Adaptive feedback linearizing control of nonholonomic wheeled mobile robots in presence of parametric and nonparametric uncertainties

In this paper, the integrated kinematic and dynamic trajectory tracking control problem of wheeled mobile robots (WMRs) is addressed. An adaptive robust tracking controller for WMRs is proposed to cope with both parametric and nonparametric uncertainties in the robot model. At first, an adaptive nonlinear control law is designed based on input–output feedback linearization technique to get asymptotically exact cancellation of the parametric uncertainty in the WMR parameters. The designed adaptive feedback linearizing controller is modified by two methods to increase the robustness of the controller: (1) a leakage modification is applied to modify the integral action of the adaptation law and (2) the second modification is an adaptive robust controller, which is included to the linear control law in the outer loop of the adaptive feedback linearizing controller. The adaptive robust controller is designed such that it estimates the unknown constants of an upper bounding function of the uncertainty due to friction, disturbances and unmodeled dynamics. Finally, the proposed controller is developed for a type (2, 0) WMR and simulations are carried out to illustrate the robustness and tracking performance of the controller.     

基于神经网络的无人机姿态自适应控制仿真

针对四旋翼无人机姿态控制中模型不完整、部分参数和扰动不确定的问题,提出了一种基于神经网络的自适应控制方法,采用RBF神经网络对无人机姿态动力学模型中不确定和扰动部分进行学习,设计了以类反步法为基础,包含反馈控制和神经网络控制的自适应控制器,实现了对未知动态的准确逼近,解决了传统控制方法中过于依赖精确模型的问题。同时设计了神经网络的权值自适应律,实现了控制过程中的在线学习和调整,并且通过李雅普诺夫方法证明了闭环系统的稳定性。仿真结果表明,在存在较大扰动的情况下,上述控制器可得到很好的控制效果,可以实现误差的快速收敛,具有较好的鲁棒性和自适应性。     

Robust continuous-time adaptive control by parameter projection

The problem of adaptive control of a continuous-time plant of arbitrary relative degree, in the presence of bounded disturbances as well as unmodeled dynamics, is addressed. The adaptation considered is the usual gradient update law with parameter projection, the latter being the only robustness enhancement modification employed. It is shown that if the unmodeled dynamics, which consists of multiplicative as well as additive system uncertainty, is small enough, then all the signals in the closed-loop system are bounded. This shows that extra modifications are not necessary for robustness with respect to bounded disturbances and small unmodeled dynamics. In the nominal case, where unmodeled dynamics and disturbances are absent, the asymptotic error in tracking a given reference signal is zero. Moreover, the performance of the adaptive controller is also robust     

基于矩阵分解的多变量鲁棒自适应反推控制

针对含有输入未建模动态的一类MIMO系统,在高频增益矩阵的顺序主子式的符号已知的前提下,给出了多变量自适应反推控制器的设计.严格地证明了对一类未建模动态,闭环适应系统的所有信号都是全局一致有界的,且输出渐近收敛于零.     

Robust adaptive control of proper systems

To date, all the adaptive control algorithms have been proposed only for strictly proper systems. In this paper, a scheme is proposed to design an adaptive controller for proper systems. To study the robustness of the adaptive controller, both additive and multiplicative types of unmodeled dynamics are considered and can also be allowed to be proper, or even improper. Global bounded input bounded output stability is established. The achievement of a small in the mean tracking error and perfect tracking/rejection of deterministic trajectories/disturbances in the absence of system unmodeled dynamics are discussed. The results are also verified by simulation studies     

大纯滞后系统的自适应补偿控制

针对工业过程中普遍存在的纯滞后对象的控制问题,提出了一种带误差补偿环节的模型参考自适应控制方法。仿真结果表明,这种自适应控制器对于一类大纯滞后系统的控制具有比较好的控制效果,且结构简单,有一定的鲁棒性。     

Robust adaptive output stabilization using dynamic normalizing signal

For a class of nonlinear systems with dynamic uncertainties, robust adaptive stabilization problem is considered in this paper. Firstly, by introducing an observer, an augmented system is obtained. Based on the system, we construct an exp-ISpS Lyapunov function for the unmodeled dynamics, prove that the unmodeled dynamics is exp-ISpS, and then obtain a dynamic normalizing signal to counteract the dynamic disturbances. By the backstepping technique, an adaptive controller is given, it is proved that all the signals in the adaptive control system are globally uniformly ultimately bounded, and the output can be regulated to the origin with any prescribed accuracy. A simulation example further demonstrates the efficiency of the control scheme.     

Robust adaptive output stabilization using dynamic normalizing signal

For a class of nonlinear systems with dynamic uncertainties, robust adaptive stabilization problem is considered in this paper. Firstly, by introducing an observer, an augmented system is obtained. Based on the system, we construct an exp-ISpS Lyapunov function for the unmodeled dynamics, prove that the unmodeled dynamics is exp-ISpS, and then obtain a dynamic normalizing signal to counteract the dynamic disturbances. By the backstepping technique, an adaptive controller is given, it is proved that all the signals in the adaptive control system are globally uniformly ultimately bounded, and the output can be regulated to the origin with any prescribed accuracy. A simulation example further demonstrates the efficiency of the control scheme.     

Robustness of the tuning functions adaptive backstepping design forlinear systems

We study robustness of the adaptive backstepping design with tuning functions for linear systems. Under assumptions on unmodeled dynamics and disturbances equal to those for certainty equivalence schemes, we address an adaptive scheme not based on the certainty equivalence principle. In the process of redesign for robustness we employ only leakage in the estimator; we do not employ normalization, neither static nor dynamic. A fundamental difference between the tuning functions design and the certainty equivalence designs is that the controller in the former is inherently nonlinear, while in the latter it is nonlinear only in the parameter estimate. As a result, achievable robustness results for the tuning functions scheme are not global but regional, with a region of attraction inversely proportional to the “size” of the unmodeled dynamics. The tracking error is proportional to the size of the uncertainties     

带有死区输入和未建模动态的神经网络控制

针对一类具有死区非线性输入和未建模动态的非线性系统,提出一种自适应神经网络控制方法。该方法将后推技术和动态面技术结合,克服了计算复杂性问题,放宽了动态不确定性的假设,取消了神经网络逼近误差有界。借助中值定理和Young’s不等式,保证整个设计只需一个自适应参数,且控制增益只需存在一个上、下界。理论分析证明闭环系统所有信号半全局一致终结有界。仿真结果验证所提方案的有效性。     

Robustness of an adaptive predictive controller

In this correspondence, robustness properties of an adaptive predictive controller are presented. The algorithm is obtained via a receding horizon control strategy by minimizing a quadratic performance index under the constraint that the output matches the reference over a suitable number of terminal steps. Both the nonadaptive and an adaptive version of the algorithm are examined in the case of unmodeled plant dynamics     

Comments on the robust stability analysis of adaptive controllersusing normalizations

Some results on robustness to unmodeled dynamics of adaptive controllers using normalization factors are analyzed. It is shown that the proofs given by various authors fail to establish that the proposed adaptive controllers provide a nonvanishing robustness margin for the class of unmodeled dynamics considered     

LMI‐Based Robust PID Controller Design for Voltage Control of Islanded Microgrid

This paper presents the design of a robust proportional integral derivative (PID) controller for the control of a single phase microgrid voltage. A microgrid consists of loads, distributed generation units and several power‐electronics interfaced LC filter and voltage source inverter. These loads are unknown and parameters are uncertain which produce unmodeled load dynamics. This unmodeled load dynamics reduces the voltage tracking performance of the microgrid. The proposed controller gives the robustness of the system with unmodeled load dynamics. Under different kinds of uncertainties, PID controller guarantees the stability and provides zero steady‐state error and fast transient response. The robustness and optimal performance of the controller is obtained by using linear matrix inequality approach. The performance of the controller under different uncertainties is studied. Results indicate the robustness and high voltage tracking performance of the microgrid system.     

船舶航向的鲁棒自适应控制器的设计和仿真

针对带参数不确定性,未知有界扰动及未建模动态的船舶航向跟踪控制问题,本文介绍了一种鲁棒自适应算法。此算法能保证系统的全局稳定,使闭环系统的所有变量一致有界。并通过仿真对两种算法进行比较,可以看出,依照本文算法设计的控制器具有很好的鲁棒性。     

基于未建模动态补偿的非线性自适应切换控制方法

针对一类不确定的离散时间零动态不稳定的单输入-单输出(Single-input single-output, SISO)非线性系统,提出了一种基于未建模动态补偿的非线性控制器. 采用自适应神经模糊推理系统(Adaptive-network-based fuzzy inference system, ANFIS)和一一映射相结合的方法估计未建模动态.在此基础上,提出了由线性自 适应控制器、非线性自适应控制器以及切换机制组成的自适应切换控制方法.该方法通过对上述两种控制器的切换, 保证闭环系统输入输出信号有界的同时,改善系统性能.本文将要求未建模动态全局有界的条件放宽为线性增长, 建立了所提自适应控制方法的稳定性和收敛性分析.通过仿真比较和水箱的液位控制实验,验证了所提方法的有效性.     

Some design guidelines for discrete-time adaptive controllers

There have been many algorithms proposed for adaptive control which will provide globally asymptotically stable controllers if some stringent conditions on the plant are met. The conditions on the plant cannot be met in practice as all plants will contain high frequency unmodeled dynamics. This paper uses a linearization analysis of a nonlinear adaptive controller to demonstrate analytically some design guidelines which alleviate some of the problems associated with adaptive control in the presence of unmodeled dynamics. The points made are further demonstrated by simulation results.     

Robustness of adaptive control of robots

In this paper we discuss the robustness of adaptive control of rigid robots and methods for improving robustness in the face of unmodeled dynamics and external disturbances. Robustness to unmodeled dynamics is achieved using a so-called composite control strategy based on a singular perturbation formulation of the manipulator dynamics together with -modificiation. Rigorous stability proofs are given using a composite Lyapunov function approach.Research partially supported by the National Science Foundation under Grants INT-8902476 and MSM-9100618 and by the University of Illinois Manufacturing Research Center.     

Robust adaptive quasi-sliding mode controller for discrete-time systems

In this paper, a discrete robust quasi-sliding mode adaptive controller is presented for the system with model uncertainties, unmodeled dynamics and bounded disturbances. The proposed method is adaptive control in conjunction with a sliding mode based controller design. The bounded motion of the state around the sliding surface and the stability of the global system in the sense that all signals remain bounded are guaranteed. In the proposed adaptive algorithms, the dead-zone method is employed even though the upper and lower bounds of the disturbances are unknown. Simulation results have shown the effectiveness of the proposed algorithms.     

Motion synchronization of dual-cylinder pneumatic servo systems with integration of adaptive robust control and cross-coupling approach

We investigate motion synchronization of dual-cylinder pneumatic servo systems and develop an adaptive robust synchronization controller. The proposed controller incorporates the cross-coupling technology into the integrated direct/indirect adaptive robust control （DIARC） architecture by feeding back the coupled position errors, which are formed by the trajectory tracking errors of two cylinders and the synchronization error between them. The controller employs an online recursive least squares estimation algorithm to obtain accurate estimates of model parameters for reducing the extent of parametric uncertainties, and uses a robust control law to attenuate the effects of parameter estimation errors, unmodeled dynamics, and disturbances. Therefore, asymptotic convergence to zero of both trajectory tracking and synchronization errors can be guaranteed. Experimental results verify the effectiveness of the proposed controller.     

An input-output view of robustness in adaptive control

The stability and robustness properties of adaptive control systems are examined using input-output stability theory, i.e. passivity and small-gain theory. A generic adaptive error system is developed based on the concept of a tuned system—an ideal converged (nonadaptive) closed-loop system. Using this error system with passivity theory gives conditions for global stability where only boundedness (in norm) is required on the external inputs, e.g. disturbance, reference and initial conditions. Small gain theory is used to develop local stability results where the magnitudes of the external inputs are restricted. In the global case, a particular system operator (not the plant) is required to be strictly-passive, a condition which is unlikely to hold in actual use due to unmodeled dynamics. The local results, however, are not so restricted and allow for unmodeled dynamics. In this latter case an estimate of the stability margin is given under a persistent excitation condition.