具有未知输出函数的非线性系统全局输出反馈控制

研究了一类具有未知输出函数的非线性系统全局输出反馈控制问题．由于输出函数未知,传统的观测器将无法实现．为解决这个问题,首先设计了一个与输出函数无关的状态补偿器,使得标称线性系统全局渐近稳定．然后,应用齐次控制方法通过适当选择增益参数,使得不确定非线性系统在有限时间内全局渐近稳定．数值算例表明该算法的有效性．     

Semi‐Global Output Feedback Stabilization for a Class of Uncertain Nonlinear Systems

This paper addresses the problem of semi‐global stabilization by output feedback for a class of nonlinear systems whose output gains are unknown. For each subsystem, we first design a state compensator and use the compensator states to construct a control law to stabilize the nominal linear system without the perturbing nonlinearities. Then, combining the output feedback domination approach with block‐backstepping scheme, a series of homogeneous output feedback controllers are constructed recursively for each subsystem and the closed‐loop system is rendered semi‐globally asymptotically stable.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive practical output tracking control for a class of uncertain nonlinear systems

This paper investigates the problem of adaptive practical tracking control by output feedback for a class of uncertain nonlinear systems without zero dynamics. The uncertain nonlinear perturbed terms of the considered systems are assumed to satisfy a generalised condition which is more relaxed than the triangular-type condition. Furthermore, in contrast to the previous work in the literature, the upper bound of the nonlinearities is a polynomial function of the output, with an unknown growth rate, multiplied by some relaxed conditions of unmeasured states. Due to the presence of unknown parametric uncertainty, a dynamic output compensator with dynamically updated gains is explicitly constructed based on non-separation principle. In particular, we show that for any positive number γ, all the states of the closed-loop systems are globally bounded and the tracking error belongs to the interval [?γ, γ] after some positive finite time. A numerical example illustrates the efficiency of the method.     

Adaptive output feedback control of a class of uncertain nonlinear systems with unknown time delays

This article studies the adaptive output feedback control problem of a class of uncertain nonlinear systems with unknown time delays. The systems considered are dominated by a triangular system without zero dynamics satisfying linear growth in the unmeasurable states. The novelty of this article is that a universal-type adaptive output feedback controller is presented to time-delay systems, which can globally regulate all the states of the uncertain systems without knowing the growth rate. An illustrative example is provided to show the applicability of the developed control strategy.     

Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.     

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

This article studied the global output feedback regulation problem for a class of uncertain nonlinear time delay systems subject to unknown measurement faults on sensors. Different from the existing works, we consider the unknown time‐varying delays on the system states and relax their conservative condition on nonlinear functions. By introducing two novel time‐varying gains, a new global output feedback regulation algorithm is proposed, which ensures control parameters can be chosen flexibly. The proposed linear‐like controller is independent of the unknown time‐varying delays. Moreover, it has a simple structure, which is convenient for the implementation in practice. Based on the Lyapunov stability theory, it is strictly proved that all signals of the resulting closed‐loop system are globally bounded with the designed controller. Finally, a simulation example is presented to illustrate the effectiveness of the proposed output feedback regulation algorithm.     

Adaptive output feedback stabilisation for planar nonlinear systems with unknown control coefficients

The paper is concerned with the global adaptive stabilisation via output feedback for a class of uncertain planar nonlinear systems. Remarkably, the unknowns in the systems are rather serious: the control coefficients are unknown constants which do not belong to any known interval, and the growth of the systems heavily depends on the unmeasured states and has the rate of unknown polynomial of output. First, a delicate state transformation is introduced to collect the unknown control coefficients, and subsequently, a suitable state observer is successfully designed with two different dynamic gains. Then, an adaptive output feedback controller is proposed by flexibly combining the universal control idea and the backstepping technique. Meanwhile, an appropriate estimation law is constructed to overcome the negative effect caused by the unknown control coefficients. It is shown that, with the appropriate choice of the design parameters, all the states of the resulting closed-loop system are globally bounded, and furthermore, the states of the original system converge to zero.     

Adaptive Output Feedback Control for a Class of Uncertain Stochastic Nonlinear Systems With Unknown Time‐Delays

This paper investigates the problem of output feedback control for a class of stochastic nonlinear systems with time‐delays. Using dynamic gain scaling technique, an adaptive update law is introduced to the observer and controller to deal with the unknown parameters. Based on the Lyapunov‐Krasovskii functional and stochastic Barbalat's lemma, it is proved that the proposed universal‐type adaptive output feedback controller can regulate all the states of the closed‐loop system almost surely. A simulation example is presented to illustrate the effectiveness of the proposed design procedure.     

Output feedback stabilization for nonholonomic systems with unknown unmeasured states‐dependent growth

This paper is concerned with the global output feedback stabilization for a class of nonholonomic systems with unknown parameter, polynomial‐of‐output, and unmeasurable states dependent growth. A dynamic high‐gain observer is first designed to reconstruct the unmeasurable system states and, in addition, to compensate the serious parameter unknowns in nonlinear drifts. Then, we design a compact adaptive controller without invoking the backstepping technique, which reduces the complexity of controller. Additionally, a switching control strategy is employed to overcome the smooth feedback obstacle associated with nonholonomic systems. It is shown that the proposed control laws guarantee that all closed‐loop system states are globally bounded and ultimately converge to zero. The simulation results demonstrate the effectiveness of the proposed control strategy.     

Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions

In this paper, the authors investigate a decentralized adaptive output-feedback controller design for large-scale nonlinear systems with input saturations and time-delayed interconnections unmatched in control inputs. The interaction terms with unknown time-varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems. This point is a main contribution of this paper compared with previous output-feedback control approaches which assume that the time-delayed bounding functions only depend on measurable output variables. The bounding functions are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique based on neural networks. The observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem. In addition, we prove that all signals in the closed-loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

Fuzzy adaptive output feedback control for a class of switched non-triangular structure nonlinear systems with time-varying delays

This paper investigates an adaptive fuzzy output feedback control design problem for switched nonlinear system in non-triangular structure form. The discussed system contains unknown nonlinear dynamics, unmeasured states and unknown time-varying delays under a batch of switching signals. Fuzzy logic systems are utilised to learn unknown nonlinear dynamics and construct a fuzzy switched nonlinear observer. By combining the property of fuzzy basis function with Lyapunov–Krasovskii functional and the command filter, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the closed-loop control system is proved via Lyapunov stability theory and average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme.     

一类关于不确定性机器人的鲁棒控制策略

基于计算力矩结构,研究参数和结构不确定的机器人轨迹跟踪的鲁棒控制策略.其 特点是利用了机器人不确定动力学的集中包络函数,在该包络函数已知的情况下,设计的非 线性连续补偿控制律能够有效消除系统的不确定性影响,保证系统达到三种不同的稳定性结 果.另外,在该包络函数参数未知时,还没计了一个新颖的在线辨识器,可保证系统指数意义 下的渐近收敛或一致有界.     

Adaptive Output‐Feedback Control of Nonlinear Systems with Multiple Uncertainties

This paper addresses the global stabilization via adaptive output‐feedback for a class of uncertain nonlinear systems. Remarkably, the systems under investigation are with multiple uncertainties: unknown control directions, unknown growth rates and unknown input bias, and can be used to describe more physical plants. Multiple uncertainties, which usually cannot be compensated by a sole compensation technique, may give rise to big technical difficulty for controller design. To overcome such difficulty and to achieve the global stabilization, a new adaptive output‐feedback scheme is proposed in this paper, by flexibly combining Nussbaum‐type function, tuning function technique and extended state observer. It is shown that, under the designed controller, the system states globally converge to zero. A simulation example on non‐zero set‐point regulation is given to demonstrate the effectiveness of the theoretical results.     

Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large‐scale systems using DSC technique

In this paper, an adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large‐scale stochastic nonlinear systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. Using the designed fuzzy state observer, and by combining the adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy decentralized output feedback control approach is developed. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing appropriate design parameters. A simulation example is provided to show the effectiveness of the proposed approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive Neural Dynamic Surface Control For Nonlinear Pure‐Feedback Systems With Multiple Time‐Varying Delays: A Lyapunov‐Razumikhin Method

This paper focuses on the problem of adaptive neural control for a class of uncertain nonlinear pure‐feedback systems with multiple unknown time‐varying delays. The considered problem is challenging due to the non‐affine pure‐feedback form and the unknown system functions with multiple unknown time‐varying delays. Based on a novel combination of mean value theorem, Razumikhin functional method, dynamic surface control (DSC) technique and neural network (NN) parameterization, a new adaptive neural controller which contains only one parameter is developed for such systems. Moreover, The DSC technique can overcome the problem of ‘explosion of complexity’ in the traditional backstepping design procedure. All closed‐loop signals are shown to be semi‐globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the proposed design.     

Adaptive output feedback control of feedforward nonlinear distributed delay systems with unknown delay kernel

This paper considers the problem of global adaptive output feedback regulation for a class of uncertain feedforward nonlinear distributed delay systems. Compared with the existing results, we reduce the conservatism of the restrictive conditions by combining the dynamic scaling technique and the backstepping method, in particular, uncertain control coefficients and unknown delay kernels are admitted. With the help of the Lyapunov–Krasovskii theorem, a delay-independent output feedback controller is proposed by constructing an input-driven observer with a novel dynamic gain, which guarantees that all the closed-loop signals are globally bounded while rendering the states of original system and the estimate states globally asymptotically to converge to zero as time goes to infinity. Finally, a numerical example is given to illustrate the usefulness of our results.     

Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization

We address the problem of output tracking for a class of nonlinearly parameterized systems with unstabilizable linearization. To achieve practical output tracking globally in the case when both the bound of reference signals and the bound of unknown time-varying parameters are not known a priori, we present a robust adaptive control method that is based on the idea of universal control combined with the new adaptive feedback design method developed recently for controlling uncertain systems with nonlinear parameterization. Continuous adaptive tracking controllers are explicitly constructed in this paper. The proposed adaptive tracking controllers use only the information of a prescribed reference signal but not its derivatives, nor its bound.     

Adaptive robust control of uncertain systems with state and input delay

In this paper, adaptive robust control of uncertain systems with multiple time delays in states and input is considered. It is assumed that the parameter uncertainties are time varying norm-bounded whose bounds are unknown but their functional properties are known. To overcome the effect of input delay on the closed loop system stability, new Lyapunov Krasovskii functional will be introduced. It is shown that the proposed adaptive robust controller guarantees globally uniformly exponentially convergence of all system solutions to a ball with any certain convergence rate. Moreover, if there is no disturbance in the system, asymptotic stability of the closed loop system will be established. The proposed design condition is formulated in terms of linear matrix inequality (LMI) which can be easily solved by LMI Toolbox in Matlab. Finally, an illustrative example is included to show the effectiveness of results developed in this paper.     

Adaptive Robust Output Tracking Control of Uncertain Nonlinear Cascade Systems with Disturbance and Multiple Unknown Time‐Varying Delays

In this paper, an adaptive robust controller is designed for a class of uncertain nonlinear cascade systems with multiple time‐varying delays under external disturbance. It is assumed that multiple time‐varying delays are not exactly known and, therefore, the delayed terms must not appear in the adaptation and control laws. Accordingly, by using a Lyapunov‐Krasovskii function, delays are deleted from the adaptation and control laws. A controller based on an adaptive backstepping approach is designed to assure the global asymptotic tracking of the desired output and boundedness of the other states. The proposed controller is proved to be robust against unknown time‐varying delays and external disturbances applying to the system. Simulation results are provided to show the effectiveness of the proposed approach.