Intelligent robust control for uncertain nonlinear time-varying systems and its application to robotic systems.

This paper addresses the problem of designing adaptive fuzzy-based (or neural network-based) robust controls for a large class of uncertain nonlinear time-varying systems. This class of systems can be perturbed by plant uncertainties, unmodeled perturbations, and external disturbances. Nonlinear H(infinity) control technique incorporated with adaptive control technique and VSC technique is employed to construct the intelligent robust stabilization controller such that an H(infinity) control is achieved. The problem of the robust tracking control design for uncertain robotic systems is employed to demonstrate the effectiveness of the developed robust stabilization control scheme. Therefore, an intelligent robust tracking controller for uncertain robotic systems in the presence of high-degree uncertainties can easily be implemented. Its solution requires only to solve a linear algebraic matrix inequality and a satisfactorily transient and asymptotical tracking performance is guaranteed. A simulation example is made to confirm the performance of the developed control algorithms.     

An adaptive fuzzy sliding-mode controller design for walking control with functional electrical stimulation: A computer simulation study

A major challenge to developing neuroprostheses for walking and to widespread acceptance of these walking systems is the design of a robust control strategy that provides satisfactory tracking performance, to be robust against time-varying properties of neuromusculoskeletal dynamics, day-today variations, muscle fatigue, and external disturbances, and to be easy to apply without requiring offline identification during different experiment sessions. The lower extremities of human walking are a highly nonlinear, highly time-varying, multi-actuator, multi-segment with highly inter-segment coupling, and inherently unstable system. Moreover, there always exist severe structured and unstructured uncertainties such as spasticity, muscle fatigue, external disturbances, and unmodeled dynamics. Robust control design for such nonlinear uncertain multi-input multi-output system still remains as an open problem. In this paper we present a novel robust control strategy that is based on combination of adaptive fuzzy control with a new well-defined sliding-mode control (SMC) with strong reachability for control of walking in paraplegic subjects. Based on the universal approximation theorem, fuzzy logic systems are employed to approximate the neuromusculoskeletal dynamics and an adaptive fuzzy controller is designed by using Lyapunov stability theory to compensate for approximation errors. The proposed control strategy has been evaluated on a planar model of bipedal locomotion as a virtual patient. The results indicate that the proposed strategy provides accurate tracking control with fast convergence during different conditions of operation, and could generate control signals to compensate the effects of muscle fatigue, system parameter variations, and external disturbances. Interesting observation is that the controller generates muscle excitation that mimic those observed during normal walking.     

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance.     

Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties

In this paper, a fuzzy adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainties: (i) nonlinear uncertainties; (ii) unmodeled dynamics and (iii) dynamic disturbances. The fuzzy logic systems are used to approximate the nonlinear uncertainties, nonlinear damping terms are used to counteract the dynamic disturbances and fuzzy approximation errors, and a dynamic signal is introduced to dominate the unmodeled dynamics. The derived fuzzy adaptive control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the output to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

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。     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive fuzzy-neural control of nonlinear dynamical systemsusing generalized projection update law and variable structurecontroller

In this paper, a robust adaptive fuzzy-neural control scheme for nonlinear dynamical systems is proposed to attenuate the effects caused by unmodeled dynamics, disturbance, and modeling errors. A generalized projection update law, which generalizes the projection algorithm modification and the switching-sigma adaptive law, is used to tune the adjustable parameters for preventing parameter drift and confining states of the system to the specified regions. Moreover, a variable structure control method is incorporated into the control law so that the derived controller is robust with respect to unmodeled dynamics, disturbances, and modeling errors. To demonstrate the effectiveness of the proposed method, several examples are illustrated in this paper.     

Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach

In this paper, a direct adaptive fuzzy robust control approach is proposed for single input and single output (SISO) strict-feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics and dynamical disturbances. No prior knowledge of the boundary of the nonlinear uncertainties is required. Fuzzy logic systems are used to approximate the intermediate stabilizing functions, and a stable direct adaptive fuzzy backstepping robust control approach is developed by combining the backstepping technique with the fuzzy adaptive control theory. The stability of the closed-loop system and the convergence of the system output are proved based on the small-gain theorem. Simulation studies are conducted to illustrate the effectiveness of the proposed approach.     

Adaptive fuzzy robust tracking controller design via small gain approach and its application

An adaptive fuzzy robust tracking control (AFRTC) algorithm is proposed for a class of nonlinear systems with the uncertain system function and uncertain gain function, which are all the unstructured (or nonrepeatable) state-dependent unknown nonlinear functions arising from modeling errors and external disturbances. The Takagi-Sugeno type fuzzy logic systems are used to approximate unknown uncertain functions and the AFRTC algorithm is designed by use of the input-to-state stability approach and small gain theorem. The algorithm is highlighted by three advantages: 1) the uniform ultimate boundedness of the closed-loop adaptive systems in the presence of nonrepeatable uncertainties can be guaranteed; 2) the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed; and 3) the adaptive mechanism with minimal learning parameterizations can be obtained. The performance and limitations of the proposed method are discussed. The uses of the AFRTC for the tracking control design of a pole-balancing robot system and a ship autopilot system to maintain the ship on a predetermined heading are demonstrated through two numerical examples. Simulation results show the effectiveness of the control scheme.     

Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties

In this paper, an adaptive fuzzy output feedback control approach based on backstepping design is proposed for a class of SISO strict feedback nonlinear systems with unmeasured states, nonlinear uncertainties, unmodeled dynamics, and dynamical disturbances. Fuzzy logic systems are employed to approximate the nonlinear uncertainties, and an adaptive fuzzy state observer is designed for the states estimation. By combining backstepping technique with the fuzzy adaptive control approach, a stable adaptive fuzzy...     

Semi-decentralized adaptive fuzzy control for cooperativemultirobot systems with H∞ motion/internal forcetracking performance

We present a semi-decentralized adaptive fuzzy control scheme for cooperative multirobot systems to achieve H(infinity) performance in motion and internal force tracking. First, we reformulate the overall system dynamics into a fully actuated system with constraints. To cope with both parametric and nonparametric uncertainties, the controller for each robot consists of two parts: 1) model-based adaptive controller; and 2) adaptive fuzzy logic controller (FLC). The model-based adaptive controller handles the nominal dynamics which results in both zero motion and internal force errors for a pure parametric uncertain system. The FLC part handles the unstructured dynamics and external disturbances. An H(infinity) tracking problem defined by a novel performance criterion is given and solved in the sequel. Hence, a robust controller satisfying the disturbance attenuation is derived being simple and singularity-free. Asymptotic convergence is obtained when the fuzzy approximation error is bounded with finite energy. Maintaining the same results, the proposed controller is further simplified for easier implementation. Finally, the numerical simulation results for two cooperative planar robots transporting an object illustrate the expected performance.     

采用扰动估计的气动人工肌肉系统非线性控制

气动人工肌肉系统凭借其材质轻便、输出力大及柔顺性好等优势, 其运动控制研究近年来逐渐成为热点问题. 然而, 气动人工肌肉(pneumatic artificial muscle, PAM)系统所固有的特性(如迟滞、蠕变、非线性时变等), 为其控制方法设计与实现带来了挑战. 考虑到实际工作过程中, 系统往往遭受未知干扰的影响, 本文针对气动人工肌肉系统, 提出了一种基于干扰估计的非线性控制策略, 可在系统存在持续不确定干扰的情况下, 在线进行扰动抑制, 实现精确的跟踪控制. 具体而言, 本文先通过模型变换, 将系统不确定性、未建模动态、外部扰动等处理成集总扰动的形式. 随后, 结合自适应更新律及正则化最小二乘算法, 在线估计未知系统参数及扰动; 在精确扰动代数估计的基础上, 通过所提基于干扰估计的非线性控制器, 消除未知扰动对系统造成的影响, 并确保跟踪误差收敛至零. 此外, 经稳定性分析证明了跟踪误差的渐近收敛性. 最后, 通过硬件实验验证了本文方法的有效性及鲁棒性.     

Observer-based adaptive FNN controller optimized by NAPSOSA for nonlinear time-delay systems

This study presents an observer-based adaptive fuzzy-neural network controller based on novel adaptive particle swarm optimization simulated annealing (NAPSOSA) for a class of uncertain nonlinear time-delay systems. Firstly, NAPSOSA is used to adjust the weighting function. Then, adaptive laws are adopted to approximate unknown nonlinear functions with unknown uncertainties, respectively. By examining the controller design, the observer-based control law and the weighting update law of the fuzzy-neural-network (FNN) controller are proposed for a class of nonlinear systems. In addition, based on strictly-positive-real (SPR) Lyapunov theory, the stabilization conditions for the closed-loop system are propounded. Furthermore, for obtaining a better performance, an algorithm consists of the adaptive FNN with NAPSOSA is presented to adjust the membership function of the controller. Finally, one simulation example is given to illustrate the effectiveness of the proposed approach.     

Adaptive fuzzy control for strict-feedback canonical nonlinear systems with H/sub /spl infin// tracking performance

In this paper, an adaptive fuzzy controller for strict-feedback canonical nonlinear systems is proposed. The completely unknown nonlinearities and disturbances of the systems are considered. Since fuzzy logic systems can uniformly approximate nonlinear continuous functions to arbitrary accuracy, the adaptive fuzzy control theory is employed to derive the control law for the strict-feedback system with unknown nonlinear functions and disturbances. Moreover, H/sub /spl infin// tracking performance is applied to substantially attenuate the effect of the modeling errors and disturbances. Finally, examples are simulated to confirm the applicability of the proposed methods.     

Motion synchronization of dual-cylinder pneumatic servo systems with integration of adaptive robust control and cross-coupling approach

We investigate motion synchronization of dual-cylinder pneumatic servo systems and develop an adaptive robust synchronization controller. The proposed controller incorporates the cross-coupling technology into the integrated direct/indirect adaptive robust control （DIARC） architecture by feeding back the coupled position errors, which are formed by the trajectory tracking errors of two cylinders and the synchronization error between them. The controller employs an online recursive least squares estimation algorithm to obtain accurate estimates of model parameters for reducing the extent of parametric uncertainties, and uses a robust control law to attenuate the effects of parameter estimation errors, unmodeled dynamics, and disturbances. Therefore, asymptotic convergence to zero of both trajectory tracking and synchronization errors can be guaranteed. Experimental results verify the effectiveness of the proposed controller.     

Robust adaptive fuzzy VSS control for a class of uncertain nonlinear systems using small gain design

In this paper, a novel robust adaptive fuzzy variable structure control (RAFVSC) scheme is proposed for a class of uncertain nonlinear systems. The uncertain nonlinear system and gain functions originating from modeling errors and external disturbances are all unstructured (or non-repeatable), state-dependent and completely unknown. The Takagi–Sugeno type fuzzy logic systems are used to approximate uncertain functions in the systems and the RAFVSC is designed by use of the input-to-state stability (ISS) approach and small gain theorem. In the algorithm, there are three advantages which are that the asymptotic stability of adaptive control in the presence of unstructured uncertainties can be guaranteed, the possible controller singularity problem in some of existing adaptive control schemes using feedback linearization techniques can be removed and the adaptive mechanism with minimal learning parameterizations can be achieved. The performance and effectiveness of the proposed methods are discussed and illustrated with two simulation examples.     

Robust adaptive control using a universal approximator for SISOnonlinear systems

This paper deals with the robust adaptive control of a class of nonlinear systems in the presence of parametric uncertainties and dominant uncertain nonlinearities. The proposed controller utilizes the robust adaptive control to guarantee uniform boundedness and convergence of tracking errors. In addition, an adaptive fuzzy logic system is used as a universal approximator to reduce the model uncertainties coming from uncertain nonlinearities and to improve tracking performance. The approach does not require the matching condition imposed on control systems by using the backstepping design procedure, and provides boundedness of tracking errors under poor parameter adaptation. The method can be applied to a class of single-input single-output (SISO) nonlinear systems, transformable to a parametric-strict-feedback form     

Adaptive fuzzy control for multi-input multi-output nonlinear systems with unknown dead-zone inputs

This paper presents an adaptive fuzzy control scheme for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with the nonsymmetric control gain matrix and the unknown dead-zone inputs. In this scheme, fuzzy systems are used to approximate the unknown nonlinear functions and the estimated symmetric gain matrix is decomposed into a product of one diagonal matrix and two orthogonal matrices. Based on the decomposition results, a controller is developed, therefore, the possible controller singularity problem and the parameter initialization condition constraints problem are avoided. In addition, a dynamic robust controller is employed to compensate for the lumped errors. It is proved that all the signals in the proposed closed-loop system are bounded and that the tracking errors converge asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.     

Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction

In this paper, a direct fuzzy adaptive robust control approach is proposed for a class of SISO nonlinear systems with completely unknown virtual control directions, unknown nonlinearities, unmodeled dynamics and dynamic disturbances. In the backstepping recursive design, fuzzy logic systems are employed to approximate the combined nonlinear uncertainties, a dynamic signal and Nussbaum gain technique are introduced into the control scheme to dominate the dynamic uncertainties and solve the unknown signs of virtual control directions, respectively. It is proved that the proposed robust fuzzy adaptive scheme can guarantee the all signals in the closed-loop system are semi-globally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated via three examples.     

Adaptive neural optimal control via command filter for nonlinear multi-agent systems including time-varying output constraints

In this article, an optimal command-filtered backstepping control approach is proposed for uncertain strict-feedback nonlinear multi-agent systems (MASs) including output constraints and unmodeled dynamics. One-to-one nonlinear mapping (NM) is utilized to recast constrained systems as corresponding unrestricted systems. A dynamical signal is applied to cope with unmodeled dynamics. Based on dynamic surface control (DSC), the feedforward controller is designed by introducing error compensating signals. The optimal feedback controller is produced applying adaptive dynamic programming (ADP) and integral reinforcement learning (IRL) techniques in which neural networks are utilized to approximate the relevant cost functions online with established weight updating laws. Therefore, the entire controller, including feedforward and feedback controllers, not only ensures that all signals in the closed-loop systems are cooperative semi-globally uniformly ultimately bounded (SGUUB) and the outputs maintain in the provided time-varying constraints, but also makes sure that the cost functions achieve minimization. A simulation example is presented to illustrate the feasibility of the proposed control algorithm.