Finite-time adaptive fuzzy control for a class of output constrained nonlinear systems with dead-zone

The article investigates the finite-time adaptive fuzzy control for a class of nonlinear systems with output constraint and input dead-zone. First, by skillfully combining the barrier Lyapunov function, backstepping design method, and finite-time control theory, a novel adaptive state-feedback tracking controller is constructed, and the output constraint of the nonlinear system is not violated. Second, the fuzzy logic system is used to approximate unknown function in the nonlinear system. Third, the finite-time command filter is introduced to avoid the problem of “complexity explosion” caused by repeated differentiations of the virtual control signal in conventional backstepping control schemes. Meanwhile, a new saturation function is added in the compensating signal for filter error to improve control accuracy. Finally, based on Lyapunov stability analysis, all the signals of the closed-loop are proved to be semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood region of the origin in a finite time. A simulation example is presented to demonstrate the effectiveness for the proposed control scheme.     

Disturbance observer-based adaptive boundary iterative learning control for a rigid-flexible manipulator with input backlash and endpoint constraint

In this article, an observer-based adaptive boundary iterative learning control law is developed for a class of two-link rigid-flexible manipulator with input backlash, the unknown external disturbance, and the endpoint constraint. To tackle the backlash nonlinearities and ensure the vibration suppression, the disturbance observers based upon the iterative learning conception are considered in the adaptive boundary control design. A barrier Lyapunov function is incorporated with boundary control law to restrict the endpoint state. Based on the defined barrier composite energy function, the tracking angle error convergence of the rigid part is guaranteed, and the vibrations of the flexible part are suppressed through the rigorous analysis. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed control.     

An adaptive iterative learning algorithm for boundary control of a flexible manipulator

In this study, we consider the boundary control problem of a flexible manipulator in the presence of system parametric uncertainty and external disturbances. The dynamic behavior of the flexible manipulator is represented by partial differential equations (PDEs). Based on the Lyapunov method, we propose an adaptive iterative learning control scheme for trajectory tracking and vibration suppressing of a flexible manipulator. The proposed control scheme is designed using both a proportional‐derivative feedback structure and an iterative term. The learning convergence of iterative learning control is achieved through rigorous analysis without any simplification or discretization of the PDE dynamics. Finally, the results are illustrated using numerical simulations for control performance verification. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive control of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics

This paper focuses on the problem of adaptive control for a class of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics. By introducing a one-to-one nonlinear mapping, the constrained pure-feedback nonlinear system with state and input unmodeled dynamics is transformed into unconstrained pure-feedback system. The controller design based on the transformed novel system is proposed by using a modified dynamic surface control method. Dynamic signal and normalization signal are designed to handle dynamical uncertain terms and input unmodeled dynamics, respectively. By adding nonnegative normalization signal into the whole Lyapunov function and using the introducing compact set in the stability analysis, all signals in the whole system are proved to be semiglobally uniformly ultimately bounded, and all states can obey the time-varying constraint conditions. A numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Nonlinear partial differential equation modeling and adaptive fault-tolerant vibration control of flexible rotatable manipulator in three-dimensional space

In this article, we investigate the problem of nonlinear modeling and adaptive boundary vibration control with actuator failure for a flexible rotatable manipulator in three-dimensional space, which is made up of a rotatable base and a flexible manipulator. In order to accurately reflect the characteristics of the distributed parameters, the Hamilton principle is introduced to derive the dynamic model expressed by partial differential equations (PDEs). Based on the model, an innovative boundary control scheme is proposed to eliminate the deflection and vibration simultaneously, and to guarantee that the rotatable base and the flexible manipulator can track the desired angle respectively. The adaptive law is developed to estimate the loss of the actuator. The effectiveness of the designed controller is verified from both theoretical analysis and numerical simulation.     

Robust adaptive tracking control for nontriangular time-delay nonlinear systems with input dead-zone and multiple uncertainties

This article studies the robust adaptive tracking control problem of nontriangular nonlinear systems that are affected by multiple state delays rather than the input-delay. Different from the related studies, the considered systems involve input dead-zone and various uncertainties arising in the control coefficients, structure parameters, time delays, and disturbances. A new adaptive control strategy is presented by introducing a dynamic-gain-based Lyapunov-Krasovskii functional and by generalizing the tuning function method in the framework of time-delay system theory. All the states of the closed-loop system are bounded and the tracking error can be adjusted sufficiently small. In the simulation, the delayed chemical system is studied to demonstrate the validity of the strategy.     

具有非线性输入的鲁棒自适应模糊滑模控制

针对一类具有死区非线性输入的SISO非线性系统,基于滑模控制原理,提出了一种稳定自适应模糊控制器设计方案.该方案通过使用积分型Lyapunov函数避免了反馈线性化方法中可能出现的控制器奇异性问题,运用两阶段法构造两个Lyapunov函数,确定出用于建模的有界闭区域,再证明跟踪误差收敛到零.通过理论分析,证明了闭环控制系统全局一致终结有界;仿真结果表明了该方法的有效性.     

Attitude control of reusable launch vehicle in reentry phase with input constraint via robust adaptive backstepping control

The paper presents an attitude control problem of reusable launch vehicles in reentry phase. The controller is designed based on synthesizing robust adaptive control into backstepping control procedure in the presence of input constraint, model uncertainty, and external disturbance. In view of the coupling between the states of translational motion and the states of attitude motion, the control‐oriented model is developed, where the uncertainties do not satisfy linear parameterization assumption. The time derivative of the virtual control input is viewed as a part of uncertain term to facilitate the analytic computations and avoid the ‘explosion of terms’ problem. The robust adaptive backstepping control scheme is first proposed to overcome the uncertainty and external disturbance. The robust adaptive law is employed to estimate the unknown bound of the uncertain term. Furthermore, the attitude control problem subjects to input constraint is studied, and the constrained robust adaptive backstepping control strategy is proposed. Within the Lyapunov theory framework, the stability analysis of the closed‐loop system is carried out, and the tracking error converges to a random neighborhood around origin. Six‐degree‐of‐freedom reusable launch vehicle simulation results are presented to show the effectiveness of the proposed control strategy. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive neural control for nonstrict‐feedback stochastic nonlinear time‐delay systems with input and output constraints

This paper investigates an adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear time‐delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time‐delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach.     

Adaptive fixed-time minimal learning force/position control of uncertain manipulators subject to input saturation

This article solves the fixed-time force/position control problem for constrained manipulators in the presence of input saturation and uncertain dynamics. Under the fixed-time stability theory, a novel fixed-time auxiliary dynamic system (ADS) is first presented to compensate for the effects of input saturation nonlinearity. System uncertainties are estimated by using radial basis function neural networks (RBF NNs) and only need to tune one neural parameter online. In addition, with a fixed-time sliding mode surface and the proposed fixed-time ADS, a novel fixed-time adaptive neural force/position controller is designed which can not only ensure the fixed-time stability of the position tracking error but also enable the manipulator to track the desired force trajectory. By using the Lyapunov method, the boundedness of all signals in the closed-loop system is proved. Finally, the effectiveness of the proposed method is demonstrated by comparative simulation works.     

绳驱动空中机械臂的自适应分数阶终端滑模控制

针对集总干扰下绳驱动空中机械臂关节空间内高精度轨迹跟踪控制问题,提出了一种基于时延估计技术的自适应鲁棒控制策略。在控制框架中,引入时延估计技术来补偿系统未建模特性、外界扰动及动力学耦合效应;采用分数阶非奇异终端滑模面来加快系统状态量的收敛速度和保证轨迹跟踪控制的精度;添加自适应律来增加控制器的鲁棒性。同时,基于李雅普诺夫稳定性理论分析了闭环系统的稳定性。最后,通过可视化仿真和地面试验对本文所设计控制器的有效性进行了验证,结果表明：与其他两种控制器相比,本文控制器具有较高的轨迹跟踪精度、较好的鲁棒性和较强的抗干扰能力。     

Model‐free fault‐tolerant control approach for uncertain state‐constrained linear systems with actuator faults

This paper investigates the robust adaptive fault‐tolerant control problem for state‐constrained continuous‐time linear systems with parameter uncertainties, external disturbances, and actuator faults including stuck, outage, and loss of effectiveness. It is assumed that the knowledge of the system matrices, as well as the upper bounds of the disturbances and faults, is unknown. By incorporating a barrier‐function like term into the Lyapunov function design, a novel model‐free fault‐tolerant control scheme is proposed in a parameter‐dependent form, and the state constraint requirements are guaranteed. The time‐varying parameters are adjusted online based on an adaptive method to prevent the states from violating the constraints and compensate automatically the uncertainties, disturbances, and actuator faults. The time‐invariant parameters solved by using data‐based policy iteration algorithm are introduced for helping to stabilize the system. Furthermore, it is shown that the states converge asymptotically to zero without transgression of the constraints and all signals in the resulting closed‐loop system are uniformly bounded. Finally, two simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive finite-time consensus tracking control for nonlinear multiagent systems in nonstrict feedback form with full-state constraints

In this article, the fuzzy adaptive finite-time consensus tracking control problem for nonstrict feedback nonlinear multiagent systems with full-state constraints is studied. The finite-time control based on command filtered backstepping is proposed to guarantee the finite-time convergence and eliminate the explosion of complexity problem caused by backstepping process, and the errors in the filtering process are compensated by using error compensation mechanism. Furthermore, based on the fuzzy logic systems, the uncertain nonlinear dynamics are approximated and the problem of state variables in nonstrict feedback form is solved by using the property of basis functions. The barrier Lyapunov functions are introduced to guarantee that all system states and compensated tracking error signals are constrained in the designed regions. A simulation example is given to verify the superiority of the proposed algorithm.     

Direct adaptive control for non‐linear uncertain systems with exogenous disturbances

A direct adaptive non‐linear control framework for multivariable non‐linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non‐linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov‐based and guarantees partial asymptotic stability of the closed‐loop system; that is, asymptotic stability with respect to part of the closed‐loop system states associated with the plant. In the case of bounded energy L₂ disturbances the proposed approach guarantees a non‐expansivity constraint on the closed‐loop input–output map. Finally, several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Neuro-adaptive output-feedback optimized stochastic control for the active suspension systems with state constraints

This article investigates an adaptive neural network (NN) output-feedback optimal control design problem for active suspension systems (ASSs) with stochastic disturbance. The ASSs under consideration contain the characteristics of spring nonlinear dynamics, unmeasured states, and state constraints. The NNs are developed to approximate the unknown nonlinear functions. Meanwhile, observer-based output feedback control design method is proposed based on the adaptive backstepping technique. Furthermore, the stability of the closed-loop system is demonstrated by constructing the barrier Lyapunov function, thus ensuring that the full-state constraints are not exceeded. In particular, the simulation validations are given for the cases of bump, C-class, and D-class road displacements inputs. Finally, the simulation results verify the effectiveness of the studied control strategy.     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

Adaptive disturbance rejection control for compartmental systems with application to intraoperative anesthesia influenced by hemorrhage and hemodilution effects

Compartmental system models involve dynamic states whose values are nonnegative. These models are widespread in biological and physiological sciences and play a key role in understanding these processes. In this paper, we develop a direct adaptive disturbance rejection control framework for compartmental dynamical systems with exogenous bounded disturbances. The proposed framework is Lyapunov based and guarantees partial asymptotic stability of the closed‐loop system, that is, asymptotic stability with respect to part of the closed‐loop system states associated with the plant dynamics. The remainder of the states associated with the adaptive controller gains are shown to be Lyapunov stable. In the case of bounded energy ??₂ disturbances, the proposed approach guarantees a nonexpansivity constraint on the closed‐loop input–output map between the plant disturbances and performance variables. Finally, a numerical example involving the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for surgery in the face of continuing hemorrhage and hemodilution is provided. Copyright © 2008 John Wiley & Sons, Ltd.     

Tracking control for flexible joint robots based on adaptive fuzzy compensation with uncertain parameters

This article presents a control scheme for flexible joint robots which has uncertain parameters based on adaptive fuzzy compensation. Considering the unknown parameters, the proposed state feedback control approach utilizes measured variables to establish a cascade structure that is based on simplified dynamics. After reducing the number of fuzzy rules, the adaptive fuzzy logic system is added as compensation to decrease the approximated errors, and the robust terms are also used to enhance the robustness of closed-loop system. Then, the global asymptotic stability could be confirmed through Lyapunov stability principle and Barbalat's lemma. Compared with the other two controllers, the proposed control method has not only higher position accuracy and better dynamic performance but also robustness to the approximation of motor inertia, friction torque and link torque. Some simulation experiments are conducted to show the validity of the proposed scheme.     

High angle of attack flight control based on switched prescribed performance

This article studies the high angle of attack (AOA) maneuver control based on an improved prescribed performance method, that is, switched prescribed performance control (SPP). Different from traditional prescribed performance control, multiple performance functions are considered in the SPP, which can appropriately adjust the output performance constraints. Furthermore, based on the SPP, an adjustable prescribed performance (APP) control method is developed, which requires only a continuous adjustable performance function. Then, based on the proposed APP and adaptive neural network (NN) technology, a robust adaptive NN flight control law is developed. To handle the input saturation, an improved auxiliary system is developed. According to the common Lyapunov function method, it can be concluded that the closed-loop system is stable and the system output can meet the corresponding prescribed performance. Finally, simulations are given to illustrate the validity of the high AOA flight control law based on the proposed APP.     

Integral barrier Lyapunov function-based adaptive fuzzy output feedback control for nonlinear delayed systems with time-varying full-state constraints

In this article, an adaptive fuzzy output feedback control method is presented for nonlinear time-delay systems with time-varying full state constraints and input saturation. To overcome the problem of time-varying constraints, the integral barrier Lyapunov functions (IBLFs) integrating with dynamic surface control (DSC) are applied for the first time to keep the state from violating constraints. The effects of unknown time delays can be removed by using designed Lyapunov-Krasovskii functions (LKFs). An auxiliary design system is introduced to solve the problem of input saturation. The unknown nonlinear functions are approximated by the fuzzy logic systems (FLS), and the unmeasured states are estimated by a designed fuzzy observer. The novel controller can guarantee that all signals remain semiglobally uniformly ultimately bounded and satisfactory tracking performance is achieved. Finally, two simulation examples illustrate the effectiveness of the presented control methods.