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.     

不匹配不确定性系统的近似变结构输出跟踪控制

针对一类具有不匹配不确定性的非线性系统,提出一种结合变结构控制方法及自适应控制方法输出跟踪控制器。首先提出一种保证不确定性系统跟踪误差指数稳定的近似变结构控制器;进而得到一种具有不确定性范数上界估计能力的自适应近似变结构控制器,并证明了所提出的自适应近似变结构控制器使跟踪误差在时间趋于无穷时收敛于零。     

高阶非线性不确定系统的自适应实际输出跟踪控制

本文研究了一类高阶非线性不确定系统的自适应实际输出跟踪控制问题, 该问题在未知控制系数的下界精确知道的假设下已经得到了研究. 基于新的鲁棒自适应控制和连续控制思想, 成功去除该假设条件. 进而应用增加幂次积分的方法, 给出了构造连续自适应实际输出跟踪控制器的系统化方法. 该控制器确保闭环系统的所有状态全局稳定, 并且经过有限时间后, 跟踪误差可以被某一事先给定的任意正数界定. 最后, 通过一个仿真算例验证了理论结果的正确性.     

Robust adaptive fuzzy controller for non‐affine nonlinear systems with dynamic rule activation

This paper describes the design of a robust adaptive fuzzy controller for an uncertain single‐input single‐output nonlinear dynamical systems. While most recent results on fuzzy controllers considers affine systems with fixed rule‐base fuzzy systems, we propose a control scheme for non‐affine nonlinear systems and a dynamic fuzzy rule activation scheme in which an appropriate number of the fuzzy rules are chosen on‐line. By using the proposed scheme, we can reduce the computation time, storage space, and dynamic order of the adaptive fuzzy system without significant performance degradation. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as for all other signals in the closed loop. No a priori knowledge of an upper bounds on the uncertainties is required. The theoretical results are illustrated through a simulation example. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays

The problem of robust tracking and model following is considered for a class of linear systems with multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In this note, it is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances, are unknown. An improved adaptation law with /spl sigma/-modification is proposed to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a class of continuous memoryless state feedback controllers is constructed for robust tracking of dynamical signals. The proposed adaptive robust tracking controller can guarantee that the tracking error decreases asymptotically to zero in the presence of multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In addition, it is also shown that this improved adaptation law with /spl sigma/-modification can be applied to the general adaptive control problems to obtain some more exact control results. Finally, a numerical example is given to demonstrate the validity of the results.     

Observer‐based adaptive robust control of a class of nonlinear systems with dynamic uncertainties

In this paper, a discontinuous projection‐based adaptive robust control (ARC) scheme is constructed for a class of nonlinear systems in an extended semi‐strict feedback form by incorporating a nonlinear observer and a dynamic normalization signal. The form allows for parametric uncertainties, uncertain nonlinearities, and dynamic uncertainties. The unmeasured states associated with the dynamic uncertainties are assumed to enter the system equations in an affine fashion. A novel nonlinear observer is first constructed to estimate the unmeasured states for a less conservative design. Estimation errors of dynamic uncertainties, as well as other model uncertainties, are dealt with effectively via certain robust feedback control terms for a guaranteed robust performance. In contrast with existing conservative robust adaptive control schemes, the proposed ARC method makes full use of the available structural information on the unmeasured state dynamics and the prior knowledge on the bounds of parameter variations for high performance. The resulting ARC controller achieves a prescribed output tracking transient performance and final tracking accuracy in the sense that the upper bound on the absolute value of the output tracking error over entire time‐history is given and related to certain controller design parameters in a known form. Furthermore, in the absence of uncertain nonlinearities, asymptotic output tracking is also achieved. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive robust output tracking of uncertain strict-feedback nonlinear time-delay systems via control schemes with simple structure

The output tracking control problem is considered for a class of uncertain strict-feedback nonlinear systems with time-varying delays. In the paper, the time-varying delays are assumed to be any non-negative continuous and bounded functions, and it is not necessary for their derivatives to be less than one. It is also assumed that the upper bounds of nonlinear delayed state perturbations and external disturbances are unknown. On the basis of backstepping algorithm, a novel design method is proposed by which some simple adaptive robust output tracking control schemes are synthesised. The proposed design method can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm, and need not know all the nonlinear upper bound functions of uncertainties, which are repeatedly employed at each step of the backstepping algorithm. In particular, it is not necessary to know any information on the time-varying delays to construct our simple output tracking control schemes. It is also shown that the tracking error can converge uniformly exponentially towards a neighbourhood of the origin. Finally, a numerical example and its simulations are provided to demonstrate the design procedure of the simple method proposed in the paper.     

Adaptive output feedback tracking control for a class of uncertain nonlinear systems using neural networks.

This correspondence addresses the problem of designing robust tracking control for a class of uncertain nonlinear MIMO second-order systems. An adaptive neural-network-based output feedback tracking controller is constructed such that all the states and signals involved are uniformly bounded and the tracking error is uniformly ultimately bounded. Only the output measurement is required for feedback. The implementation of the neural network basis functions depends only on the desired reference trajectory. Therefore, the intelligent adaptive output feedback controller developed here possesses the properties of computational simplicity and easy implementation. A simulation example of controlling mass-spring-damper mechanical systems is made to confirm the effectiveness and performance of the developed control scheme.     

Distributed adaptive robust tracking and model matching control with actuator faults and interconnection failures

In this paper, direct adaptive-state feedback control schemes are developed to solve the robust tracking and model matching control problem for a class of distributed large scale systems with actuator faults, faulty and perturbed interconnection links, and external disturbances. The adaptation laws are proposed to update the controller parameters on-line when all the eventual faults, the upper bounds of perturbations and disturbances are assumed to be unknown. Then a class of distributed state feedback controllers is constructed to automatically compensate the fault, perturbation and disturbance effects based on the information from adaptive schemes. The proposed distributed adaptive tracking controller can ensure that the resulting adaptive closed-loop large-scale system is stable and the tracking error decreases asymptotically to zero in the presence of uncertain faults of actuators and interconnections, perturbations in interconnection channels, and disturbances. The proposed adaptive design technique is finally evaluated in the light of a simulation example.     

On robust regulation via sliding mode for nonlinear systems

A robust control scheme for the output tracking of nonlinear systems is proposed. The scheme is based on the nonlinear regulator theory and the sliding mode approach. It is shown that if perturbations and/or uncertainties appear on the system, the sliding mode controller is able to perform approximate asymptotic tracking, in the sense that the output tracking error remains bounded, provided the upper bounds of the uncertain terms are known.     

p‐Times differentiable unbounded functions for robust control of uncertain switched nonlinear systems with tracking constraints

This paper investigates the problem of robust controller design for output‐constrained and state‐constrained uncertain switched nonlinear systems. By using the idea of p‐times differentiable unbounded functions and the backstepping technique, a constructive method is proposed to design effective controllers such that the output of a class of uncertain switched nonlinear systems in lower triangular form can asymptotically track a constant reference signal without violation of the output tracking error constraint. Furthermore, the explored method is applied to the state‐constrained robust stabilization problem for a class of general uncertain switched nonlinear systems. Finally, a simulation example is provided to demonstrate the effectiveness of the developed results. Copyright © 2014 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.     

Recursive filtering adaptive fault‐tolerant tracking control for uncertain switched multivariable nonlinear systems

This article synthesizes a recursive filtering adaptive fault‐tolerant tracking control method for uncertain switched multivariable nonlinear systems. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. A piecewise constant adaptive law generates adaptive parameters by solving the error dynamics with the neglection of unknowns, and the recursive least squares is employed to minimize the residual error by categorizing the total uncertainty estimates into matched and mismatched components. A filtering control law is designed to compensate the actuator faults and nonlinear uncertainties such that a good tracking performance is delivered with guaranteed robustness. The matched component is canceled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is performed to eliminate the effect of the mismatched component on the output. By exploiting the average dwell time principle, the error bounds are derived for the states and control inputs compared with the virtual reference system which defines the best performance that can be achieved by the closed‐loop system. Both numerical and practical examples are provided to illustrate the effectiveness of the proposed switching recursive filtering adaptive fault‐tolerant tracking control architecture, comparisons with model reference adaptive control are also carried out.     

一类不确定非线性系统自适应输出反馈跟踪控制的新结果

研究了一类不确定非线性系统的自适应输出反馈实际跟踪控制问题. 解决该控制问题的困难主要源于此类系统控制系数不确定, 并具有依赖于不可测状态的增长且其增速是关于输出的多项式函数. 首先, 通过推广现有的K–滤波器, 引入了新的动态高增益K–滤波器, 并基于此构造了状态观测器. 然后, 应用反推技术, 成功的设计了系统的自适应输出反馈跟踪控制器. 主要结果表明, 通过设计参数的适当选择, 所构造的控制器能保证闭环系统的所有状态全局有界, 并且当时间足够大时, 跟踪误差收敛到零点的既定小邻域内.     

Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control

In this paper, we focus on the problem of adaptive stabilization for a class of uncertain switched nonlinear systems, whose non-switching part consists of feedback linearizable dynamics. The main result is that we propose adaptive controllers such that the considered switched systems with unknown parameters can be stabilized under arbitrary switching signals. First, we design the adaptive state feedback controller based on tuning the estimations of the bounds on switching parameters in the transformed system, instead of estimating the switching parameters directly. Next, by incorporating some augmented design parameters, the adaptive output feedback controller is designed. The proposed approach allows us to construct a common Lyapunov function and thus the closed-loop system can be stabilized without the restriction on dwell-time, which is needed in most of the existing results considering output feedback control. A numerical example and computer simulations are provided to validate the proposed controllers.     

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints. The fuzzy logic system is used to design the approximator, which deals with uncertain and continuous functions in the process of backstepping design. The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint, but also mixes the states and errors to directly constrain the state, reducing the conservativeness of the constraint satisfaction condition. Considering that the states in most nonlinear systems are immeasurable, a fuzzy adaptive states observer is constructed to estimate the unknown states. Combined with adaptive backstepping technique, an adaptive fuzzy output feedback control method is proposed. The proposed control method ensures that all signals in the closed-loop system are bounded, and that the tracking error converges to a bounded tight set without violating the full state constraint. The simulation results prove the effectiveness of the proposed control scheme.      

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed. Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods.     

不确定Markov 跳跃线性系统的鲁棒跟踪与模型跟随

讨论一类带wiener过程的不确定Markov跳跃线性系统的鲁棒跟踪和模型跟随问题．通过构造一组非线性鲁棒状态反馈跟踪控制器来跟踪给定的动态信号，该控制器确保系统当时间趋于无穷时是以扰动衰减系数鲁棒随机稳定的，且跟踪误差有界．最后给出了算例，说明所设计的鲁棒跟踪控制器具有较好的跟踪性能．     

Decentralised direct adaptive output feedback fuzzy controller for a class of large-scale nonaffine nonlinear systems and its applications

A novel cooperation-based decentralised direct adaptive fuzzy control via output feedback is developed for a class of large-scale nonaffine uncertain nonlinear systems using a direct adaptive fuzzy approach in this article. Under assumption that all the controllers share their prior information about the subsystem reference models, the interconnections between subsystems are relaxed to arbitrarily strong nonlinearities without matching conditions. The assumption on input gains is extended from typical positive constants to highly nonlinear functions. The feedback and adaptation mechanisms require neither the typical observation error filtering nor the famous strictly positive-real condition. Based on Lyapunov's direct method, the tracking errors of the closed-loop large-scale system are guaranteed to converge to tunable neighbourhoods of the origin. The proposed algorithm is applied to controlling two mechanical large-scale systems and simulation results substantiate its effectiveness.     

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.