Adaptive neural prescribed performance control for a class of strict-feedback stochastic nonlinear systems under arbitrary switchings

This paper presents an adaptive neural tracking control scheme for strict-feedback stochastic nonlinear systems with guaranteed transient and steady-state performance under arbitrary switchings. First, by utilising the prescribed performance control, the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, radial basis function neural networks approximation are used to handle unknown nonlinear functions and stochastic disturbances. At last, by using the common Lyapunov function method and the backstepping technique, a common adaptive neural controller is constructed. The designed controller overcomes the problem of the over-parameterisation, and further alleviates the computational burden. Under the proposed common adaptive controller, all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded, and the prescribed tracking control performance are guaranteed under arbitrary switchings. Three examples are presented to further illustrate the effectiveness of the proposed approach.     

Disturbance observer-based tracking control with prescribed performance specifications for a class of nonlinear systems subject to mismatched disturbances

This work investigates simultaneous prescribed performance tracking control and mismatched disturbance rejection problems for a class of strict-feedback nonlinear systems. A novel control scheme combining prescribed performance control, disturbance observer technique, and backstepping method is proposed. The disturbance estimations are introduced into the design of virtual control law design in each step to compensate the mismatched disturbances. To further improve the control performance, a prescribed performance function characterizing the error convergence rate, maximum overshoot, and steady-state error is used to construct the composite controller. The proposed controller guarantees transient and steady-state performance specifications of tracking error and provides much better disturbance attenuation ability simultaneously. Rigorous stability analysis for the closed-loop system is established by direct Lyapunov function method. It is shown that all the states in the resulting closed-loop system are stable, and the tracking error evolves within the prescribed performance boundaries and asymptotically converges to zero even in the presence of mismatched external disturbances. Finally, theoretical results are illustrated and demonstrated by two simulation examples.     

基于预设性能的非仿射非线性系统自适应有限时间控制

针对一类具有死区的非仿射非线性系统,将预设性能控制与有限时间控制相结合,提出一种具有预设性能的自适应有限时间跟踪控制方法.基于Backstepping技术、模糊逻辑系统及有限时间Lyapunov稳定理论,给出使系统半全局实际有限时间稳定(semi-globally practically finite-time stable,SGPFS)的充分条件和设计步骤.该控制策略不仅使系统的输出误差在有限时间内收敛到一个预先设定区域,同时保证其收敛速度、最大超调量和稳态误差均满足预先设定的性能要求.最后通过仿真示例验证了所提出设计方法的有效性.     

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.     

Distributed low-complexity output feedback tracking control for nonlinear multi-agent systems with unmodeled dynamics and prescribed performance

This paper investigates the prescribed performance distributed output consensus problem under directed graphs. With the utilisation of a filter, the original system of each follower can be converted into a strict-feedback system. Then, we design a prescribed performance output feedback distributed control protocol by applying the backstepping approach in the converted system. The proposed protocol can guarantee that the consensus tracking error of each agent evolves in predefined decaying bounds to achieve the prescribed performance, that is, the consensus tracking error of each agent converges to a predetermined residual set at a convergence rate no less than a prespecified value and exhibiting a maximum overshoot less than a preassigned constant. Moreover, during the process of consensus, all the signals in the closed-loop system are globally uniformly bounded. A simulation example is given to verify the effectiveness of the proposed control protocol.     

Robust approximation-free prescribed performance control for nonlinear systems and its application

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.     

Command filter-based finite-time adaptive tracking control for MIMO dynamic systems with external disturbances and prescribed performance constraints

This paper investigates command filter-based finite-time stability of multi-input multi-output (MIMO) dynamic systems with prescribed performance constraints and external disturbances. A novel finite-time differentiator is introduced into command filter-based control scheme, which improves transient performance of each subsystem. Meanwhile, disturbance observers are utilized to eliminate negative effects on control system caused by external disturbances. Furthermore, featured with a selected performance function, it can be guaranteed that tracking errors remain in prescribed performance region. Stability analysis of the proposed controller is presented by using a Lyapunov function including transformed filter errors, parameter errors of neural networks, and observed errors of lumped disturbances. Effectiveness of proposed control method is verified by a numerical example and a practical system of inverted pendulums, respectively.     

Integrated interceptor guidance and control with prescribed performance

Robustness and transient performance are the key performance indexes of the integrated interceptor guidance and control. However, these two performances have not yet been guaranteed comprehensively before. In this paper, a robust integrated interceptor guidance and autopilot controller is presented with prescribed steady state and transient performances of interception. On the basis of the dynamic surface control technique, the robustness of the proposed controller is improved by signal compensation. By utilizing the prescribed performance control theory, the transformed system of original integrated guidance and control model is stabilized to guarantee the prescribed performance of interception. It is proven that the stability of the transformed system is obtained by the loose selection of controller parameters, and therefore, the system robustness has been improved. Simulation results are included to verify the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Distributed prescribed performance control for consensus output tracking of nonlinear semi-strict feedback systems using finite-time disturbance observers

The distributed consensus output tracking problem is dealt with for a class of nonlinear semi-strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances and uncertain nonlinear virtual control coefficients of the subsystems. The systems are under a directed communication graph, where the leader node is the root. The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid direct differentiation. At each step of virtual controller design, a prescribed performance controller is constructed to achieve prescribed transient performance so that the system states remain in the feasible domain. Then each virtual controller is enhanced by a finite-time disturbance observer which estimates the disturbance term in a finite-time. The properties of the control system are analysed theoretically. It is clarified that the prescribed performance control technique ensures that the system signals stay in the feasible domain, whereas sufficiently small ultimate control errors can be achieved by the finite-time disturbance observers. Finally, the performance of the proposed methods is confirmed by numerical studies.     

Robust resilient control for parametric strict feedback systems with prescribed output and virtual tracking errors

This paper investigates the robust resilient control problem for a class of parametric strict feedback nonlinear systems with prescribed output and virtual tracking errors performance. The resilience is governed by a continuously nonlinear control gains function, which endows the virtual and actual controllers with self‐adjusting abilities with respect to transformed error surfaces. The proposed control scheme is adaptation, estimation, and approximation‐free in the presence of unknown parameters and nonlinearities, and only a number of control gains, which is equal to the relative degree of the considered plants, need to be selected in applications. It is proved by rigorous analysis that the output tracking errors are confined in predefined prescribed performance functions under some nonrestrictive initial conditions, and the bounds of states are obtained characterized as control gains and systemic function‐associated constants. Finally, comparative illustrative examples are given to demonstrate the effectiveness of the proposed control scheme.     

Robust estimation‐free decentralized prescribed performance control of nonaffine nonlinear large‐scale systems

In this paper, a low‐complexity robust estimation‐free decentralized prescribed performance control scheme is proposed and analyzed for nonaffine nonlinear large‐scale systems in the presence of unknown nonlinearity and external disturbance. To tackle the high‐order dynamics of each tracking error subsystem, a time‐varying stable manifold involving the output tracking error and its high‐order derivatives is constructed, which is strictly evolved within the envelope of user‐specialized prescribed performance. Sequentially, a robust decentralized controller is devised for each manifold, under which the output tracking error and its high‐order derivatives are proven to converge asymptotically to a small residual domain with prescribed fast convergence rate. Additionally, no specialized approximation technique, adaptive scheme, and disturbance observer are needed, which alleviates the complexity and difficulty of robust decentralized controller design dramatically. Finally, 3 groups of illustrative examples are used to validate the effectiveness of the proposed low‐complexity robust decentralized control scheme for uncertain nonaffine nonlinear large‐scale systems.     

基于修正闭环子空间辨识--分段线性结构的 环管式丙烯聚合反应过程非线性模型预测控

本文提出一种非奇异终端滑模funnel控制(NTSMFC)方法, 实现带有饱和输入电机伺服系统的指定性能跟踪控制. 根据中值定理, 非光滑饱和函数转化为放射形式, 并且应用一个简单的神经网络进行逼近和补偿. 为保证跟踪误差被限制在指定的界限内, 同时为避免构建复杂的barrier李雅普诺夫函数或逆函数, 本文采用一个新的限制变量. 然后, 构建非奇异终端滑模funnel控制器保证电机伺服系统的指定跟踪性能. 该方法无需事先已知输入饱和函数的界限等先验知识, 且基于李雅普诺夫函数设计可以保证位置跟踪误差的收敛性, 最后给出仿真对比实例证明了该方法的有效性.     

带有饱和的电机伺服系统非奇异终端滑模funnel控制

本文提出一种非奇异终端滑模funnel控制(NTSMFC)方法, 实现带有饱和输入电机伺服系统的指定性能跟踪控制. 根据中值定理, 非光滑饱和函数转化为放射形式, 并且应用一个简单的神经网络进行逼近和补偿. 为保证跟踪误差被限制在指定的界限内, 同时为避免构建复杂的barrier李雅普诺夫函数或逆函数, 本文采用一个新的限制变量. 然后, 构建非奇异终端滑模funnel控制器保证电机伺服系统的指定跟踪性能. 该方法无需事先已知输入饱和函数的界限等先验知识, 且基于李雅普诺夫函数设计可以保证位置跟踪误差的收敛性, 最后给出仿真对比实例证明了该方法的有效性.     

无人艇轨迹跟踪的预设性能抗扰控制研究

针对海洋环境干扰下的无人艇轨迹跟踪问题,提出一种预设性能轨迹跟踪抗扰控制方法。首先,该方法通过引入具有约束作用的性能函数设计预设性能反演控制器。同时采用干扰观测器精确补偿外界未知扰动,并引入带σ修正漏项自适应律对海洋环境干扰的界进行估计,实现了无人艇轨迹跟踪抗扰控制,且同时保证其暂态性能和稳态性能。然后根据李雅普诺夫稳...     

Adaptive fixed-time prescribed performance control of vehicular platoons with unknown dead-zone and actuator saturation

This article focuses on the problem of fixed-time prescribed performance platoon control for heterogeneous vehicles with unknown dead-zone and actuator saturation. First, an equivalent transformation is developed to approximate the actuator nonlinearity (i.e., dead-zone and saturation), which reduces the complexity of controller design. Then, to guarantee the tracking errors converge to the predetermined region in the given time, a modified prescribed performance function is presented. Based on this, a novel adaptive sliding mode control scheme is developed in the context of fixed-time theory, which is proved to be capable of ensuring individual vehicle stability and string stability in fixed time. In addition, under the proposed control scheme, the convergence time is independent of initial conditions of the system. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.     

分布式航天器编队约定时间姿轨耦合协同控制

针对具有参数不确定性、外部扰动和预设性能需求的航天器编队约定时间姿轨耦合控制问题, 本文基于预设性能控制方法提出了一种低复杂度的约定时间编队姿轨耦合协同控制器, 使得航天器在设定时间内形成编队, 且编队误差满足预设的各种性能指标. 首先, 通过结合有限时间稳定概念引入一种约定时间性能函数, 其系统稳定时间可以由使用者任意设定; 然后, 把约定时间性能函数与预设性能控制方法结合起来, 提出了不依赖航天器质量和转动惯量等信息的约定时间编队协同控制器, 保证了编队状态量的收敛性能和收敛时间, 并使用李雅普诺夫理论证明了其稳定性. 最后, 通过仿真验证了该控制方案的有效性     

具有输入输出约束的无人直升机预设性能安全跟踪控制

针对无人直升机姿态与高度系统存在未知外部干扰、输入饱和、姿态与高度约束等问题, 本文提出一种具 有输入输出约束的预设性能安全跟踪控制方法. 首先, 针对无人直升机的姿态与高度约束, 通过设计一类边界保护 算法, 构建了新的安全期望跟踪信号. 为了保证系统对于安全期望跟踪信号的跟踪性能, 将预设性能函数与边界保 护算法进行结合, 并对跟踪误差进行转换. 针对系统的输入饱和现象, 使用Sigmoid函数进行逼近; 同时, 针对饱和函 数的逼近误差与未知外部干扰构成的复合干扰, 采用参数自适应方法对其上界进行逼近. 然后, 结合反步控制方法 设计了安全跟踪控制器, 并通过Lyapunov稳定性理论证明了闭环系统所有信号的收敛性, 保证了无人直升机的安全 跟踪性能. 最终, 通过数值仿真验证了所提控制方法的有效性.     

飞翼飞行器的操纵面故障自适应补偿控制

本文针对具有操纵面卡死、失效故障以及执行器饱和的飞翼飞行器纵向运动,考虑系统的预定动态性能,提出了一种自适应反步补偿跟踪控制方案.设计预定动态性能(prescribed performance bound,PPB)边界以保证系统的跟踪误差,采用二阶指令滤波器限制执行器的饱和,通过控制分配避免执行器故障后对横侧向运动的影响.所设计的自适应反步补偿跟踪控制律能够保证系统对参考信号的渐近跟踪.仿真结果表明了本文方法的有效性.     

Adaptive prescribed performance tracking control for strict‐feedback nonlinear systems with zero dynamics

This paper focuses on the adaptive tracking control problem for strict‐feedback nonlinear systems with zero dynamics via prescribed performance. Based on polynomial fitting, an adjustable performance function is firstly proposed, whose parameters can be adjusted in real time according to the tracking error. Furthermore, an adaptive prescribed performance tracking controller is constructed via the backstepping method, which guarantees that all the states in the closed‐loop system are bounded. Meanwhile, the output tracking error falls within an adjustable performance boundary and asymptotically converges to zero. Simulation comparison demonstrates the advantages of the developed controller as follows: (1) the parameters of the adjustable performance function are adjusted online according to the tracking errors for a faster convergent performance boundary; (2) the steady‐state performance of the system is further optimized simultaneously.     

Robust adaptive trajectory tracking control of underactuated autonomous underwater vehicles with prescribed performance

In this paper, a novel robust adaptive trajectory tracking control scheme with prescribed performance is developed for underactuated autonomous underwater vehicles (AUVs) subject to unknown dynamic parameters and disturbances. A simple error mapping function is proposed in order to guarantee that the trajectory tracking error satisfies the prescribed performance. A novel additional control based on Nussbaum function is proposed to handle the underactuation of AUVs. The compounded uncertain item caused by the unknown dynamic parameters and disturbances is transformed into a linear parametric form with only single unknown parameter called virtual parameter. On the basis of the above, a novel robust adaptive trajectory tracking control law is developed using dynamic surface control technique, where the adaptive law online provides the estimation of the virtual parameter. Strict stability analysis indicates that the designed control law ensures uniform ultimate boundedness of the AUV trajectory tracking closed‐loop control system with prescribed tracking performance. Simulation results on an AUV in two different disturbance cases with dynamic parameter perturbation verify the effectiveness of our adaptive trajectory tracking control scheme.