Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input

Based on the universal approximation property of the fuzzy-neural networks, an adaptive fuzzy-neural observer design algorithm is studied for a class of nonlinear SISO systems with both a completely unknown function and an unknown dead-zone input. The fuzzy-neural networks are used to approximate the unknown nonlinear function. Because it is assumed that the system states are unmeasured, an observer needs to be designed to estimate those unmeasured states. In the previous works with the observer design based on the universal approximator, when the dead-zone input appears it is ignored and the stability of the closed-loop system will be affected. In this paper, the proposed algorithm overcomes the affections of dead-zone input for the stability of the systems. Moreover, the dead-zone parameters are assumed to be unknown and will be adjusted adaptively as well as the sign function being introduced to compensate the dead-zone. With the aid of the Lyapunov analysis method, the stability of the closed-loop system is proven. A simulation example is provided to illustrate the feasibility of the control algorithm presented in this paper.     

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction

This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.     

Adaptive control of nonlinear uncertain active suspension systems with prescribed performance

This paper proposes adaptive control designs for vehicle active suspension systems with unknown nonlinear dynamics (e.g., nonlinear spring and piece-wise linear damper dynamics). An adaptive control is first proposed to stabilize the vertical vehicle displacement and thus to improve the ride comfort and to guarantee other suspension requirements (e.g., road holding and suspension space limitation) concerning the vehicle safety and mechanical constraints. An augmented neural network is developed to online compensate for the unknown nonlinearities, and a novel adaptive law is developed to estimate both NN weights and uncertain model parameters (e.g., sprung mass), where the parameter estimation error is used as a leakage term superimposed on the classical adaptations. To further improve the control performance and simplify the parameter tuning, a prescribed performance function (PPF) characterizing the error convergence rate, maximum overshoot and steady-state error is used to propose another adaptive control. The stability for the closed-loop system is proved and particular performance requirements are analyzed. Simulations are included to illustrate the effectiveness of the proposed control schemes.     

Indirect adaptive fuzzy fault-tolerant tracking control for MIMO nonlinear systems with actuator and sensor failures

In this paper, an active fuzzy fault tolerant tracking control (AFFTTC) scheme is developed for a class of multi-input multi-output (MIMO) unknown nonlinear systems in the presence of unknown actuator faults, sensor failures and external disturbance. The developed control scheme deals with four kinds of faults for both sensors and actuators. The bias, drift, and loss of accuracy additive faults are considered along with the loss of effectiveness multiplicative fault. A fuzzy adaptive controller based on back-stepping design is developed to deal with actuator failures and unknown system dynamics. However, an additional robust control term is added to deal with sensor faults, approximation errors, and external disturbances. Lyapunov theory is used to prove the stability of the closed loop system. Numerical simulations on a quadrotor are presented to show the effectiveness of the proposed approach.     

Decentralized adaptive neural prescribed performance control for high-order stochastic switched nonlinear interconnected systems with unknown system dynamics

In this paper, the problem of decentralized adaptive neural backstepping control is investigated for high-order stochastic nonlinear systems with unknown interconnected nonlinearity and prescribed performance under arbitrary switchings. For the control of high-order nonlinear interconnected systems, it is assumed that unknown system dynamics and arbitrary switching signals are unknown. First, by utilizing the prescribed performance control (PPC), the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, at each recursive step, only one adaptive parameter is constructed to overcome the over-parameterization, and RBF neural networks are employed to tackle the difficulties caused by completely unknown system dynamics. At last, based on the common Lyapunov stability method, the decentralized adaptive neural control method is proposed, which decreases the number of learning parameters. It is shown that the designed common controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the prescribed tracking control performance is guaranteed under arbitrary switchings. The simulation results are presented to further illustrate the effectiveness of the proposed control scheme.     

Decentralized adaptive control of interconnected nonlinear systems with unknown control directions

In this paper, we propose a decentralized adaptive control scheme for a class of interconnected strict-feedback nonlinear systems without a priori knowledge of subsystems' control directions. To address this problem, a novel Nussbaum-type function is proposed and a key theorem is drawn which involves quantifying the interconnections of multiple Nussbaum-type functions of the subsystems with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of subsystems' output are proved and a simulation example is given to illustrate the effectiveness of the proposed control scheme.     

Adaptive fuzzy approach for a class of uncertain nonlinear systems in strict-feedback form

Adaptive fuzzy control is proposed for a class of affine nonlinear systems in strict-feedback form with unknown nonlinearities. The unknown nonlinearities include two types of nonlinear functions: one satisfies the "triangularity condition" and can be directly approximated by fuzzy logic system, while the other is assumed to be partially known and consists of parametric uncertainties. Takagi-Sugeno type fuzzy approximators are used to approximate unknown system nonlinearities and the design procedure is a combination of adaptive backstepping and generalized small gain design techniques. It is proved that the proposed adaptive control scheme can guarantee the uniformly ultimately bounded (UBB) stability of the closed-loop systems. Simulation studies are shown to illustrate the effectiveness of the proposed approach.     

Adaptive output feedback tracking of nonlinear systems with uncertain nonsymmetric dead-zone input

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective.     

Adaptive output-feedback control with prescribed performance for trajectory tracking of underactuated surface vessels

In this paper, we address the problem of trajectory tracking control of underactuated surface vessels in a quantitative method with only position and attitude available. Combined with high-gain observer, parameter compression algorithm and performance function, an adaptive control scheme with prescribed performance is proposed. The high-gain observer is constructed to estimate the velocities, and the parameter compression algorithm is adopted to address persistent perturbations and model uncertainties in a more concise way. By prescribed performance function, the controller can be designed with prescribed performance. The results about system stability is given and proved by using the Lyapunov direct method. The signals concerning with all the errors converge to a bounded set. Compared with the existing methods, the developed scheme can reduce the number of tuning parameters, and guarantee the tracking errors bounded within the prescribed performance constraints in the transformed coordinate, which means the steady errors, convergence rates and maximum overshoots can be guaranteed by the performance function. Comparison and numerical simulations are given to demonstrate the effectiveness of the proposed scheme.     

Anti-disturbance dynamic surface control scheme for a class of uncertain nonlinear systems with asymmetric dead-zone nonlinearity

This study proposes anti-disturbance dynamic surface control scheme for nonlinear strict-feedback systems subjected simultaneously to unknown asymmetric dead-zone nonlinearity, unmatched external disturbance and uncertain nonlinear dynamics. Radial basis function-neural network (RBF-NN) is invoked to approximate the uncertain dynamics of the system, and the dead-zone nonlinearity is represented as a time-varying system with a bounded disturbance. The nonlinear disturbance observer (NDO) is proposed to estimate the unmatched external disturbance which further will be used to compensate the effect of the disturbance. Then, by integrating RBF-NN, NDO and dynamic surface control (DSC) approaches, the proposed anti-disturbance control scheme is designed. Stability analysis of the closed-loop system shows that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error can be made arbitrarily small by proper selection of the design parameters. In comparison with the existing methods, the proposed scheme deals with the unmatched external disturbance, uncertain dynamics and unknown asymmetric dead-zone nonlinearity, simultaneously; it avoids the "explosion of complexity" problem and develops the simple control law without singularity concern. Furthermore, some imposed assumptions to the dead-zone input and disturbances are relaxed. Simulation and comparison results verify the effectiveness of the proposed approach.     

Recurrent fuzzy neural network backstepping control for the prescribed output tracking performance of nonlinear dynamic systems

This paper proposes a backstepping control system that uses a tracking error constraint and recurrent fuzzy neural networks (RFNNs) to achieve a prescribed tracking performance for a strict-feedback nonlinear dynamic system. A new constraint variable was defined to generate the virtual control that forces the tracking error to fall within prescribed boundaries. An adaptive RFNN was also used to obtain the required improvement on the approximation performances in order to avoid calculating the explosive number of terms generated by the recursive steps of traditional backstepping control. The boundedness and convergence of the closed-loop system was confirmed based on the Lyapunov stability theory. The prescribed performance of the proposed control scheme was validated by using it to control the prescribed error of a nonlinear system and a robot manipulator.     

Adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators

This study proposes an adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators. A transformation with respect to tracking error using certain performance functions is used to ensure the transient and steady-state performances of the trajectory tracking control for robotic manipulators. Using the transformed error, a nonsingular terminal sliding mode surface is proposed. A continuous terminal sliding mode control (SMC) is presented to stabilize the system. To compensate for the uncertainty and external disturbance, a novel sliding mode disturbance observer is proposed. Considering the unknown boundary of the derivative of a lumped disturbance, an adaptive law based on the idea of equivalent control is designed. Combining the adaptive law, continuous nonsingular terminal SMC, and sliding mode disturbance observer, the adaptive sliding mode disturbance rejection control with prescribed performance is developed. Simulations are carried out to demonstrate the effectiveness of the proposed approach.     

An adaptive three-stage extended Kalman filter for nonlinear discrete-time system in presence of unknown inputs

Considering the performances of conventional Kalman filter may seriously degrade when it suffers stochastic faults and unknown input, which is very common in engineering problems, a new type of adaptive three-stage extended Kalman filter (AThSEKF) is proposed to solve state and fault estimation in nonlinear discrete-time system under these conditions. The three-stage UV transformation and adaptive forgetting factor are introduced for derivation, and by comparing with the adaptive augmented state extended Kalman filter, it is proven to be uniformly asymptotically stable. Furthermore, the adaptive three-stage extended Kalman filter is applied to a two-dimensional radar tracking scenario to illustrate the effect, and the performance is compared with that of conventional three stage extended Kalman filter (ThSEKF) and the adaptive two-stage extended Kalman filter (ATEKF). The results show that the adaptive three-stage extended Kalman filter is more effective than these two filters when facing the nonlinear discrete-time systems with information of unknown inputs not perfectly known.     

Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics

In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms.     

Improved prescribed performance control for air-breathing hypersonic vehicles with unknown deadzone input nonlinearity

An improved prescribed performance controller is proposed for the longitudinal model of an air-breathing hypersonic vehicle (AHV) subject to uncertain dynamics and input nonlinearity. Different from the traditional non-affine model requiring non-affine functions to be differentiable, this paper utilizes a semi-decomposed non-affine model with non-affine functions being locally semi-bounded and possibly in-differentiable. A new error transformation combined with novel prescribed performance functions is proposed to bypass complex deductions caused by conventional error constraint approaches and circumvent high frequency chattering in control inputs. On the basis of backstepping technique, the improved prescribed performance controller with low structural and computational complexity is designed. The methodology guarantees the altitude and velocity tracking error within transient and steady state performance envelopes and presents excellent robustness against uncertain dynamics and deadzone input nonlinearity. Simulation results demonstrate the efficacy of the proposed method.     

Adaptive fuzzy predictive sliding control of uncertain nonlinear systems with bound-known input delay

In this paper, a new Adaptive Fuzzy Predictive Sliding Mode Control (AFP-SMC) is presented for nonlinear systems with uncertain dynamics and unknown input delay. The control unit consists of a fuzzy inference system to approximate the ideal linearization control, together with a switching strategy to compensate for the estimation errors. Also, an adaptive fuzzy predictor is used to estimate the future values of the system states to compensate for the time delay. The adaptation laws are used to tune the controller and predictor parameters, which guarantee the stability based on a Lyapunov-Krasovskii functional. To evaluate the method effectiveness, the simulation and experiment on an overhead crane system are presented. According to the obtained results, AFP-SMC can effectively control the uncertain nonlinear systems, subject to input delays of known bound.     

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies.     

An unknown input multiobserver based on a discrete uncoupled multimodel for uncertain nonlinear systems: Experimental validation on a transesterification reactor

In the present paper, an unknown input multiobserver (UIMO) is designed for the state estimation of uncertain non-linear systems. A discrete decoupled state multimodel is exploited to describe the behavior of non-linear systems. A particular transformation of uncertainties to unknown inputs is considered. The LMI approach is used to establish the convergence conditions of the state estimation error. The efficiency of the proposed strategy is emphasized through an illustrative example and a real time application on a semi-batch reactor that lead to good performance in terms of robustness, convergence speed and precision.     

非线性时滞系统自适应模糊动态面控制

针对含完全未知时滞的不确定非线性系统的控制问题,提出了一种自适应模糊动态面控制方案.首先采用模糊逻辑系统逼近系统的未知时滞函数,进而用参考信号代换逼近器输入中的未知时滞信号,取消了对未知时滞常作的假设,摆脱了控制器构造对时滞假设条件的依赖性.模糊逼近和时滞代换产生的误差则采用自适应边界技术处理.基于Lyapunov-Krasovskii泛函,证明了闭环系统所有信号半全局一致最终有界,通过调节设计参数可以实现任意的跟踪精度.仿真实例进一步说明了该方案的可行性.     

Adaptive fuzzy sliding-mode controller of uncertain nonlinear systems

This paper deals with the design of adaptive fuzzy sliding-mode controllers for the T-S fuzzy model based on the Lyapunov function. It is shown that the Lyapunov function can be used to establish fuzzy sliding surfaces by solving a set of linear matrix inequalities (LMIs). The design of the fuzzy sliding surfaces and the adaptive fuzzy sliding-mode controllers is proposed. The adaptive mechanism is also used to deal with unknown parameter perturbations and external disturbances. Two examples illustrate the feasibility of the proposed methods.