一类非线性参数化系统的自适应鲁棒控制

针对一类含有非线性参数化不确定项的非线性系统,本文提出了一种基于浸入和不变流形的自适应鲁棒控制器.由于浸入和不变流形方法将调节函数引入到参数估计律的设计中,增加了控制器设计自由度,保证对系统中未知参数的渐近估计,使得设计出的自适应鲁棒控制器在克服非线性参数化不确定项和外界扰动影响的同时,保证了良好的动态和稳态性能.最后通过仿真实例验证了所提算法的有效性.     

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.     

基于参数估计误差的鲁棒自适应律设计及验证

针对传统自适应控制系统设计的自适应律参数收敛慢进而影响控制系统瞬态性能的问题,研究一类新的基于参数估计误差修正的鲁棒自适应律设计.首先引入滤波操作给出参数估计误差的提取方法,构建出含参数估计误差修正项的自适应律,进而将该自适应律用于控制器设计和分析中,可同时实现控制误差和参数估计误差指数收敛.对比分析了几类传统自适应律和所提出自适应律的收敛性和鲁棒性,并给出了保证参数收敛所需持续激励条件的一种直观、简便的在线判别方法.数值仿真及基于自制三自由度直升机系统俯仰轴实验结果表明,基于参数误差修正的自适应律及控制器可得到优于传统自适应方法的跟踪控制和参数估计性能.     

基于观测器的不确定非线性系统的自适应鲁棒模糊控制

针对单输入单输出不确定非线性系统提出了一种自适应鲁棒模糊控制算法.该算法通过设计观测器来估计系统的状态向量,因此不要求假设系统的状态向量是可测的.在这个算法中,主要的假设为最优逼近参数向量与标称参数向量之差的范数和逼近误差的界限是未知的.通过只对未知界限估计的调节,该算法减轻了在线计算量并且提高了系统的鲁棒性.所设计的自适应鲁棒模糊控制算法保证了闭环系统的所有信号是一致有界的并且跟踪误差估计收敛到一个小的零邻域内.仿真例子证实了所提方法的可行性.     

一类非线性系统鲁棒自适应控制器

反步设计法是针时不确定非线性系统的进行鲁棒自适应控制器设计的主要方法之一,它主要是靠递推来完成,方法简单,但存在过参数化问题.在反步设计法的基础上,通过引入调节函数,选取合适的虚拟控制律,设计一种鲁棒自适应控制器.然后,利用Lyapunov稳定性理论证明了该设计不仅能够克服过参数化的问题,而且能够保证所设计的系统具有鲁棒自适应稳定性.仿真实例证明了该方法的有效性.     

分布式多输入系统的自律鲁棒自适应分散控制

为了实现一类分布式多输入系统的分散鲁棒自适应控制, 基于状态扩张和反演干扰抑制控制, 提出一种自律鲁棒自适应分散控制的新方法. 结合直接反馈线性化和最优控制, 给出了自律最优鲁棒自适应分散控制的设计方法. 仿真结果表明, 所提出方法能够有效实现各子系统的自律鲁棒稳定、全系统整体鲁棒稳定和不确定参数自适应, 同时通过求解LMI, 具备了最优干扰抑制的功能.

     

基于Lagrangian支持向量机的机械手鲁棒自适应控制

提出了一种基于Lagrangian支持向量机的不确定机械手鲁棒自适应控制方法。Lagrangian支持向量机采用梯度投影法学习机械手系统的未知部分,来对机械手系统进行非线性补偿。根据Lyapunov稳定性理论设计自适应律进一步在线调整支持向量机的参数,并叠加一个滑模控制项,以保证控制系统的稳定性和鲁棒性。对两关节机械手的仿真结果证明了以上控制方法的有效性。     

不确定性系统的自适应鲁棒跟踪控制

针对存在未知干扰和未建模动态等不确定性的系统的自适应鲁棒跟踪控制问题进行了 探讨.首选将l1优化控制器的有限拍设计方法结合给出了最优鲁棒稳态跟踪控制器的设计方法． 然后利用集员辨识的思想,将名义模型的参数和未建模动态及干扰的大小作为未知参数,提出了 一种递推参数估计方法.最后将上述研究结果结合起来提出了一种自适应鲁棒跟踪控制策略,证 明了自适应算法的全局收敛性并给出了鲁棒跟踪性能指标的一下较紧的上界.与现有的结果相 比,本文提出的自适应控制具有非保守的鲁棒稳定性,具有渐近最优的鲁棒跟踪性能.     

不匹配不确定线性时滞系统的鲁棒自适应控制

对一类同时具有匹配不确定性及结构确定不匹配不确定性的不确定时滞系统进行鲁棒自适应控制。首先,采用李雅谱诺夫函数方法,结合基于线性矩阵不等式的鲁棒控制器设计方法和变结构控制方法,设计鲁棒控制器,保证闭环系统的二次渐近稳定。利用自适应参数估计方法,设计具有匹配不确定性范数界估计能力的鲁棒自适应控制器,保证闭环系统的一致终结有界。结合算例,进行控制器的设计和仿真研究,验证所提出的设计方法的有效性。     

具有状态参数约束的鲁棒自适应最优控制设计

在传统Backstepping 鲁棒自适应设计中, 虚拟控制函数的设计参数缺乏约束, 对此, 采用新的设计方法得到了新坐标系下的系统模型和参数替换律, 结合直接反馈线性化和最优控制策略, 最终给出了具有参数约束的非线性鲁棒自适应最优控制的设计方法. 以具体励磁系统参数为例进行仿真实验研究, 所得结果表明, 该鲁棒自适应控制方法可以实现状态参数的最优约束, 并能有效控制状态参数的收敛速度.     

基于系统浸入和流形不变自适应方法的静止无功补偿器非线性鲁棒自适应控制方法

本文提出一种将系统浸入和流形不变(I&I)自适应控制方法与L2-增益抑制鲁棒控制方法相结合的静止无功补偿器(SVC)的非线性鲁棒自适应控制方法.所提方法首先通过参数估计误差和鲁棒控制律的设计,使得所构造的表示参数估计误差函数的流形不变且吸引,从而使参数估计误差在这一流形上收敛于零.然后,通过所设计的可调参数对参数估计误差的收敛性能进行控制,以此来保证参数估计器对不确定参数的自适应估计能力.最后,采用自适应逆推算法推导鲁棒控制律,并通过使不确定外部扰动满足从输入到输出的耗散性来保证系统对不确定扰动的鲁棒性.仿真结果表明,利用所提方法设计的SVC控制器和参数替换律在参数估计、发电机功角动态响应方面优于传统自适应逆推算法,从而提高了输电系统的稳定水平.     

一类不确定非线性系统基于特征模型的复合自适应控制

针对一类不确定非线性系统的跟踪控制问题,提出一种基于特征模型的复合自适应控制方法.该方法的创新性在于基于系统的误差特征模型,构建一种综合跟踪控制误差和模型估计误差的特征参量复合自适应律,该自适应律用于控制器设计和分析,可同时实现跟踪控制误差和模型估计误差的收敛.此外,为便于特征参量自适应律的设计和分析,根据特征参量的慢时变特性,将其视为未知标称常数项和时变误差项之和,并且选用其中常数项的估计量作为自适应控制参数.进一步,为抑制特征参量中时变误差项对系统稳定性和模型估计误差收敛性的影响,在控制器及复合自适应律设计中引入带饱和函数的非线性环节.理论分析证明闭环控制系统稳定,且跟踪控制误差和模型估计误差收敛到原点的一个邻域内.仿真结果表明,与现有仅根据模型估计误差调节的基于特征模型的自适应控制方法相比,所提出的复合自适应控制方法具有更好的控制性能.     

A Combined Adaptive Law for Fuzzy Iterative Learning Control of Nonlinear Systems With Varying Control Tasks

To deal with the iterative control of uncertain nonlinear systems with varying control tasks, nonzero initial resetting state errors, and nonrepeatable mismatched input disturbance, a new adaptive fuzzy iterative learning controller is proposed in this paper. The main structure of this learning controller is constructed by a fuzzy learning component and a robust learning component. For the fuzzy learning component, a fuzzy system used as an approximator is designed to compensate for the plant nonlinearity. For the robust learning component, a sliding-mode-like strategy is applied to overcome the nonlinear input gain, input disturbance, and fuzzy approximation error. Both designs are based on a time-varying boundary layer which is introduced not only to solve the problem of initial state errors but also to eliminate the possible undesirable chattering behavior. A new adaptive law combining time- and iteration-domain adaptation is derived to search for suitable values of control parameters and then guarantee the closed-loop stability and error convergence. This adaptive algorithm is designed without using projection or deadzone mechanism. With a suitable choice of the weighting gain, the memory size for the storage of parameter profiles can be greatly reduced. It is shown that all the adjustable parameters as well as internal signals remain bounded for all iterations. Moreover, the norm of tracking state error vector will asymptotically converge to a tunable residual set even when the desired tracking trajectory is varying between successive iterations.     

含有参数化和非参数化不确定性系统重复学习控制

针对含有参数化和非参数化的高阶非线性系统,设计了一种重复学习控制方案.假设未知时变参数和参考信号的共同周期是已知的,通过参数重组技巧,将所有未知时变项合并为一个周期时变向量.将改进Backstepping方法与分段积分机制相结合,构造了微分-差分参数自适应律和重复学习控制律,使跟踪误差在误差平方范数意义下渐近收敛于零.利用Lyapunov泛函,给出了闭环系统收敛的充分条件.仿真结果验证了该方法的有效性.     

Precision Synchronization Motion Trajectory Tracking Control of Multiple Pneumatic Cylinders

This paper deals with the synchronized motion trajectory tracking control problem of multiple pneumatic cylinders. An adaptive robust synchronization controller is developed by incorporating the cross‐coupling technology into the integrated direct/indirect adaptive robust control (DIARC) architecture. The position synchronization error and the trajectory tracking error of each cylinder are combined to construct the so‐called coupled position error. The proposed adaptive robust synchronization controller is designed with the feedback of this coupled position error and is composed of two parts: an on‐line parameter estimation algorithm and a robust control law. The former is employed to obtain accurate estimates of model parameters for reducing the extent of parametric uncertainties, while the latter is utilized to attenuate the effects of parameter estimation errors, unmodelled dynamics, and external disturbances. Theoretically, both the position synchronization and trajectory tracking errors will achieve asymptotic convergence simultaneously. Moreover, the effectiveness of the proposed controller is verified by the extensive experimental results performed on a two‐cylinder pneumatic system.     

基于变中心互相关熵的比例自适应滤波算法研究

针对传统自适应滤波算法对于非零均值非高斯噪声干扰环境下稀疏系统参数估计存在稳态精度低的问题,以变中心互相关熵为代价函数,引入比例更新机制,应用随机梯度法设计一种新的稀疏自适应滤波算法。变中心互相关熵的中心可位于任何位置,其可很好地匹配非零均值的误差分布,而比例更新机制为每个权值参数赋予可变的步长参数,因此可增强算法的跟踪能力。进一步设计在线学习方法来估计核宽度和中心位置,以提高算法性能。另外根据能量守恒关系研究了算法的收敛性。仿真实验结果表明,该算法相对于传统自适应滤波算法对于非零均值非高斯噪声环境下的稀疏参数估计具有明显的优越性和鲁棒性。     

Composite Adaptive Control of Uncertain Euler‐Lagrange Systems with Parameter Convergence without PE Condition

This work proposes a novel composite adaptive controller for uncertain Euler‐Lagrange (EL) systems. The composite adaptive law is strategically designed to be proportional to the parameter estimation error in addition to the tracking error, leading to parameter convergence. Unlike conventional adaptive control laws which require the regressor function to be persistently exciting (PE) for parameter convergence, the proposed method guarantees parameter convergence from a milder initially exciting (IE) condition on the regressor. The IE condition is significantly less restrictive than PE, since it does not rely on the future values of the signal and that it can be verified online. The proposed adaptive controller ensures exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met. Simulation results corroborate the efficacy of the proposed technique and also establishes it's robustness property in the presence of unmodeled bounded disturbance.     

Adaptive robust control for four-motor driving servo system with uncertain nonlinearities

A novel adaptive robust control (ARC) is presented for the four-motor driving servo systems with the uncertain nonlinearities and actuation failures, such that the load tracking control is achieved with the proximate optimal-time. By applying the proposed scheme, several control objectives are achieved. First, the nonlinear synchronization algorithm is presented to maintain the velocity synchronization of each motor, which provides fast convergence without chatting. Moreover, the time-varying bias torque is applied to eliminate the effect of backlash and reduce the waste of energy. Then, the ARC is designed to achieve the proximate optimal-time output tracking with the transient performance in $L_2$ norm, where the friction and actuation failures are addressed by the adaptive scheme based on the norm estimation of unknown parameter vector. Finally, the extensive simulated and experimental results validate the effectiveness of the proposed method.     

Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.