Optimal Fault-Tolerant Control for Discrete-Time Nonlinear Strict-Feedback Systems Based on Adaptive Critic Design

Abstract

This paper investigates the problem of optimal fault-tolerant control (FTC) for a class of unknown nonlinear discrete-time systems with actuator fault in the framework of adaptive critic design (ACD). A pivotal highlight is the adaptive auxiliary signal of the actuator fault, which is designed to offset the effect of the fault. The considered systems are in strict-feedback forms and involve unknown nonlinear functions, which will result in the causal problem. To solve this problem, the original nonlinear systems are transformed into a novel system by employing the diffeomorphism theory. Besides, the action neural networks (ANNs) are utilized to approximate a predefined unknown function in the backstepping design procedure. Combined the strategic utility function and the ACD technique, a reinforcement learning algorithm is proposed to set up an optimal FTC, in which the critic neural networks (CNNs) provide an approximate structure of the cost function. In this case, it not only guarantees the stability of the systems, but also achieves the optimal control performance as well. In the end, two simulation examples are used to show the effectiveness of the proposed optimal FTC strategy.

Reverse-Order Multi-Objective Evolution Algorithm for Multi-Objective Observer-Based Fault-Tolerant Control of T-S Fuzzy Systems

“…If the robust H ∞ performance in (19) is satisfied with positive definite weighting matrixQ 1 and a prescribed disturbance attenuation level β > 0 and the system is free of external disturbance, the left-hand side in (19) is bounded above byx T (0)Px(0) for any time, i.e., the summation of the state energyx(t) from zero to infinite time is bounded. As a result, it reveals the state variables will converge to zero by the proposed controller, i.e., the asymptotically stability for fuzzy observer-based FTC system in (18) is guaranteed.…”

“…where E = 0 0 0 0 1 0 0 0 0 0 0 1 . Therefore, to meet the head-on condition for the MO H 2 /H ∞ observer-based fault-tolerant control, the weighing matricesQ 1 andQ 2 in (19) and (20) should be specified as:…”

“…which satisfies the optimal H 2 constraint in (22). On the other hand, for the robust H ∞ FTC performance in (19), we have…”

“…Thus, it is expected that the FTC design can not only achieve the great FTC performance while the system is affected by the fault but also achieve some prescribed robust control performance for the disturbance attenuation. For this reason, several mixed FTC designs such as mixed optimal FTC control schemes [18], [19] and mixed robust FTC control schemes [20], [21] are developed. By extending the concept of mixed control method [22], [23], the multiobjective (MO) design has become a popular issue and addressed in many research topics on control and estimation [24]- [29].…”

Fuzzy Optimal Tracking Control of Hypersonic Flight Vehicles via Single-Network Adaptive Critic Design

“…1) The control structure complexity is low via concise SACD for the sake of guaranteeing real-time performance. Different from the existing studies [27], [28], [33], this paper proposes a single-adaptive-parameter-based strategy to construct the critic network which has only one adaptive parameter.…”