomous ground vehicle (AGV) is provided to illustrate the effectiveness of proposed method. Index terms: Observer-based tracking control, polynomial fuzzy system, stochastic control, fault-tolerant control, sum of square (SOS).