Output feedback tracking control for rigid body attitude via immersion and invariance angular velocity observers

A novel immersion and invariance (I&I) angular velocity observer is presented for the attitude tracking control of a rigid body with the lack of angular rate. Global exponential convergence of angular velocity estimate errors are guaranteed by an innovative filter design for the estimates' Euclidean norm. The proposed method requires fewer filter states compared with existing I&I angular velocity observer designs, which achieves a simpler closed-loop structure (dynamic reduction). The observer synthesis and convergence are independent of the control torque, which leads to much convenience in establishing “separation property” when combining a proportional-derivative attitude tracking controller driven by angular velocity estimates. A rigorous stability analysis is provided to ensure the (almost) global asymptotic convergence of the overall closed-loop tracking errors, and several numerical simulations are carried out to demonstrate the effectiveness of the combined implementation of proposed angular velocity observer and full-state feedback attitude tracking controller.     

A generalized global adaptive tracking control scheme for robot manipulators with bounded inputs

In this work, a generalized adaptive scheme for the global motion control of robot manipulators with constrained inputs is proposed. It gives rise to various families of bounded adaptive controllers defined through a general class of saturation functions. Compared with adaptive tracking control algorithms previously developed in a bounded input context, the proposed adaptive approach guarantees the motion control objective for any initial condition, avoiding discontinuities throughout the scheme, preventing the inputs to reach their natural saturation bounds, and permitting innovation on the saturating structure through its generalized form, giving a wide range of possibilities for performance improvement. Experimental results corroborate the efficiency of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

基于自适应模糊滑模控制的机器人轨迹跟踪算法

针对控制参数的不确定性以及存在未知外部扰动情况下移动机器人的轨迹跟踪问题,提出一种基于光滑非线性饱和函数的自适应模糊滑模轨迹跟踪控制算法。通过建立不确定非线性移动机器人运动控制模型,利用自适应模糊逻辑系统构建自适应模糊滑模控制器。为了增强轨迹跟踪控制算法对随机不确定外部扰动适应能力的同时削弱滑模控制算法中的输入抖振现象,利用有界输入有界输出(BIBO)稳定的方法,通过带有自适应调节算法的模糊系统对滑模控制律中非线性函数项进行自适应逼近,并设计了模糊系统中可调参数的自适应控制律,保证了控制系统的稳定与收敛。实验结果表明,所设计的控制器对系统参数不确定性和外界扰动均具有较强的轨迹跟踪性能和鲁棒性。与传统的滑模控制算法相比,该算法不仅能有效减小输入抖振而且轨迹跟踪控制精度提高了18.89%。     

扭矩输入有界的机器人模糊PD轨迹跟踪

针对轨迹跟踪控制中机器人关节驱动器输出扭矩受限的问题,提出一种基于模糊自适应PD的输入有界轨迹跟踪控制算法。不同于以往的控制策略,该算法在控制律中引入具有饱和特性的改进反正切函数,以确保扭矩控制输入的有界性,并结合模糊自适应原理实现PD增益的在线自整定,以改善系统的动态特性。通过对位置跟踪误差进行线性滤波得到速度跟踪误差替代信号,使得整个系统的闭环控制仅需位置输出反馈。利用奇异摄动理论对系统进行了稳定性分析,证明在一定约束下的PD增益自整定过程中,仍能保证系统稳定。仿真和比较结果表明,该算法能够在严格保证控制输入有界的前提下,减小超调量,缩短系统调整时间,具有更优的轨迹跟踪性能。     

Decentralized optimal tracking control for large-scale nonlinear systems with tracking error constraints

In this article, a decentralized optimal tracking control strategy is proposed for a class of nonlinear systems with tracking error constraints by utilizing adaptive dynamic programming (ADP). It should be noted that ADP technology cannot be directly used to solve decentralized optimal tracking problem of large-scale interconnected nonlinear system with nonzero equilibrium points, since that an infinite domain performance index function may result in an unsolvable solution. In addition, by introducing a smooth function, the constrained tracking error is transformed into an unconstrained one. Then, the error dynamics and a new infinite domain performance index function are designed, such that ADP technology can be used. Following the designed performance index function, the tracking error can be ensured within a small neighborhood of zero. Finally, the feasibility and the effectiveness of the proposed decentralized optimal control scheme are verified through two simulation examples.     

Online optimal and adaptive integral tracking control for varying discrete-time systems using reinforcement learning

Conventional closed-form solution to the optimal control problem using optimal control theory is only available under the assumption that there are known system dynamics/models described as differential equations. Without such models, reinforcement learning (RL) as a candidate technique has been successfully applied to iteratively solve the optimal control problem for unknown or varying systems. For the optimal tracking control problem, existing RL techniques in the literature assume either the use of a predetermined feedforward input for the tracking control, restrictive assumptions on the reference model dynamics, or discounted tracking costs. Furthermore, by using discounted tracking costs, zero steady-state error cannot be guaranteed by the existing RL methods. This article therefore presents an optimal online RL tracking control framework for discrete-time (DT) systems, which does not impose any restrictive assumptions of the existing methods and equally guarantees zero steady-state tracking error. This is achieved by augmenting the original system dynamics with the integral of the error between the reference inputs and the tracked outputs for use in the online RL framework. It is further shown that the resulting value function for the DT linear quadratic tracker using the augmented formulation with integral control is also quadratic. This enables the development of Bellman equations, which use only the system measurements to solve the corresponding DT algebraic Riccati equation and obtain the optimal tracking control inputs online. Two RL strategies are thereafter proposed based on both the value function approximation and the Q-learning along with bounds on excitation for the convergence of the parameter estimates. Simulation case studies show the effectiveness of the proposed approach.     

模型不确定的下肢康复机器人轨迹跟踪自适应控制

为了实现康复训练过程中高精度的轨迹跟踪控制,针对下肢康复机器人的模型参数和外界干扰等不确定性因素对其轨迹跟踪造成严重影响,提出一种模型不确定的下肢康复机器人轨迹跟踪自适应控制方法。根据所提方案,设计了相应的轨迹跟踪自适应控制器;并进行了轨迹跟踪控制仿真实验对比分析,结果表明,计算力矩控制方法在系统模型不确定时,膝关节的最大角度跟踪误差高达11.3°,髋关节最大稳态误差4.6°;而轨迹跟踪自适应控制方法在模型不确定的情况下,髋关节和膝关节的角度跟踪稳态误差均收敛于零;轨迹跟踪自适应控制方法可以显著提高下肢康复机器人轨迹跟踪的精度。     

Design of a power system stabilizer using decentralized adaptive model following tracking control approach

This paper presents the design of a power system stabilizer using decentralized adaptive model following tracking control (DAMFTC) approach to damp oscillations of generators in transient response subjected to uncertainties and generating fault actuators. The power system is represented as a collection of interconnected dynamical subsystems each described by a set of differential/algebraic equations using a clear representation of load voltage magnitude with matched and unmatched time‐varying uncertainties. All adaptive learning algorithms in this control system are derived in the sense of Lyapunov stability analysis subject to state errors due to uncertainties and fault section, so that stability and robustness of the closed‐loop system are ensured and asymptotic‐state tracking can be achieved. An adaptive bound estimation algorithm is investigated to relax the requirement for the bound of uncertainties. The effectiveness of the proposed approach is demonstrated by distributing a detailed simulation of the three‐machine nine‐bus system with nonlinear interactions, uncertainties, and fault actuators. The simulation includes the effects of network and stator transients. Copyright © 2009 John Wiley & Sons, Ltd.     

Anti-unwinding adaptive attitude tracking control for spacecraft with quantized torques

The adaptive attitude tracking control with limited communication to actuators is addressed in this paper. To avoid unwinding, a rotation matrix rather than a quaternion is used to describe the attitude, for which the stability is proved by Morse-Lyapunov function. To meet the need of restricted communication, two different quantizers, logarithmic quantizer and hysteres quantizer, are used to quantize the control torque signal. Two robust adaptive control techniques, indirect and direct, are proposed to deal with the impacts of quantization error and external disturbances. The proposed control schemes, in conjunction with quantizers, guarantee the global boundedness of all signals in the closed-loop system, allowing the attitude tracking error to converge toward an ultimately bounded region. Finally, numerical simulations are conducted to illustrate the performance of the proposed controllers.     

Robust adaptive tracking control for nontriangular time-delay nonlinear systems with input dead-zone and multiple uncertainties

This article studies the robust adaptive tracking control problem of nontriangular nonlinear systems that are affected by multiple state delays rather than the input-delay. Different from the related studies, the considered systems involve input dead-zone and various uncertainties arising in the control coefficients, structure parameters, time delays, and disturbances. A new adaptive control strategy is presented by introducing a dynamic-gain-based Lyapunov-Krasovskii functional and by generalizing the tuning function method in the framework of time-delay system theory. All the states of the closed-loop system are bounded and the tracking error can be adjusted sufficiently small. In the simulation, the delayed chemical system is studied to demonstrate the validity of the strategy.     

An adaptive design for quantized feedback control of uncertain switched linear systems

This paper addresses the problem of asymptotic tracking for switched linear systems with parametric uncertainties and dwell‐time switching, when input measurements are quantized due to the presence of a communication network closing the control loop. The problem is solved via a dynamic quantizer with dynamic offset that, embedded in a model reference adaptive control framework, allows the design of the adaptive adjustments for the control parameters and for the dynamic range and dynamic offset of the quantizer. The overall design is carried out via a Lyapunov‐based zooming procedure, whose main feature is overcoming the need for zooming out at every switching instant, in order to compensate for the possible increment of the Lyapunov function at the switching instants. It is proven analytically that the resulting adjustments guarantee asymptotic state tracking. The proposed quantized adaptive control is applied to the piecewise linear model of the NASA Generic Transport Model aircraft linearized at multiple operating points.     

Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

This work presents a new adaptive control algorithm for a class of discrete‐time systems in strict‐feedback form with input delay and disturbances. The immersion and invariance formulation is used to estimate the disturbances and to compensate the effect of the input delay, resulting in a recursive control law. The stability of the closed‐loop system is studied using Lyapunov functions, and guidelines for tuning the controller parameters are presented. An explicit expression of the control law in the case of multiple simultaneous disturbances is provided for the tracking problem of a pneumatic drive. The effectiveness of the control algorithm is demonstrated with numerical simulations considering disturbances and input‐delay representative of the application.     

Immersion and Invariance-based Non-linear Coordinated Control for Generator Excitation and Static Synchronous Compensator of Power Systems

In this article, a non-linear coordinated control of generator excitation and a static synchronous compensator is proposed to enhance the transient stability of an electrical power system. The coordinated controller proposed is designed via immersion and invariance methodology. In particular, a non-linear model of the power system and immersion and invariance design method are used to achieve not only power angle stability but also frequency and voltage regulations following a large disturbance (a symmetrical three-phase short-circuit fault) on one transmission line or a small perturbation to mechanical power input to synchronous generators in the system. The controller design is validated using a simulation study on a single-machine infinite bus. Simulation results show that the proposed controller can not only keep the system transiently stable but also simultaneously achieve power angle stability and frequency and voltage regulation.     

Adaptive fault‐tolerant attitude tracking control for spacecraft formation with unknown inertia

In this paper, an adaptive fault‐tolerant attitude coordinated tracking problem for spacecraft formation is investigated under a directed communication topology containing a spanning tree with the leader as the root, where inertia matrices and external disturbances are unknown time‐varying. With no prior knowledge of faults and inertia, an adaptive approach is proposed to reject the influence of disturbances and uncertainties. Meanwhile, combining with a consensus algorithm and graph theory, an adaptive fault‐tolerant attitude synchronization tracking control law is presented to regulate the attitude to a common time‐varying reference state. Aiming at optimizing the control law, a dynamic adjustment function is introduced to adjust the control gain according to the attitude tracking error. The effectiveness of the proposed control approach is demonstrated through simulation results.     

Command governor‐based adaptive control for dynamical systems with matched and unmatched uncertainties

In this paper, we propose a command governor‐based adaptive control architecture for stabilizing uncertain dynamical systems with not only matched but also unmatched uncertainties and achieving the desired command following performance of a user‐defined subset of the accessible states. In our proposed solution, online least‐squares solutions for the matched and unmatched parameters are obtained through integration method and they are employed in the adaptive control framework. Specifically, the matched uncertainty is identified and its effect upon the system behavior is entirely attenuated. Moreover, using the unmatched uncertainty approximation obtained through radial basis function neural networks, the command governor signal is designed to achieve the desired command following performance of the user‐defined subset of the accessible states. With this command governor‐based model reference adaptive control architecture, the tracking error of the selected states can be made arbitrarily small by judiciously tuning the design parameters. In addition to the analysis of the closed‐loop system stability using methods from the Lyapunov theory, our findings are also illustrated through numerical examples.     

红外图像目标瞄准点测量和基于自适应Kalman滤波的瞄准点跟踪

前视红外图像(FLIR)包含有关目标形状的丰富信息,可据以识别目标的背景干扰,从而增强抗干扰能力,且可根据目标要害部的亮度特点及预定范围,确定并进而跟踪瞄准点,本文提出目标瞄准点的序贯相关测量与Kalman滤波相结合的跟踪方法,在用110帧红外序列图像目标瞄准点跟踪仿真研究中,获得令人满意的结果,本文给出仿真误差方差、误差曲线和代表性的跟踪照片。     

A simplified adaptive tracking control for nonlinear pure-feedback systems with input delay and full-state constraints

This article investigated the adaptive backstepping tracking control for a class of pure-feedback systems with input delay and full-state constraints. With the help of mean value theorem, the system is transformed into strict-feedback one. By introducing the Pade approximation method, the effect of input delay was compensated. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. Furthermore, in order to reduce the computational burden by introducing backstepping design technique, dynamic surface control technique was employed. In addition, the number of the adaptive parameters that should be updated online was also reduced. By utilizing the barrier Lyapunov function, the closed-loop nonlinear system is guaranteed to be semi-globally ultimately uniformly bounded. Finally, a numerical simulation example is given to show the effectiveness of the proposed control strategy.     

Experimental implementation of a novel model-free adaptive fractional-order sliding mode controller for a flexible-link manipulator

This paper presents an experimental study of a robust control scheme for a single flexible-link manipulator. Regarding the nonlinear dynamics of flexible manipulators and vibration problems associated with these robots, this study aims to propose a novel fractional-order controller for efficient reference tracking, even in the presence of noise and total disturbances. In this regard, the control term is formulated by adopting the intelligent proportional–integral–derivative (PID) (iPID) technique and sliding mode control. As for estimating unknown states of the system, and ensuring that time-variable disturbances are well-handled and they do not excite vibrating modes, the generalized proportional integral (GPI) observer is utilized. Then, the adaptive reaching laws are derived along with the Lyapunov stability analysis, and finite-time convergence of the sliding surface is proven. Finally, well-trajectory tracking and robustness of the system are illustrated by the experimental results. The effectiveness of the fractional calculus in terms of accuracy, control effort, and vibration suppression is depicted as well.     

Passivity‐based control for stabilization,regulation and tracking purposes of a class of nonlinear systems

In this paper, a new passivity‐based control (PBC) scheme based on state feedback is proposed in order to solve tracking, regulation and stabilization problems for a class of multi‐input multi‐output (MIMO) nonlinear systems expressed in the normal form, with time‐invariant parameters and locally bounded reference weakly minimum phase. For the proposed control scheme two new different state feedbacks, one non‐adaptive for the case when the system parameters are assumed to be known and the other adaptive for the case of unknown parameters, are developed. For the adaptive case it is assumed that the unknown parameters appear linearly in the equations. Analysis of the transient behaviour of the proposed control schemes is presented through the simulation of two examples. Copyright © 2006 John Wiley & Sons, Ltd.     

发电机励磁与SVC的改进自适应反步无源协调控制

考虑了阻尼系数的不确定性,提出了一种改进自适应反步无源协调控制策略,设计了发电机励磁与静止无功补偿器(SVC)的非线性协调控制器。采用浸入与不变(I & I)自适应控制设计了阻尼系数的自适应估计律,提高了控制器的自适应能力。基于反步法逐步递推,设计了SVC的控制律,并结合无源性理论,得到了发电机励磁的控制律。在反步法设计过程中,为了减小“微分爆炸”,将虚拟控制量的导数看作不确定项,并引入非线性阻尼算法对其进行处理。仿真结果表明,所设计的协调控制器明显地改善了电力系统的稳定性,并且具备较强的自适应性和鲁棒性。