Neural adaptive fault-tolerant control for high-speed trains with input saturation and unknown disturbance

Abstract

The problem of the position and velocity tracking control for high-speed trains (HSTs) subject to unknown basic resistance, extra resistance and actuator faults is investigated. Neural adaptive control strategies based on a novel sliding mode surface technique are presented for three different cases (actuator faults and input saturation are neither considered; only the former is considered, and both are considered) to tackle the problem. For each case, the radial basis function (RBF) neural networks is introduced to approximate the unknown extra resistance consisting of ramp resistance, tunnel resistance, curve resistance, and so on; unknown coefficients of sliding mode surface and dynamics formulation are obtained online via adaptive laws. Simulation results demonstrate the effectiveness of the presented control methodologies.

Introduction

Along with the higher and higher requirements of reliability and safety in actual systems, increasing attention on faults, such as actuator faults, sensor faults, components faults, and so on [1], [2], [3], [4], [5] are focused. In [3], to compensate the effect of actuator faults, an adaptive fuzzy fault-tolerant control scheme is proposed. In [5], sliding mode observers are designed via ${\mathcal{H}}_{\infty }$ concepts to detect and reconstruct actuator and sensor faults. It is well known that the occurrence of faults is inescapable. Consequently, to gain desired performances, tolerant control approach which first originated in the computer system [6], [7] is put forward [8], [9], [10]. During the procedure of designing the tolerant control strategy, there are numerous algorithms to be applied to tackle the above problem, which include proportional-integral-derivative (PID) control [11], [12], sliding mode control [13], [14], adaptive control [15], [16], [17], fuzzy control [18], [19], neural networks control [20], [21], [22], ${\mathcal{H}}_{\infty }$ control [23], [24], [25], disturbance-observer-based control (DOBC) [26], [27], [28], optimal control [29], [30], etc. Specifically, combined with an auto-tuning PID controller, the novel tolerant control algorithm is presented to ensure the convergence of the model predicted tracking error [12]; In [13], to guarantee the asymptotic stability and the robustness of the nonlinear system subject to uncertainties and actuator faults, an integral sliding mode fault-tolerant control by means of fuzzy logic is designed; In [15], the adaptive fault- tolerant control scheme is proposed for the nonlinear system which is subject to actuator faults, input constraints and state constraints; In [21], the radial basis function (RBF) neural networks are investigated to approximate a continuous function; To ensure the stability of the fault networked control system, a fault-tolerant ${\mathcal{H}}_{\infty }$ control scheme is proposed, which is based on a stochastic variable satisfying the Bernoulli random distribution in [24]; A nonlinear DOBC approach is presented to reject the mismatched disturbances and recover the property of nominal performance in [27]; According to an optimal fault-tolerant path-tracking control method, the cost function of the states and inputs of systems is reduced as much as possible in [30].

Note in the above literatures input saturation is not taken into consideration. However, input saturation, which means to impose restrictions on the control input magnitudes to a certain extent, is an extremely crucial element that affects system performances in practical systems [31], [32], [33]. Therefore, it becomes a topic of considerable interest to enhance and better performances for complex systems subject to input saturation [34], [35], [36]. In [34], an adaptive controller is investigated to guarantee the global stability of the dynamic system with input saturation; In [36], based on backstepping approaches and robust adaptive control algorithms, input saturation and unknown external disturbance are taken into account simultaneously.

Obviously, high-speed trains (HSTs) dynamical system is just such a system which is subject to faults and saturation [37], [38]. Although a series of control strategies are put forwards to compensate the effects resulting from faults and saturation, there is few research for HSTs [39], [40], [41], [42]. For instance, Li et al. investigate the adaptive coordinated control strategy to ensure safe and efficient operation for HSTs with input saturation [39]; Song et al. propose a fault-tolerant control of HSTs subject to actuator faults.

Motivated by the current analysis, it is especially necessary and significative to do research for HSTs where faults and saturation are taken into account simultaneously. Consequently, in this paper, the problem of position and velocity tracking control for HSTs subject to traction force, braking force, running resistance, actuator faults and input saturation is to be considered, which is shown in Fig. 1. A novel sliding mode surface is constructed, which is similar to PID control strategy. Differed from the known controller parameters k_P and k_D of the latter, coefficients of the former is unknown and can be designed via adaptive laws. Furthermore, during the procedure of controller design, neural networks is applied to approximate the unknown extra resistance which is regarded as a disturbance. In order to compensate effects of unknown parameters resulting from sliding mode surface and dynamics formulation, adaptive laws are designed. Under some reasonable assumptions, effective control strategies are presented for three different cases: (1) HSTs dynamical system is subject to neither actuator faults nor input saturation; (2) HSTs dynamical system is subject to actuator faults; (3) HSTs dynamical system is subject to both actuator faults and input saturation.

The rest of the paper is structured as follows. In Section 2, a description of HSTs dynamical system which is subject to the basis resistance and additional resistance is presented and RBF neural networks are briefly explained. In Section 3, the main results are gained and the stability is analyzed by appropriate Lyapunov functions. To illustrate the effectiveness of the proposed control strategies, some theoretical results for three separate cases are demonstrated in Section 4 which is followed by a conclusion in Section 5.