基于障碍Lyapunov 函数的输出有界全局收敛鲁棒控制

为了克服基于障碍Lyapunov函数反演控制方法在输出约束控制中约束变量收敛区间小和要求模型精确已知的缺陷,提出一种输出有界且全局收敛的鲁棒控制策略。将收敛区间扩展到全局,并使输出保持在约束区间内;同时消除了由未知干扰和模型不确定性引起的稳态误差,放宽了对指令信号连续可导的限制。应用于电动舵机位置伺服控制的仿真结果表明,舵面能够全局稳定且摆幅有界,稳态无静差,动态响应快,抗扰动能力强。     

A new control method for state-constrained nonlinear switched systems with application to chemical process

This paper presents a new control method for a class of nonlinear switched systems in strict feedback form with a state constraint. In the proposed approach, a nonlinear mapping is first introduced to transform the problem of controlling the switched system with state constraint to a new problem of regulating the transformed system without a constraint. By using the backstepping technique, the designed state-feedback controller ensures that the corresponding closed-loop system is asymptotically stable without violation of the constraint, and that all closed-loop signals keep bounded. Furthermore, we explore the use of a coordinate transformation to deal with an asymmetric state constraint as a generalised approach. In the end, an application example on a chemical process is shown to demonstrate the efficacy of the obtained results.     

Approximation-based adaptive fuzzy tracking control for a class of switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy tracking control is investigated for switched nonlinear pure-feedback systems under arbitrary switching. By utilising mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Compared with the existing results, a priori knowledge of control directions is not required. On the other hand, differing from the existing literatures, the piecewise switched adaptive laws are designed to replace the common adaptive laws, which can reduce the conservativeness. Furthermore, the difficulties from how to deal with the unknown control directions and design common virtual control are overcome. Based on the backstepping technique and the common Lyapunov functions, an adaptive fuzzy control scheme is developed to guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded with the tracking error converging to a neighbourhood of the origin. Simulation results are provided to demonstrate the effectiveness of the proposed techniques.     

Control of nonlinear systems with partial state constraints using a barrier Lyapunov function

This article addresses the problem of control design for strict-feedback systems with constraints on the states. To prevent the states from violating the constraints, we employ a barrier Lyapunov function (BLF), which grows to infinity whenever its arguments approaches some finite limits. Based on BLF-based backstepping, we show that asymptotic output tracking is achieved without violation of any constraint, provided that the initial states and control parameters are feasible. We also establish sufficient conditions to ensure feasibility, which can be checked offline without precise knowledge of the initial states. The feasibility conditions are relaxed when handling the partial state constraint problem as compared to the full state constraint problem. In the presence of parametric uncertainties, BLF-based adaptive backstepping is useful in preventing the states from transgressing the constrained region during the transient stages of online parameter adaptation. To relax the feasibility conditions, asymmetric error bounds are considered and asymmetric barrier functions are used for control design. The performance of the BLF-based control is illustrated with two simulated examples.     

Stabilization of state‐constrained switched nonlinear systems in p‐normal form

This paper is concerned with the stabilization problem for a class of state‐constrained switched nonlinear system in p‐normal form in a domain. A key point in the backstepping design procedure is to find a common stabilizing function at each step. A barrier Lyapunov function, which grows to infinity when its arguments approach some limits, is introduced to ensure that the state constraint is not violated at any time. Bounded state feedback controllers of individual subsystems and a common Lyapunov function are explicitly constructed to asymptotically stabilize the closed‐loop system under arbitrary switchings. An example is given to show the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Tracking control and disturbance rejection for nonlinear switched control systems with saturation effects

This article focuses on the concerns of a tracking control and active disturbance rejection for nonlinear switched systems described by Takagi–Sugeno fuzzy framework with state-dependent nonlinear perturbations, actuator saturations and disturbances. Especially, a nonlinear equivalent-input-disturbance technique is employed to guarantee that only the external disturbances are rejected while retaining the beneficial nonlinearity of the system. Notably, with the aid of the lifting technique, the modified repetitive control are accurately described by a continuous-discrete two-dimensional model is designed to improve the tracking precision. The fuzzy-membership-function-dependent piecewise Lyapunov–Krasovskii functional (LKF) by exploiting the knowledge of the membership functions are built to assure the exponential stability of the investigated system. Moreover, the controller and observer gains can be obtained as solutions to a set of strict linear matrix inequalities. Finally, an application example based on the cognitive radio model is given to verify the efficacy of the proposed control protocol.     

输出受限迟滞非线性系统的反步控制器设计

针对一类含有Bouc-Wen迟滞的输出受限非线性系统设计了反步控制器.首先分析了Bouc-Wen模型的特性并得到其上界值,然后设计了对称型障碍Lyapunov函数(barrier Lyapunov function,BLF),保证了BLF有界,从而满足了输出受限的条件,最后利用反步法设计控制器.该方法消除了迟滞引起的振荡和超调并且使得系统输出约束在设定的范围内,同时解决了迟滞和系统输出受限两个方面的影响,提高了控制精度.仿真和实验结果表明了控制方法的可行性.     

Multiple Lyapunov functions‐based adaptive neural network tracking control of uncertain switched nonlinear systems

In this paper, the problem of adaptive neural network (NN) tracking control of a class of switched strict‐feedback uncertain nonlinear systems is investigated by state‐feedback, in which the solvability of the problem of adaptive NN tracking control for individual subsystems is unnecessary. A multiple Lyapunov functions (MLFs)–based adaptive NN tracking control scheme is established by exploiting backstepping and the generalized MLFs approach. Moreover, based on the proposed scheme, adaptive NN controllers of all subsystems and a state‐dependent switching law simultaneously are constructed, which guarantee that all signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. The scheme provided permits removal of a technical condition in which the adaptive NN tracking control problem for individual subsystems is solvable. Finally, the effectiveness of the design scheme proposed is shown by using two examples.     

Observer-based adaptive output-constrained control design of switched stochastic nonlinear systems with input saturation

In this article, the problem of adaptive fuzzy control for output-constrained switched stochastic nonlinear systems subject to input saturation is addressed. By employing the trigonometric function mapping method, the constrained systems are transformed into unconstrained ones, and the control goals of the original constrained systems are not affected. Meanwhile, an auxiliary system is established to deal with the issue of input saturation, and an observer is constructed to estimate the unmeasured states. Then, the unknown nonlinear functions in the system are approximated by the fuzzy logic systems (FLSs). Based on the backstepping technique and Lyapunov function method, an output feedback control strategy is designed, where the dynamic surface control technique is applied in the backstepping design process to overcome the issue of a large number of online calculations. The designed controller can guarantee that all the signals of the system satisfy bounded conditions, and the output can track given reference signals within a small error range. Finally, a simulation example is given to verify the effectiveness of the proposed control scheme.     

Adaptive fuzzy backstepping control for a class of switched nonlinear systems with actuator faults

This paper investigates the problem of fault-tolerant control (FTC) for a class of switched nonlinear systems. These systems are under arbitrary switchings and are subject to both lock-in-place and loss-of-effectiveness actuator faults. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. Under the framework of the backstepping control design, FTC, fuzzy adaptive control and common Lyapunov function stability theory, an adaptive fuzzy control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop switched system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error remains an adjustable neighbourhood of the origin. Two simulation examples are provided to illustrate the effectiveness of the proposed approach.