Active disturbance rejection control for nonlinear fractional‐order systems

This paper investigates active disturbance rejection control involving the fractional‐order tracking differentiator, the fractional‐order PID controller with compensation and the fractional‐order extended state observer for nonlinear fractional‐order systems. Firstly, the fractional‐order optimal‐time control scheme is studied to propose the fractional‐order tracking differentiator by the Hamilton function and fractional‐order optimal conditions. Secondly, the linear fractional‐order extend state observer is offered to acquire the estimated value of the sum of nonlinear functions and disturbances existing in the investigated nonlinear fractional‐order plant. For the disturbance existing in the feedback output, the effect of the disturbance is discussed to choose a reasonable parameter in fractional‐order extended state observer. Thirdly, by this observed value, the nonlinear fractional‐order plant is converted into a linear fractional‐order plant by adding the compensation in the controller. With the aid of real root boundary, complex root boundary, and imaginary boot boundary, the approximate stabilizing boundary with respect to the integral and differential coefficients is determined for the given proportional coefficient, integral order and differential order. By choosing the suitable parameters, the fractional‐order active disturbance rejection control scheme can deal with the unknown nonlinear functions and disturbances. Finally, the illustrative examples are given to verify the effectiveness of fractional‐order active disturbance rejection control scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

控制方向未知的全状态约束非线性系统的鲁棒自适应跟踪控制

针对一类控制方向未知的含有时变不确定参数和未知时变有界扰动的全状态约束非线性系统,本文提出了一种基于障碍Lyapunov函数的反步自适应控制方法.障碍Lyapunov函数保证了系统状态在运行过程中始终保持在约束区间内;Nussbaum型函数的引入解决了系统控制方向未知的问题;光滑投影算法确保了不确定时变参数的有界性.障碍Lyapunov函数、Nussbaum型函数及光滑投影算法与反步自适应方法的有效结合首次解决了控制方向未知的全状态约束非线性系统的跟踪控制问题.所设计的自适应鲁棒控制器能在满足状态约束的前提下确保闭环系统的所有信号有界.通过恰当地选取设计参数,系统的跟踪误差将收敛于0的任意小的邻域内.仿真结果表明了控制方案的可行性.     

A new event‐driven output‐based discrete‐time control for the sporadic MIMO tracking problem

This paper presents a new sporadic control approach to the tracking problem for MIMO closed‐loop systems. An LTI sampled data plant with unmeasurable state affected by external unknown disturbances is considered. The plant is interconnected to an event‐based digital dynamic output‐feedback controller via a network. Both the external reference and the unknown disturbance are assumed to be generated as the free output response of unstable LTI systems. The main feature of the new event‐driven communication logic (CL) is that it works without the strict requirement of a state vector available for measurement. The purpose of the CL is to reduce as much as possible the number of triggered messages along the feedback and feedforward paths with respect to periodic sampling, still preserving internal stability and without appreciably degrading the control system tracking capability. The proposed event‐driven CL is composed of a sensor CL (SCL) and of a controller CL (CCL). The SCL is based on the computation of a quadratic functional of the tracking error and of a corresponding suitably computed time‐varying threshold: a network message from the sensor to the controller is triggered only if the functional equals or exceeds the current value of the threshold. The CCL is directly driven by the SCL: the dynamic output controller sends a feedforward message to the plant only if it has received a message from the sensor at the previous sampled instant. Formulation of the controller in discrete‐time form facilitates its implementation and provides a minimum inter‐event time given by the sampling period. An example taken from the related literature shows the effectiveness of the new approach. The focus of this paper is on the stability and performance loss problems relative to the sporadic nature of the control law. Other topics such as network delay or packets dropout are not considered. Copyright © 2012 John Wiley & Sons, Ltd.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Global Practical Tracking for Nonlinear Systems With More Unknowns via Adaptive Output‐Feedback

This paper investigates the global practical tracking via adaptive output‐feedback for a class of uncertain nonlinear systems. Essentially different from the closely related literature, the system under investigation possesses unknown time‐varying control coefficients and a polynomial‐of‐output growth rate, and meanwhile, the system nonlinearities and the reference signal allow serious unknowns. For this, an adaptive observer is designed to reconstruct the system unmeasured states, where a new dynamic gain is introduced to compensate the serious unknowns in the system nonlinearities and the reference signal. Based on this and by backstepping technique, an adaptive output‐feedback controller is successfully designed, such that all the states of the closed‐loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical simulation is provided to demonstrate the effectiveness of the proposed method.     

Adaptive Fault‐Tolerant Control of Uncertain MIMO Systems with Reduced Requirement on Desired Trajectory Under Unknown Control Direction

This paper aims at investigating the tracking control problem for a class of multi‐input multi‐output (MIMO) nonlinear systems with non‐square control gain matrix subject to unknown control direction and uncertain desired trajectory. By using the artificial neural network (NN) reconstructs the target trajectory with actual disguised trajectory, we are able to design a practical and stable tracking control scheme without the need for the unavailable desired trajectory. Nussbaum‐type function is incorporated in the control law to handle the unknown control direction. The remarkable feature of the proposed scheme is that it is robust against modeling uncertainties and tolerant to actuation faults, yet guarantees that the closed‐loop system is stable in the sense of ultimately uniformly bounded (UUB). The effectiveness of the proposed control schemes are illustrated through simulation results.     

Data‐driven robust backstepping control of unmanned surface vehicles

In this article, a novel data‐driven robust backstepping control (DRBC) approach for tracking of unmanned surface vehicles (USVs) with uncertainties and unknown parametric dynamics has been developed. Main contributions are fourfold: (a) Unlike previous approaches, within the DRBC scheme, backstepping decoupled technique and data‐driven sliding‐mode control (DSMC) can be effectively cohered. (b) Using backstepping philosophy, a new data‐driven PI‐type sliding‐mode surface is devised, such that strong robustness with simple structure can be ensured. (c) Complex unknowns including couplings, uncertainties and parametric dynamics are sufficiently lumped, and are totally compensated by the extended state observer. (d) The entire DRBC scheme eventually achieves accurate tracking of USVs with strong couplings, uncertainties and unknown parametric dynamics. The efficacy and superiority of the proposed DRBC approach is validated on a prototype USV.     

Transverse function control with prescribed performance guarantees for underactuated marine surface vehicles

This paper studies the problem of stabilizing reference trajectories (also called as the trajectory tracking problem) for underactuated marine vehicles under predefined tracking error constraints. The boundary functions of the predefined constraints are asymmetric and time‐varying. The time‐varying boundary functions allow us to quantify prescribed performance of tracking errors on both transient and steady‐state stages. To overcome difficulties raised by underactuation and nonzero off‐diagonal terms in the system matrices, we develop a novel transverse function control approach to introduce an additional control input in backstepping procedure. This approach provides practical stabilization of any smooth reference trajectory, whether this trajectory is feasible or not. By practical stabilization, we mean that the tracking errors of vehicle position and orientation converge to a small neighborhood of zero. With the introduction of an error transformation function, we construct an inverse‐hyperbolic‐tangent‐like barrier Lyapunov function to show practical stability of the closed‐loop systems with prescribed transient and steady‐state performances. To deal with unmodeled dynamic uncertainties and external disturbances, we employ neural network (NN) approximators to estimate uncertain dynamics and present disturbance observers to estimate unknown disturbances. Subsequently, we develop adaptive control, based on NN approximators and disturbance estimates, that guarantees the prescribed performance of tracking errors during the transient stage of on‐line NN weight adaptations and disturbance estimates. Simulation results show the performance of the proposed tracking control.     

Asymptotic tracking control for constrained nonstrict‐feedback MIMO nonlinear systems via parameter compensations

This paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme.