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.     

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.     

永磁同步电机有限时间预设性能控制

为实现扰动作用下对永磁同步电机角位置伺服系统的高瞬态和稳态跟踪性能控制,本文提出一种具有预设性能约束的有限时间控制方法.首先,设计扰动观测器实现对负载力矩扰动的估计与补偿.其次,引入有限时间预设性能函数以保证角跟踪误差的动态性能,并通过可逆变换将受不等式约束的角位置跟踪误差转换为等效的无约束误差形式.然后,将有限时间指...     

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.     

Distributed finite-time trajectory tracking control for multiple nonholonomic mobile robots with uncertainties and external disturbances

This paper investigates the distributed finite-time trajectory tracking control for a group of nonholonomic mobile robots with time-varying unknown parameters and external disturbances. At first, the tracking error system is derived for each mobile robot with the aid of a global invertible transformation, which consists of two subsystems, one is a first-order subsystem and another is a second-order subsystem. Then, the two subsystems are studied respectively, and finite-time disturbance observers are proposed for each robot to estimate the external disturbances. Meanwhile, distributed finite-time tracking controllers are developed for each mobile robot such that all states of each robot can reach the desired value in finite time, where the desired reference value is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers, and the followers are assumed to have only local interaction. The effectiveness of the theoretical results is finally illustrated by numerical simulations.     

Disturbance observer-based fixed-time prescribed performance tracking control for robotic manipulator

ABSTRACT

This paper investigates the fixed-time prescribed performance tracking control for the n-DOF uncertain manipulator. First, a novel Barrier Lyapunov Function (BLF) is proposed to guarantee the prescribed performance for the manipulator tracking error. Then, we introduce a disturbance observer to estimate the system uncertainty and disturbance accurately in a predefined time. Next, a composite controller based on the nonsingular fast integral terminal sliding mode is constructed. It is strictly proved that the closed-loop system is stable in fixed-time, which is independent of the initial conditions. Moreover, both transient and steady-state performances of the outputs can be preserved. Finally, numerical simulations and experimental studies are presented to demonstrate the effectiveness of the proposed methods.     

Leader-follower finite-time formation control of multiple quadrotors with prescribed performance

This paper investigates the leader-follower formation problem for a group of quadrotors. Finite-time control scheme and prescribed performance control method, which are regarded as two highlights, are introduced in this paper. First, a control scheme with prescribed performance is used to control the translational movements to ensure the quadrotors obtain a relative gentle transient process and an adjustable steady-state error bound. Then, the desired orientations for the rotation subsystem provided by translational movements part are stabilised by a fixed-time control law. Finally, by designing a finite-time formation controller, followers can track the desired position and heading angle in finite time, which is important for the practical application. Several simulation results are given to show the effectiveness of the designed control strategy.     

Disturbance-observer-based adaptive finite-time dynamic surface control for PMSM with time-varying asymmetric output constraint

This article presents a disturbance-observer-based adaptive finite-time dynamic surface control scheme, capable of guaranteeing transient behavior for the PMSM with arbitrary asymmetric time-varying output constraint and unmatched external disturbance. The major challenge of this paper is devising efficient strategies to tackle the nonsymmetric output restraints with arbitrary characteristics and unmatched external perturbation for the system under the finite-time backstepping framework. Given this, a nonlinear transformation function is adopted to coordinate from the output-constrained dynamic model to an uncontained one, and a finite-time disturbance observer is introduced to evaluate the unmatched external perturbation. Then, a dynamic surface control approach having adaptive properties for PMSM is conceived by combing a neural network to evaluate the nonlinear functions and a first-order filter to handle the “explosion of complexity.” Additionally, it is proved that the signals in the closed-loop system can narrow down to a bounded region and the tracking error can merge in a limited time to tiny vicinity of zero by employing a fast finite-time stability principle. Eventually, simulation cases and contrast results reveal the tracking performance and immunity to the disturbance of the devised controller.     

一类输出受限非线性系统的降维非递归预设性能控制策略

针对一类非匹配受扰非线性系统在输出受限条件下的跟踪控制问题, 本文在预设性能控制过程中引入非递归设计框架, 提出了一种降维非递归预设性能控制方案, 以缓解常用的递归预设性能控制过程中出现的复杂性爆炸问题, 大幅简化了系统的控制器设计过程, 便于实际工程应用. 本文设计的降维非递归控制策略能够实现控制器设计过程与稳定性分析的分离, 并且具有控制器形式简洁、控制参数选取机制简单的优点. 最后, 选取具有代表性的数值仿真和永磁同步电机位置跟踪控制实验阐释了所提出的控制策略的有效性及简洁性.     

随机激励下板球系统建模与有限时间全状态预设性能跟踪控制

研究板球系统受到随机激励时的数学建模与轨迹跟踪控制问题.首次建立了板球系统的随机数学模型,并结合backstepping方法、有限时间预设性能函数、全状态约束及新的预设性能推导方法设计了具有未知输入饱和的随机板球系统实际有限时间全状态预设性能跟踪控制器,实现了随机激励下板球系统的有限时间预设性能轨迹跟踪控制.所设计的控制器保证了系统跟踪误差能够被预先给定的有限时间性能函数约束,并且能在任意给定的停息时间内收敛到预先给定的邻域内.最后通过仿真实验验证了所设计控制器具有更好的控制效果.     

Optimal prescribed performance tracking control of nonlinear motor driven systems via adaptive dynamic programming

Although optimal regulation problem has been well studied, resolving optimal tracking control via adaptive dynamic programming (ADP) has not been completely resolved, particularly for nonlinear uncertain systems. In this paper, an online adaptive learning method is developed to realize the optimal tracking control design for nonlinear motor driven systems (NMDSs), which adopts the concept of ADP, unknown system dynamic estimator (USDE), and prescribed performance function (PPF). To this end, the USDE in a simple form is first proposed to address the NMDSs with bounded disturbances. Then, based on the estimated unknown dynamics, we define an optimal cost function and derive the optimal tracking control. The derived optimal tracking control is divided into two parts, that is, steady-state control and optimal feedback control. The steady-state control can be obtained with the tracking commands directly. The optimal feedback control can be obtained via the concept of ADP based on the PPF; this contributes to improving the convergence of critic neural network (CNN) weights and tracking accuracy of NMDSs. Simulations are provided to display the feasibility of the designed control method.     

Reduced-order observer-based output feedback control of nonlinear time-delay systems with prescribed performance

This paper studies the problem of output feedback control for a class of nonlinear time-delay systems with prescribed performance. The system is in the form of triangular structure with unmodelled dynamics. First, we introduce a reduced-order observer to provide the estimate of the unmeasured states. Then, by setting a new condition with the performance function, we design the state transformation with prescribed performance control. By employing backstepping method, we construct the output feedback controller. It is proved that the resulting closed-loop system is asymptotically stable and both transient and steady-state performance of the output are preserved with the changing supply function idea. Finally, a simulation example is conducted to show the effectiveness of the main results.     

Full-state prescribed performance pose tracking of space proximity operations with input saturation

This paper investigates the relative position tracking and attitude synchronization control for spacecraft close-range proximity missions with input saturation and model uncertainties. A robust saturated relative motion controller is proposed for this purpose. Prescribed performance functions are designed to guarantee the transient and steady-state response of the system and the full-state constraints. Then, a nonlinear disturbance observer is developed to estimate the lumped disturbance that comprises the effects of parametric uncertainties and kinematic couplings. At the same time, a linear compensator system is incorporated into the controller design to deal with the control input saturation. Finally, it can be proved via the Lyapunov theory that the closed-loop system is uniformly ultimately bounded stable. Simulation results on the spacecraft close-range rendezvous and docking mission validate the effectiveness of the proposed control approach.     

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.     

Finite-time command filter-based adaptive tracking control for nonstrict feedback nonlinear systems with full-state restrictions and unmodeled dynamics

The finite-time command filter tracking control for a class of nonstrictly feedback nonlinear systems with unmodeled dynamics and full-state constraints is investigated in this paper. The hyperbolic tangent function is used as a nonlinear mapping technique to solve the obstacle of the full-state constraints. A new adaptive finite time control method is proposed through command filtering reverse engineering, and the shortcomings of the dynamic surface control (DSC) method are overcome by the error compensation mechanism. Dynamic signal is designed to handle dynamical uncertain terms. Normalization signal is designed to handle input unmodeled dynamics. Unknown nonlinear functions are approximated by radial basis function neural networks. Based on the Lyapunov stability theory, it is proved that all signals in the closed-loop system are semi-globally consistent and finally bounded and the output tracking error converges in finite time. Two numerical examples are utilized to verify the effectiveness of the proposed control approach.     

Improved prescribed performance control for nonlinear systems with unknown control direction and input dead-zone

In view of the input dead-zone, unknown control direction and difficulty in satisfying the prescribed performance that suffered in practical systems, an improved prescribed performance-based adaptive control scheme is stressed for uncertain nonlinear systems in this paper. Firstly, by adopting a characteristic function, the input dead-zone is linearized to a model with bounded perturbation. To settle the “computation complexity” issue, an adaptive controller is built via command filter design method, where the fuzzy logic systems are introduced to approximate the unknown nonlinearities. Meanwhile, the Nussbaum function is brought in controller design to counter the hardship of unknown control direction. Besides, the tracking error can be restricted in the prescribed boundary in finite time with the improved performance function. The presented control approach can not only ensure the finite-time convergence property of tracking error and the boundedness of all signals in the closed-loop system, but also easily implement in engineering. Finally, the simulation examples confirm the validity of the designed control scheme.     

Command filter-based adaptive control of flexible-joint manipulator with input saturation and output constraints

This paper focuses on the topic of adaptive neural tracking control for flexible-joint manipulator systems with output restrictions and input saturation. With the aid of the error compensation mechanism, command filter-based adaptive neural control is proposed for robotic systems driven by permanent magnet synchronous machine (PMSM). An auxiliary signal produced by the first-order linear system designed by the property of unmodeled dynamics is used to erase the dynamical uncertainties. The input saturation of system is estimated by $$-function with mathematical transformation. Using barrier Lyapunov function (BLF), each component constraint of output is tackled. During the virtual control design phase, radial basis function neural networks (RBFNNs) may reliably assess the unknown nonlinear continuous function. All the variables in the closed-loop system are proved to be semiglobally uniform ultimate bounded (SGUUB) by integrating all compensation signals into the overall Lyapunov function and using the defined compact set in the stability analysis of dynamic surface control (DSC). An applied example on robotic system is used to verify the effectiveness of the constructed design idea.     

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.     

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.     

Finite-time optimal tracking control for a class of nonlinear systems with prescribed performance

In this paper, a finite-time optimal tracking control scheme based on integral reinforcement learning is developed for partially unknown nonlinear systems. In order to realize the prescribed performance, the original system is transformed into an equivalent unconstrained system so as to a composite system is constructed. Subsequently, a modified nonlinear quadratic performance function containing the auxiliary tracking error is designed. Furthermore, the technique of experience replay is used to update the critic neural network, which eliminates the persistent of excitation condition in traditional optimal methods. By combining the prescribed performance control with the finite-time optimization control technique, the tracking error is driven to a desired performance in finite time. Consequently, it has been shown that all signals in the partially unknown nonlinear system are semiglobally practical finite-time stable by stability analysis. Finally, the provided comparative simulation results verify the effectiveness of the developed control scheme.