Decentralised adaptive control for a class of stochastic switched interconnected nonlinear systems

In this paper, we focus on the problem of adaptive stabilisation for a class of interconnected uncertain switched stochastic nonlinear systems. Classical adaptive and backstepping technique are employed for control synthesis. Instead of estimating the switching parameters directly, we design the adaptive controller based on the estimations of bounds on switching time-varying parameters. A smooth function is introduced to deal with the difficulties caused by unknown interactions and tuning function approach is used to circumvent the overparameter problem. It is shown that under the action of the proposed controller all the signals of the overall closed-loop systems are globally uniformly bounded in probability under arbitrary switching. Simulation results are presented to illustrate the effectiveness of the proposed approach.     

Adaptive neural network tracking control for a class of switched stochastic pure-feedback nonlinear systems with backlash-like hysteresis

In this paper, an adaptive neural network tracking control approach is proposed for a class of switched stochastic pure-feedback nonlinear systems with backlash-like hysteresis. In the design procedure, an affine variable is constructed, which avoids the use of the mean value theorem, and the additional first-order low-pass filter is employed to deal with the problem of explosion of complexity. Then, a common Lyapunov function and a state feedback controller are explicitly obtained for all subsystems. It is proved that the proposed controller that guarantees all signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error remains an adjustable neighbourhood of the origin. Finally, simulation results show the effectiveness of the presented control design approach.     

一类纯反馈非线性系统的反推控制

研究了一类纯反馈非线性系统的输出跟踪问题.通过引入一个新的坐标变换,提出了一种基于反推设计的状态反馈控制算法.所得控制算法不仅保证了系统跟踪误差全局渐近稳定,同时使得闭环系统所有信号有界.最后,一个仿真实例验证了本文控制算法的有效性.     

Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems

In this paper,a new fuzzy adaptive control approach is developed for a class of SISO uncertain pure-feedback nonlinear systems with immeasurable states.Fuzzy logic systems are utilized to approximate the unknown nonlinear functions;and the filtered signals are introduced to circumvent algebraic loop systems encountered in the implementation of the controller,and a fuzzy state adaptive observer is designed to estimate the immeasurable states.By combining the adaptive backstepping technique,an adaptive fuzzy output feedback control scheme is developed.It is proven that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded(SGUUB),and the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters.Simulation studies are included to illustrate the efectiveness of the proposed approach.     

Full state constraints-based adaptive control for switched nonlinear pure-feedback systems

This paper investigates the problem of full state constraints-based adaptive control for a class of switched nonlinear pure-feedback systems under arbitrary switchings. First, the switched pure-feedback system is transformed into a switched strict-feedback system with non-affine terms based on the mean value theorem. Then, by exploiting the common Lyapunov function (CLF) method, the Barrier Lyapunov function method and backstepping, state feedback controllers of individual subsystems and a common Barrier Lyapunov function (CBLF) are constructed, which guarantee that all signals in the closed-loop system are global uniformly bounded under arbitrary switchings, and full state constraints are not violated. Furthermore, the tracking error can converge to a bounded compact set. Two examples, which include a single-link robot as a practical example, are provided to demonstrate the effectiveness of the proposed design method.     

一类纯反馈非线性系统的动态面控制

针对一类非仿射输入纯反馈非线性系统,提出了一种动态面控制算法.不同于运用中值定理,该算法通过引入一个辅助系统,将原系统转化为输入仿射系统,结合动态面控制与反推设计法,消除了反推法中"计算膨胀"问题.所设计控制器保证了闭环系统所有信号半全局一致最终有界,且通过选择合适的设计参数可使跟踪误差收敛到原点的一个小邻域内.一个仿真实例进一步验证了所提控制算法的有效性.     

Approximation-based adaptive fuzzy control for a class of non-strict-feedback stochastic nonlinear systems

This paper considers the problem of adaptive fuzzy control of a class of single-input/single-output （SISO） nonlinear stochastic systems in non-strict-feedback form. Fuzzy logic systems are used to approximate the uncertain nonlinearities and backstepping technique is utilized to construct an adaptive fuzzy controller. The proposed controller guarantees that all the signals in the resulting closed-loop system are bounded in probability. The main contribution of this note lies in providing a control strategy for a class of nonlinear systems in non- strict-feedback form. Simulation result is used to test the effectiveness of the suggested approach.     

一类非线性切换系统任意切换采样控制设计

本文针对一类具有非严格反馈形式的非线性切换系统,在输出只在采样点可获得的情况下,提出了一种基于模糊采样观测器的自适应输出反馈控制方法.该方法降低了现有任意切换控制研究结果中因共同控制思想导致的控制器设计的保守性,避免了迭代过程对虚拟控制的反复求导引发的计算爆炸现象及控制器高增益的弊端.切换的自适应律突显了每个子系统的特...     

一类不确定非线性纯反馈系统的自适应鲁棒模糊控制

针对一类带有不确定性的非线性MIMO纯反馈系统,提出一种自适应鲁棒模糊控制方法,该方法放宽了已有文献对系统模型的限制条件,基于李雅普诺夫分析方法获得了控制输入和自适应律．在控制输入设计中,鲁棒控制项用于补偿逼近误差向量．通过选择适当的设计参数。提出的控制方法使得闭环系统的所有信号是一致有界的和跟踪误差向量的范数收敛到小的零邻域内．仿真结果表明了所提出方法的有效性．     

Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input

This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.     

Adaptive fuzzy output-feedback fault-tolerant tracking control of a class of uncertain nonlinear switched systems

ABSTRACT

This paper considers the output-feedback fault-tolerant tracking control problem for a class of uncertain nonlinear switched systems with nonlinear faults and strict-feedback form, where the faults which are nonaffine occur on the actuator. As a kind of specialised function approximating tool, fuzzy logic systems (FLSs), are employed to approximate the unknown smooth nonlinear functions. A switched fuzzy observer is designed to address the problem of unmeasurable states, filtered signals are used to address algebraic loop problem and the average dwell time (ADT) method is further utilised to prove the stability of the resulting closed-loop systems under a type of slowly switching signals. Based on the backstepping recursive design technique and Lyapunov function method, an adaptive fuzzy output-feedback control scheme is developed. The developed control method can ensure all the signals are semi-globally uniformly ultimately bounded (SGUUB) and the system output tracks the reference signal tightly even if unknown fault occurs. A simulation carried on an example demonstrates the validity of the obtained control scheme.     

Observer-based tracking control for MIMO pure-feedback nonlinear systems with time-delay and input quantisation

In addressing the adaptive neural backstepping control for multiple-input and multiple-output nonlinear systems in pure-feedback form with time-delay and input quantisation, we construct a high-gain state observer and an output-feedback adaptive control scheme using backstepping method, with neural networks to estimate the uncertain nonlinear functions. Then, we propose an output feedback neural controller that ensures all the state trajectories in the time-delay quantised nonlinear systems are ultimately bounded, with the control signal being quantised by either a hysteretic quantiser or a logarithmic quantiser. An illustrative example is presented to show the applicability of the new control method developed.     

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.     

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.     

Adaptive tracking of switched nonlinear systems with prescribed performance using a reference-dependent reparametrisation approach

In this paper, adaptive tracking control of switched nonlinear systems in the parametric strict-feedback form is investigated. After defining a reparametrisation lemma in the presence of a non-zero reference signal, we propose a new adaptive backstepping design of the virtual controllers that can handle the extra terms arising from the reparametrisation (and that the state-of-the-art backstepping designs cannot dominate). The proposed adaptive design guarantees, under arbitrarily fast switching, an a priori bound for the steady-state performance of the tracking error and a tunable bound for the transient error. Finally, the proposed method, by overcoming the need for subsystems with common sign of the input vector field, enlarges the class of uncertain switched nonlinear systems for which the adaptive tracking problem can be solved. A numerical example is provided to illustrate the proposed control scheme.     

Robust adaptive neural control of uncertain pure-feedback nonlinear systems

In this paper, a robust adaptive neural control design approach is presented for a class of uncertain pure-feedback nonlinear systems. To reduce the complexity of the both controller structure and computation, only one neural network is used to approximate the lumped unknown function of the system at the last step of the recursive design process. By this approach, the complexity growing problem existing in conventional methods can be eliminated completely. Stability analysis shows that all the closed-loop system signals are uniformly ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness and merits of the proposed approach.     

Adaptive neural tracking control for a class of stochastic nonlinear systems

This paper investigates the problem of adaptive neural control design for a class of single‐input single‐output strict‐feedback stochastic nonlinear systems whose output is an known linear function. The radial basis function neural networks are used to approximate the nonlinearities, and adaptive backstepping technique is employed to construct controllers. It is shown that the proposed controller ensures that all signals of the closed‐loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. The salient property of the proposed scheme is that only one adaptive parameter is needed to be tuned online. So, the computational burden is considerably alleviated. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function

This article focuses on the tracking control problem for switched nonlinear systems in strict-feedback form subject to an output constraint. In order to prevent transgression of the constraint, a barrier Lyapunov function is employed, which grows to infinity when its arguments approach domain boundaries. Under the simultaneous domination assumption, a continuous controller for the switched system is constructed. Furthermore, asymptotic tracking is achieved without violation of the constraint, and all closed-loop signals keep bounded, when a mild requirement on the initial condition is satisfied. Finally, a simulation example is provided to illustrate the effectiveness of the proposed results.     

Observer-based fuzzy adaptive fault control for a class of MIMO nonlinear systems

In this paper, the fault-tolerant control (FTC) problem is investigated for a class of multi-input multiple output nonlinear systems with time-varying delays, and an active FTC method is proposed. The controlled system contains unknown nonlinear functions, unknown control gain functions and actuator faults, which integrates time-varying bias and gain faults. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions and unknown control gain functions, fuzzy adaptive observers are used for fault detection and isolation. Further, based on the obtained information, an accommodation method is proposed for compensating the actuator faults. It is shown that all the variables of the closed-loop system are semi-globally uniformly bounded, the tracking error converges to an arbitrary small neighbourhood of the origin. A simulation is given to demonstrate the effectiveness of the proposed approach.     

Robust fault-tolerant prescribed performance tracking for uncertain switched pure-feedback nonlinear systems under arbitrary switching

This paper presents a model-free prescribed performance design methodology for the robust fault-tolerant tracking (RFTT) of uncertain switched pure-feedback nonlinear systems under arbitrary switching. Unexpected faults in switched non-affine nonlinearities and in an actuator are considered. Using the prescribed performance design and the common Lyapunov function method, a common RFTT scheme is proposed to ensure that the tracking error remains within preassigned performance bounds and finally converges to a preselected neighbourhood of the origin, regardless of arbitrary switching and unexpected faults. Contrary to existing results in the literature, the proposed methodology does not require fault compensation mechanisms such as adaptive techniques and function approximators using neural networks or fuzzy systems. Thus, the structure of the proposed RFTT scheme is simpler than that of the existing control schemes. Moreover, the proposed approach can predesign the transient performance bounds at the instants when switching and faults occur. Finally, the simulation results are provided to demonstrate the effectiveness of the proposed theoretical approach.