A robust output-feedback adaptive dynamic surface control for linear systems with input disturbance

In this paper, a robust output-feedback adaptive control is proposed for linear time-invariant (LTI) singleinput single-output (SISO) plants with unmeasurable input disturbance. Using dynamic surface control (DSC) technique, it is shown that the explosion of complexity problem in backstepping control can be eliminated. Furthermore, the proposed adaptive DSC scheme has the following merits: 1) by introducing an initialization technique, the L∞ performance of system tracking error can be guaranteed even if the plant high-frequency gain is unknown and the input disturbance exists, and 2) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. It is proved that with the proposed scheme, all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.     

未知参数多变量线性系统自适应模糊广义预测控制

对未知参数多变量线性系统提出了自适应模糊广义预测控制方法.该方法直接用模糊逻辑系统组成的向量设计广义预测控制器,并基于广义误差向量估计值对控制器中的未知向量和广义误差估计值中的未知矩阵进行白适应调整.该方法不但能保证闭环系统所有信号有界,而且可使广义误差向量收敛到原点的一个邻域内.     

Adaptive neural dynamic surface control for servo systems with unknown dead-zone

An adaptive neural controller is proposed for nonlinear systems with a nonlinear dead-zone and multiple time-delays. The often used inverse model compensation approach is avoided by representing the dead-zone as a time-varying system. The “explosion of complexity” in the backstepping synthesis is eliminated in terms of the dynamic surface control (DSC) technique. A novel high-order neural network (HONN) with only a scalar weight parameter is developed to account for unknown nonlinearities. The control singularity and some restrictive requirements on the system are circumvented. Simulations and experiments for a turntable servo system with permanent-magnet synchronous motor (PMSM) are provided to verify the reliability and effectiveness.     

Adaptive actuator failure compensation for nonlinear MIMO systems with an aircraft control application

A direct adaptive approach is developed for control of a class of multi-input multi-output (MIMO) nonlinear systems in the presence of uncertain failures of redundant actuators. An adaptive failure compensation controller is designed which is capable of accommodating uncertainties in actuator failure time instants, values and patterns. A realistic situation is studied with fixed grouping of actuators and proportional actuation within actuator groups. The adaptive control system is analyzed, to show its desired stability and asymptotic tracking properties in the presence of actuator failure uncertainties. As an application, such an adaptive controller is used for actuator failure compensation of a twin otter aircraft longitudinal model, with design conditions verified and control structure and adaptive laws developed for a nonlinear aircraft dynamic model. The effectiveness of adaptive failure compensation is demonstrated by simulation results.     

基于ISS的非线性纯反馈系统的自适应动态面控制

研究一类具有未知死区的非线性纯反馈系统的自适应控制问题．基于输入状态稳定理论和小增益定理,提出一种自适应动态面控制方案．该方案有效地减少了可调参数的数目,避免了传统后推设计中由于需要对虚拟控制反复求导而导致的计算复杂性．理论分析证明了闭环系统是半全局一致终结有界的．     

Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form

In this paper, adaptive dynamic surface control (DSC) is developed for a class of pure-feedback nonlinear systems with unknown dead zone and perturbed uncertainties using neural networks. The explosion of complexity in traditional backstepping design is avoided by utilizing dynamic surface control and introducing integral-type Lyapunov function. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system, with arbitrary small tracking error by appropriately choosing design constants. Simulation results demonstrate the effectiveness of the proposed approach.     

Adaptive dynamic surface control for uncertain nonaffine nonlinear systems

This paper focuses on the problem of adaptive control for uncertain nonaffine nonlinear systems. The original nonaffine systems are transformed into the augmented affine systems via adding an auxiliary integrator, which makes the explicit control design possible. By introducing a modified sliding mode filter in each step, a novel adaptive dynamic surface controller is proposed, where the ‘explosion of complexity’ problem inherent in the backstepping design is avoided. It is proven rigorously that for any initial control condition, the proposed adaptive scheme is able to ensure the semiglobal uniformly ultimately boundedness of all signals in the closed loop. An illustrative example is carried out to verify the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

A robust adaptive dynamic surface control for linear systems

In this article, a robust output-feedback adaptive dynamic surface control (DSC) is proposed for linear time-invariant single-input single-output plants with unmodelled dynamics and unmeasurable output disturbance. With the proposed adaptive DSC scheme, the ‘explosion of terms’ problem inherent in backstepping control is eliminated and the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. More importantly, it is proved that with an initialisation technique, the ?_∞ performance of the tracking error can be guaranteed even with unmodelled dynamics, bounded output disturbance exists and the plant high-frequency gain is unknown.     

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.     

Adaptive neural control for strict-feedback stochastic nonlinear systems with time-delay

The problem of robust stabilization is investigated for strict-feedback stochastic nonlinear time-delay systems via adaptive neural network approach. Neural networks are used to model the unknown packaged functions, then the adaptive neural control law is constructed by a novel Lyapunov-Krasovskii functional and backstepping. It is shown that all the variables in the closed-loop system are semi-globally stochastic bounded, and the state variables converge into a small neighborhood in the sense of probability.     

Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems

An adaptive fuzzy control approach is proposed for a class of multiple-input-multiple-output (MIMO) nonlinear systems with completely unknown nonaffine functions. The MIMO systems are composed of n subsystems and each of subsystems is in the nested lower triangular form. It is difficult and complicated to control this class of systems due to the existence of unknown nonaffine functions and the couplings among the nested subsystems. This difficulty is overcome by introducing some special type Lyapunov functions and taking advantage of the mean-value theorem, the backstepping design method and the approximation property of the fuzzy systems. The proposed control approach can guarantee that all the signals in the closed-loop system are bounded. A simulation experiment is utilized to verify the feasibility of the proposed approach.     

Adaptive control of linear time-varying systems

Single-input single-output uncertain linear time-varying systems are considered, which are affected by unknown bounded additive disturbances; the uncertain time-varying parameters are required to be smooth and bounded but are neither required to be sufficiently slow nor to have known bounds. The output, which is the only measured variable, is required to track a given smooth bounded reference trajectory. The undisturbed system is assumed to be minimum-phase and to have known and constant relative degree, known sign of the ‘high frequency gain’, known upper bound on the system order. An adaptive output feedback control algorithm is designed which assures: (i) boundedness of all closed-loop signals; (ii) arbitrarily improved transient performance of the tracking error; (iii) asymptotically vanishing tracking error when parameter time derivatives are L₁ signals and disturbances are L₂ signals.     

Adaptive fuzzy dynamic surface control for uncertain nonlinear systems

In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.     

Adaptive control of PDEs

This paper presents several recently developed techniques for adaptive control of PDE systems. Three different design methods are employed—the Lyapunov design, the passivity-based design, and the swapping design. The basic ideas for each design are introduced through benchmark plants with constant unknown coefficients. It is then shown how to extend the designs to reaction-advection-diffusion PDEs in 2D. Finally, the PDEs with unknown spatially varying coefficients and with boundary sensing are considered, making the adaptive designs applicable to PDE systems with an infinite relative degree, infinitely many unknown parameters, and open loop unstable.     

Adaptive dynamic surface control for pure‐feedback systems

This paper proposes a novel dynamic surface control algorithm for a class of uncertain nonlinear systems in completely non‐affine pure‐feedback form. Instead of using the mean value theorem, we construct an affine variable at each design step, and then neural network is employed to deduce a virtual control signal or an actual control signal. As a result, the unknown control directions and singularity problem raised by the mean value theorem is circumvented. The proposed scheme is able to overcome the explosion of complexity inherent in backstepping control and guarantee the tracking performance by introducing an initialization technique based on a surface error modification. Simulation results are presented to demonstrate the efficiency of the proposed scheme. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive dynamic surface control for MIMO nonlinear time-varying systems with prescribed tracking performance

In this paper, an adaptive dynamic surface control scheme is proposed for a class of multi-input multi-output (MIMO) nonlinear time-varying systems. By fusing a bound estimation approach, a smooth function and a time-varying matrix factorisation, the obstacle caused by unknown time-varying parameters is circumvented. The proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step. Moreover, all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot. Such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

纯反馈非线性离散系统的自适应神经网络控制

针对一类未知的纯反馈非线性离散系统,提出了基于反步法设计的自适应神经网络控制方法.为避免反步法设计中可能出现的因果矛盾问题,首先将系统进行等价变换,然后利用隐函数定理证实了理想虚拟控制输入和实际控制输入的存在性.利用高阶神经网络估计这些控制量,并基于反步法设计自适应神经网络控制系统,证明了闭环系统半全局一致最终有界.仿真结果验证了所提出方法的有效性.     

Adaptive neural network dynamic surface control for perturbed nonlinear time-delay systems

This paper proposes an adaptive neural network control method for a class of perturbed strict-feedback nonlinear systems with unknown time delays. Radial basis function neural networks are used to approximate unknown intermediate control signals. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown time delay terms have been compensated. Dynamic surface control technique is used to overcome the problem of "explosion of complexity" in backstepping design procedure. In addition, the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is proved. A main advantage of the proposed controller is that both problems of "curse of dimensionality" and "explosion of complexity" are avoided simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the approach.     

基于矩阵分解的多变量鲁棒自适应反推控制

针对含有输入未建模动态的一类MIMO系统,在高频增益矩阵的顺序主子式的符号已知的前提下,给出了多变量自适应反推控制器的设计.严格地证明了对一类未建模动态,闭环适应系统的所有信号都是全局一致有界的,且输出渐近收敛于零.     

一类不确定非线性纯反馈系统的自适应鲁棒模糊控制

针对一类带有不确定性的非线性MIMO纯反馈系统,提出一种自适应鲁棒模糊控制方法,该方法放宽了已有文献对系统模型的限制条件,基于李雅普诺夫分析方法获得了控制输入和自适应律．在控制输入设计中,鲁棒控制项用于补偿逼近误差向量．通过选择适当的设计参数。提出的控制方法使得闭环系统的所有信号是一致有界的和跟踪误差向量的范数收敛到小的零邻域内．仿真结果表明了所提出方法的有效性．