Event-triggered adaptive backstepping tracking control for a class of nonlinear fractional order systems

This article investigates the problem of event-trigger based adaptive backstepping control for a class of nonlinear fractional order systems. By introducing an appropriate transformation of frequency distributed model, the fractional-order indirect Lyapunov method with is obtained. In addition, the event-triggered adaptive controller is developed by employing the event-triggered control approach. Meanwhile, by the proposed adaptive control scheme, all the closed-loop signals are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Finally, simulation results are provided to testify the availability of the presented controller.     

Adaptive prescribed performance tracking control for uncertain strict-feedback Multiple Inputs and Multiple Outputs nonlinear systems based on generalized fuzzy hyperbolic model

This article proposes an adaptive prescribed performance tracking control methodology for a class of strict-feedback Multiple Inputs and Multiple Outputs nonlinear systems. A combination of backstepping technique and the generalized fuzzy hyperbolic model was used in recursive design of adaptive controller. A novel performance constraint function guarantees the tracking control performance. Lyapunov stability analysis proves that the designed controller can ensure the predefined transient and all signals within the closed-loop systems are semiglobally uniformly ultimately bounded. In the end, simulation results illustrate the validity of the proposed approach.     

双轴励磁同步发电机非线性鲁棒自适应控制

利用Backstepping和扰动抑制方法设计了双轴励磁同步发电杌的自适应控制器。对于含有各种不确定参数和有界扰动的非线性双轴励磁同步杌模型，实现了对转子同步的鲁棒调节。文中的方法可用于其他不确定电力系统的控制设计。     

Indirect model reference adaptive control with dynamic adjustment of parameters

The paper discusses in detail a new method for indirect model reference adaptive control (MRAC) of linear time-invariant continuous-time plants with unknown parameters. The method involves not only dynamic adjustment of plant parameter estimates but also those of the controller parameters. Hence the overall system can be described by a set of non-linear differential equations as in the case of direct control. Many of the difficulties encountered in the conventional indirect approach, where an algebraic equation is solved to determine the control parameters, are consequently bypassed in this method. The proof of stability of the equilibrium state of the overall system is found to be different from that used in direct control. Using Lyapunov's theory, it is first shown that the parameter errors between the parameter estimates of the identifier and the true parameters of the plant, as well as those between the actual parameters of the controller and their desired values, are bounded. Following this, using growth rates of signals in the adaptive loop as well as order arguments, it is shown that the error equations are globally uniformly stable and that the tracking (control) error tends to zero asymptotically. This in turn establishes the fact that both direct and indirect model reference adaptive schemes require the same amount of prior information to achieve stable adaptive control.     

不确定性时滞关联大系统的分散变结构自适应控制

针对一类具有系统参数摄动、时滞关联和外界干扰的线性大系统,提出了一种基于Lyapunov稳定性理论的分散变结构自适应控制方案。通过引入积分滑模和能在线估计不确定性扰动与时滞关联的界的自适应算法,保证了闭环系统的渐近稳定性,实现了系统的鲁棒自适应控制。该方案具有较强的工程实用性,算例仿真的结果表明了该控制方案的可行性。     

Discrete-time combined model reference adaptive control

The discrete-time version of continuous-time combined model reference adaptive control (CMRAC) is presented in this paper. A global stability proof of the overall adaptive scheme is given using arguments similar to those used in discrete-time direct model reference adaptive control (DMRAC) but properly modified to account for the different structure of CMRAC with respect to DMRAC. © 1997 by John Wiley & Sons, Ltd.     

Reinforcing robustness of adaptive dynamic surface control

Adaptive dynamic surface control (ADSC) design was proposed as an alternative to adaptive backstepping, capable of curing the ‘explosion of complexity’ problem, caused by the repeated differentiations of the so called intermediate control signals. However, as it is clearly demonstrated in this work, ADSC schemes are sensitive to modeling uncertainties and/or additive external disturbances. In fact, it is shown that a uniformly bounded exogenous perturbation of unknown upper bound may easily destabilize the closed‐loop system. Subsequently, a constructive methodology based on the recently developed by the authors prescribed performance control technique, is proposed, which combined with an ADSC design, results in a modified scheme possessing significantly increased robustness properties. Simulation studies illustrate the approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed adaptive output consensus control of a class of uncertain nonlinear multiagents systems

This paper addresses the leader‐follower output consensus problem for a class of uncertain nonlinear multiagent systems in a directed communication topology. By employing the backstepping method, the dynamic surface control technique, neutral networks, and the graph theory, a distributed adaptive control scheme is developed recursively for each follower using its own and neighbors' information. The key features of this strategy are that it reduces the computational burden by introducing the dynamic surface control approach and there is no requirement for a priori knowledge about uncertain dynamics of the system. Moreover, in theory, it is proved that the designed control approach can steer the output signals of followers in a directed graph to track the desired trajectory of the leader and guarantee all signals in the closed‐loop system cooperatively semiglobally uniformly ultimately bounded. Furthermore, two examples are included, and the simulation results demonstrate the effectiveness of the proposed strategy.     

Composite learning adaptive backstepping control using neural networks with compact supports

The ability to learn is crucial for neural network (NN) control as it is able to enhance the overall stability and robustness of control systems. In this study, a composite learning control strategy is proposed for a class of strict‐feedback nonlinear systems with mismatched uncertainties, where raised‐cosine radial basis function NNs with compact supports are applied to approximate system uncertainties. Both online historical data and instantaneous data are utilized to update NN weights. Practical exponential stability of the closed‐loop system is established under a weak excitation condition termed interval excitation. The proposed approach ensures fast parameter convergence, implying an exact estimation of plant uncertainties, without the trajectory of NN inputs being recurrent and the time derivation of plant states. The raised‐cosine radial basis function NNs applied not only reduces computational cost but also facilitates the exact determination of a subregressor activated along any trajectory of NN inputs so that the interval excitation condition is verifiable. Numerical results have verified validity and superiority of the proposed approach.     

A new approach to model reference adaptive control

A new approach to model reference adaptive control, based on a combination of direct and indirect control methods, is introduced in this paper. The controller structure is identical to that used in the direct method, but the algorithm used to update the controller parameters depends both on the output error as in direct control and on the plant parameter estimates as in indirect control. The global stability of the overall system is assured by the existence of a Lyapunov function. In the ideal case discussed here, the combined approach results in improved transient response with smaller amplitude of the control input as compared to the constituent methods.     

Decentralized adaptive control for a class of large‐scale systems with multiple delays in the interconnections

In this paper, we consider the decentralized stabilization problem of a class of large‐scale systems subject to uncertain parameters and multiple time‐varying delays in the interconnections and non‐linear inputs. The interconnection matrices are subject to perturbations whose bounds are unknown. Decentralized memoryless adaptive controllers are synthesized within an LMI framework to guarantee that the state trajectories of the large‐scale system are uniformly exponentially convergent towards a ball with any prespecified exponential convergence rate. The problem is formulated as an optimization problem with LMI constraints. Finally, an example is included to illustrate the results developed in this paper. Copyright © 2004 John Wiley & Sons, Ltd.     

Robust adaptive output‐feedback control for a class of nonlinear systems with time‐varying actuator faults

A robust adaptive output‐feedback control scheme is proposed for a class of nonlinear systems with unknown time‐varying actuator faults. Additional unmodelled terms in the actuator fault model are considered. A new linearly parameterized model is proposed. The boundedness of all the closed‐loop signals is established. The desired control performance of the closed‐loop system is guaranteed by appropriately choosing the design parameters. The properties of the proposed control algorithm are demonstrated by two simulation examples. Copyright © 2010 John Wiley & Sons, Ltd.     

感应电机系统的非线性反推自适应控制

针对感应电机的动态特性,在电机参数未知的前提下,研究了磁链与转速的渐近跟踪特性和整个系统的全局稳定性问题.应用反推技术设计了自适应控制器,对所有参数进行估计,实现了电机对给定信号的输出跟踪控制,保证了整个系统的全局稳定性.系统的转子磁链与转速能渐近跟踪给定的参考信号,仿真结果验证了该控制策略的有效性.     

Transient performance improvement in indirect model reference adaptive control using perturbation‐based extremum seeking identifier

One of the main drawbacks of model reference adaptive control (MRAC) is the weakness of its transient performance. The key reason of this imperfection is parameter's estimation error convergence. For many cases in the closed‐loop control, the plant input signal cannot satisfy the persistence of excitation (PE) condition which yields poor parameters estimation error convergence. In this paper, we use a fast perturbation‐based extremum seeking (PES) scheme without steady‐state oscillation as the parameter identifier in indirect MRAC. The estimated parameters through the PES identifier contain the additive sinusoidal signals with distinct frequencies in the transient, which satisfy the PE condition of the plant input. Therefore, convergence of the parameters estimation error to zero will be guaranteed that results in improvement of transient performance for indirect MRAC. Also, the contrary effects on the steady‐state behaviour is eliminated since the sinusoidal excitation signals amplitude exponentially converge to zero and reinitiate with every change in the unknown parameters. Simulation results for a second order example have been presented to illustrate the effectiveness of the proposed scheme.     

基于复合自适应的Buck变换器预设性能控制

针对Buck型变换器在复杂环境下发生负载波动时输出电压受扰的问题,提出了一种复合自适应预设性能控制方案以提升其控制效果。首先,利用自适应律对模型中包含负载项的非线性函数进行预测估计,同时通过在自适应律更新过程中构建并行估计模型获取预测误差,并将预测误差和跟踪误差融合以设计自适应参数更新律。然后,采用广义比例积分观测器来对剩余不确定性和外部扰动进行估计,并在控制律中进行补偿。最后,结合指令滤波反步控制和指定时间预设性能控制技术,提出了Buck型变换器复合自适应预设性能控制方案。所提出的方案保证了对负载波动的高精度预测,避免了在突发情况下输出电压超出预设函数范围,此外还证明了闭环控制系统中的信号收敛性。实验结果表明,复合自适应预设性能控制在负载突然减小的情况下系统最大偏离电压为0.376 V,相比于传统自适应反步控制的1.773 V减少了78.7%,验证了所提方案的有效性以及优越性。     

Prescribed performance adaptive fuzzy control for nonstrict-feedback nonlinear systems with dead zone outputs

This paper presents an adaptive fuzzy control scheme for a class of nonstrict-feedback nonlinear systems with dead zone outputs and prescribed performance. By utilizing the monotonically increasing property of system bounding functions and the Nussbaum function, the design difficulties caused by the nonstrict-feedback structure and dead zone output are overcome. Combining backstepping technique with prescribed performance algorithm, a feasible adaptive fuzzy controller is designed to guarantee the boundedness of all signals of the closed-loop system and the prescribed tracking performance of the system. Finally, simulation results are depicted to illustrate the effectiveness of the proposed control approach.     

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.     

Finite-time adaptive control for nonlinear systems with uncertain parameters based on the command filters

The trajectory tracking control problem for a class of nonlinear systems with uncertain parameters is considered in this article. A new adaptive finite-time tracking control is designed based on the adaptive backstepping method via the command filters. The command filter mechanism can avoid the calculation of partial derivatives and solve the “explosion of complexity” in the backstepping design. The compensation signals are introduced to eliminate errors produced by the command filters. The proposed adaptive backstepping control can guarantee the tracking error remains in a small neighborhood of the origin in finite time, while the practical finite-time stability of the control systems with uncertain parameters is proven by the stability criterion. The effectiveness of the proposed scheme is verified by some simulation results.     

Unifying adaptive control with the nonlinear PI methodology: Designs for unknown strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities

In this paper, we extend the nonlinear PI control methodology within an adaptive control framework. An adaptive nonlinear PI controller is proposed for output tracking of strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities and unknown control directions. The current approach relaxes the standard assumption of known bounds for the associated system nonlinearities made in earlier nonlinear PI schemes. New theoretical boundedness results have been proved that enable the successful combination of backstepping and linear parametric approximators with the nonlinear PI approach and ensure semiglobal approximate tracking of the output to some reference trajectory. Following recent extensions of the nonlinear PI method to strict‐feedback systems, the intermediate virtual control laws are derived through suitable integral equations. Simulation results are also presented in this paper that verify our theoretical analysis.     

Direct adaptive neural tracking control for a class of stochastic pure‐feedback nonlinear systems with unknown dead‐zone

This paper considers the problem of adaptive neural tracking control for a class of nonlinear stochastic pure‐feedback systems with unknown dead zone. Based on the radial basis function neural networks' online approximation capability, a novel adaptive neural controller is presented via backstepping technique. It is shown that the proposed controller guarantees that all the signals of the closed‐loop system are semi‐globally, uniformly bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the suggested control scheme. Copyright © 2012 John Wiley & Sons, Ltd.