A new periodic adaptive control approach for time-varying parameters with known periodicity

A new adaptive control approach is proposed to deal with nonlinear systems with a class of time-varying parametric uncertainties, which are in an unknown compact set, periodic, nonvanishing, rapid time-varying, and the only prior knowledge is the periodicity. Unlike most continuous time adaptation laws which are of differential types, in this work a periodic type adaptation law is introduced for continuous time systems. The new adaptive controller updates the parameters and the control signal periodically in a pointwise manner over one entire period, in the sequel achieves the asymptotic tracking convergence.     

周期时变时滞非线性参数化系统的自适应学习控制

针对一阶未知非线性参数化周期时变时滞系统, 设计了一种自适应学习控制方案. 假设未知时变参数, 时变时滞和参考信号的共同周期是已知的, 通过重构系统方程, 将包含时变时滞在内的所有未知时变项合并成为一个周期时变向量, 采用周期自适应律估计该向量. 通过构造一个Lyapunov-Krasovskii型复合能量函数证明了所有信号有界并且跟踪误差收敛. 结果被推广到一类含有混合参数的高阶非线性系统. 通过两个仿真例子说明本文所提出的控制算法的有效性.     

Partial-period adaptive repetitive control by symmetry

This paper presents a partial-period adaptive repetitive control method for a class of periodically time-varying nonlinear systems. To reduce the size of memory usage, the symmetric feature of periodic parameters is explored to form partial-period adaptation mechanisms. Both Half- and quarter-period adaptation strategies are proposed, and characterized analytically. The stability of the closed-loop system with each repetitive control is established, along with tracking error convergence to zero. In addition, the saturated-adaptation is suggested for providing bounded estimation.     

Adaptive learning tracking control of robotic manipulators with uncertainties

An adaptive learning tracking control scheme is developed for robotic manipulators by a synthesis of adaptive control and learning control approaches. The proposed controller possesses both adaptive and learning properties and thereby is able to handle robotic systems with both time-varying periodic uncertainties and time invariant parameters. Theoretical proofs are established to show that proposed controllers ensure asymptotical tracking performance. The effectiveness of the proposed approaches is validated through extensive numerical simulation results.     

周期时变系统的鲁棒自适应重复控制

针对周期时变系统,提出一种鲁棒自适应重复控制方法.该方法利用周期学习律估计周期时变参数,并结合鲁棒自适应方法处理非周期不确定性.与现有重复控制不同的是,在控制器设计中引入了新变量—周期数,利用周期系统的重复特性,使界的逼近误差随周期数的增加而逐渐减少,保证了系统的全局渐近稳定性.同时将该方法应用于一类非线性参数化系统,使系统在非参数化扰动的情形下,输出误差仍能收敛于0,倒立摆模型的仿真验证了此结果.该设计方法适用于消除神经网络逼近误差对重复控制系统的影响,理论证明了基于神经网络的鲁棒自适应重复控制系统中所有变量的有界性和输出误差的渐近收敛性,关于机械臂模型的仿真结果验证了受控系统具有良好的跟踪性能.     

Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays

The problem of robust tracking and model following is considered for a class of linear systems with multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In this note, it is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances, are unknown. An improved adaptation law with /spl sigma/-modification is proposed to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a class of continuous memoryless state feedback controllers is constructed for robust tracking of dynamical signals. The proposed adaptive robust tracking controller can guarantee that the tracking error decreases asymptotically to zero in the presence of multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In addition, it is also shown that this improved adaptation law with /spl sigma/-modification can be applied to the general adaptive control problems to obtain some more exact control results. Finally, a numerical example is given to demonstrate the validity of the results.     

基于联合滤波算法的复杂时变系统在线自适应逆控制

针对一类结构和参数均具备时变特性的复杂时变系统,提出一种新的基于联合滤波算法的在线自适应逆控制方法.该方法在处理参数时变问题的同时可兼顾系统的结构时变特性,实现复杂动态系统的在线跟踪控制.同时提出新的联合Volterra核函数滤波算法,该算法克服了原Volterra滤波器计算复杂运算速度慢的缺点,实现了动态非线性系统的在线跟踪控制.通过仿真分析可以得出,对于此类线性、非线性复杂时变系统,基于新的联合滤波器的自适应逆控制方法可以快速有效的实现动态对象在线建模与控制.     

输入饱和非线性系统的周期自适应补偿学习控制

针对一类输入饱和不确定Brunovsky标准型非线性时滞系统,提出一种周期自适应跟踪补偿学习算法. 利用信号置换思想重组系统,基于最小公倍周期函数变换,将时滞时变项和不确定项合并为辅助参数,进而设计周期自适应学习律估计该辅助量,并利用饱和补偿器逼近和补偿超出饱和限的部分,由此构成综合控制器,以保证系统状态对有界期望值的跟踪,解决了饱和输入周期系统的重复迭代学习控制问题. 最后通过构造Lyapunov-Krasovskii复合能量函数的差分,计算证明了系统跟踪误差的收敛性和闭环信号值的有界性. 常见耦合非线性机械臂系统的力矩控制仿真,进一步验证了该算法的有效性.     

一类高阶非线性参数化系统自适应重复学习控制

针对一类高阶非线性参数化系统,利用参数重组技巧,提出了一种自适应重复学习控制方法.该方法结合反馈线性化,可以处理参数在一个未知紧集内周期性、快时变的非线性系统.通过引进微分-差分参数自适应律,设计了一种自适应控制策略,使广义跟踪误差在误差平方范数意义下渐近收敛于零.通过构造Lyapunov泛函,给出了闭环系统收敛的一个充分条件.实例仿真结果说明了该方法的可行性和有效性.     

Robust adaptive state-feedback tracking for nonlinear systems

For a class of singie-input/single-output uncertain nonlinear systems, affected both by uncertain time-varying parameters (with known bounds) and unknown time-varying bounded disturbances, a new robust adaptive state-feedback control algorithm is presented. It guarantees: boundedness of all signals and arbitrary disturbance attenuation when both disturbances and time-varying parameters are present, and asymptotic tracking with arbitrary transient performance when no disturbance is acting on the system and parameters are constant. The adaptation may be switched off, still guaranteeing bounded signals and disturbance attenuation     

未知时变时滞非线性参数化系统自适应迭代学习控制

针对含有未知时变参数和时变时滞的非线性参数化系统,提出了一种新的自适应迭代学习控制方法.该方法将参数分离技术与信号置换思想相结合,可以处理含有时变参数和时滞相关不确定性的非线性系统.设计了一种自适应控制策略,使跟踪误差的平方在一个有限区间上的积分渐近收敛于零.通过构造Lyapunov-Krasovskii型复合能量函数,给出了闭环系统收敛的一个充分条件.给出两个仿真例子验证了控制方法的有效性.     

Discrete-time robust backstepping adaptive control for nonlineartime-varying systems

This paper studies the problem of adaptive control for a class of nonlinear time-varying discrete-time systems with nonparametric uncertainties. The plant parameters considered here are not necessarily slowly time-varying in a uniform way. They are allowed to have a finite number of big jumps. By using the backstepping procedures with parameter projection update laws, a robust adaptive controller can be designed to achieve adaptive tracking of a reference signal for this class of systems. It is shown that the proposed controller can guarantee the global boundedness of the states of the whole adaptive system in the presence of parametric and nonparametric uncertainties. It can also ensure that the tracking error falls within a compact set whose size is proportional to the size of the uncertainties and disturbances. In the ideal case when there is no nonparametric uncertainties and time-varying parameters, perfect tracking can be achieved     

Adaptive tracking of nonlinear systems with non-symmetric dead-zone input

Quite successfully adaptive control strategies have been applied to uncertain dynamical systems subject to dead-zone nonlinearities. However, adaptive tracking of systems with non-symmetric dead-zone characteristics has not been fully discussed with minimal knowledge of the dead-zone parameters. It is shown that the controlled system preceded by a non-symmetric dead-zone input can be represented as an uncertain nonlinear system subject to a linear input with time-varying input coefficient. To cope with this problem, a new adaptive compensation algorithm is employed without constructing the dead-zone inverse. The proposed adaptive scheme requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. The new control scheme ensures bounded-error trajectory tracking and assures the boundedness of all the signals in the adaptive closed loop. By appropriate selections of the controller parameters, we show that the smoothness of the controller does not affect the accuracy of trajectory tracking control. A numerical example is included to show the effectiveness of the theoretical results.     

Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delays

First of all, an adaptive iterative learning control strategy is developed for a class of nonlinearly parameterized systems with two unknown time-varying parameters and one unknown time-varying delay. The proposed control law includes a PID-type feedback term in time domain and an adaptive learning term used to estimate the unknown time-varying vector in iteration domain. By constructing a Lyapunov-Krasovskii-like composite energy function, we prove the stability of the closed-loop system and the convergence of the tracking error. Then, the design idea is further extended to a broader class of systems with mixed parameters in which the unknown time-invariant vector is estimated by a PI-type learning law in time domain. The simulation results, for a time-delay chaotic system, confirm the effectiveness of the proposed control scheme.     

Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization

We address the problem of output tracking for a class of nonlinearly parameterized systems with unstabilizable linearization. To achieve practical output tracking globally in the case when both the bound of reference signals and the bound of unknown time-varying parameters are not known a priori, we present a robust adaptive control method that is based on the idea of universal control combined with the new adaptive feedback design method developed recently for controlling uncertain systems with nonlinear parameterization. Continuous adaptive tracking controllers are explicitly constructed in this paper. The proposed adaptive tracking controllers use only the information of a prescribed reference signal but not its derivatives, nor its bound.     

环卫车辆轨迹跟踪系统的无模型自适应迭代学习控制

针对环卫车辆周期重复性工作特点,考虑模型时变以及未知扰动问题,提出一种基于无模型自适应迭代学习的环卫车辆轨迹跟踪控制方法.首先,针对环卫车辆建立了两轮移动机器人的运动学模型,然后,给出带时变参数和非线性不确定项的迭代域下全格式动态线性化数据模型,引入时间差分估计算法,设计基于最优性能指标的轨迹跟踪无模型自适应迭代学习控...     

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.     

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.     

一类非线性参数化系统自适应重复学习控制

针对一类高阶非线性参数化系统, 利用分段积分机制, 提出了一种新的自适应重复学习控制方法. 该方法结合反馈线性化, 可以处理参数在一个未知紧集内周期性快时变的非线性系统, 通过引进微分-差分混合型参数自适应律, 设计了一种自适应控制策略, 使广义跟踪误差在误差平方范数意义下渐近收敛于零, 通过构造Lyapunov泛函, 给出闭环系统收敛的一个充分条件. 实例仿真结果说明了该方法的可行性.     

Robust control of robot manipulators with fast load adaptation

Many adaptive robot controllers have been proposed in the literature to solve manipulator trajectory tracking problems for high-speed operations in the presence of parameter uncertainties. However, most of these controllers stem from the applications of the existing adaptive control theory, which is traditionally focused on tracking slowly time-varying parameters. In fact, manipulator dynamics have fast transient processes for high-speed operations and load changes are abrupt. These observations motivate the present research to incorporate change detection techniques into self-tuning schemes for tracking abrupt load variations and achieving fast load adaptation. To this end, a robustly global stabilizing controller for a robot model with parametric and non-parametric uncertainies is developed based on the Lyapunov second method, and it is then made adaptive via the self-tuning regulator concept. The two-model approach to online change detection in load is used and the estimation algorithm is reinitialized once load changes are detected. This allows a much faster adaptive identification of load parameters than the ordinary forgetting factor approach. Simulation results demonstrate that the proposed controller achieves better tracking accuracy than the existing adaptive and non-adaptive controllers.