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.     

Decentralized robust adaptive control of nonlinear systems withunmodeled dynamics

The authors present a decentralized robust adaptive output feedback control scheme for a class of large-scale nonlinear systems of the output feedback canonical form with unmodeled dynamics. A modified dynamic signal is introduced for each subsystem to dominate the unmodeled dynamics and an adaptive nonlinear damping is used to counter the effects of the interconnections. It is shown that under certain assumptions, the proposed decentralized adaptive control scheme guarantees that all the signals in the closed-loop system are bounded in the presence of unmodeled dynamics, high-order interconnections and bounded disturbances. Furthermore, by choosing the design constants appropriately, the tracking error can be made arbitrarily small regardless of the interconnections, disturbances, and unmodeled dynamics in the system. An illustration example demonstrates the effectiveness of the proposed scheme     

Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated thai there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implication of the existence of such infinite-gain operators is that 1) sinusoidal reference inputs at specific frequencies and/or 2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.     

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.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

Design of observer-based adaptive controller for nonlinear systems with unmodeled dynamics and actuator dead-zone

This paper presents an up-to-date study on the observer-based control problem for nonlinear systems in the presence of unmodeled dynamics and actuator dead-zone. By introducing a dynamic signal to dominate the unmodeled dynamics and using an adaptive nonlinear damping to counter the effects of the nonlinearities and dead-zone input, the proposed observer and controller can ensure that the closed-loop system is asymptotically stable in the sense of uniform ultimate boundedness. Only one adaptive parameter is needed no matter how many unknown parameters there are. The system investigated is more general and there is no need to solve Linear matrix inequality (LMI). Moreover, with our method, some assumptions imposed on nonlinear terms and dead-zone input are relaxed. Finally, simulations illustrate the effectiveness of the proposed adaptive control scheme.     

具有全状态约束和未建模动态的严格反馈系统有限时间自适应动态面控制

针对一类具有全状态约束、未建模动态和动态扰动的严格反馈非线性系统,通过构造非线性滤波器,并利用Young’s不等式,提出一种新的有限时间自适应动态面控制方法.引入非线性映射处理全状态约束,将有约束系统变成无约束系统,利用径向基函数逼近未知光滑函数,利用辅助系统产生的动态信号处理未建模动态.对于变换后的系统,利用改进的动态面控制和有限时间方法设计的控制器结构简单,移去现有有限时间控制中出现的“奇异性”问题,可加快系统的收敛速度.理论分析表明,闭环系统中的所有信号在有限时间内有界,全状态不违背约束条件.数值算例的仿真结果表明,所提出的自适应动态面控制方案是有效的.     

具有输入未建模动态的纯反馈非线性系统自适应控制

对一类具有状态和输入未建模动态且控制增益符号未知的纯反馈非线性系统,利用非线性变换、改进的动态面控制方法以及Nussbaum函数性质,提出两种自适应动态面控制方案.利用正则化信号来约束输入未建模动态,从而有效地抑制其产生的扰动.通过引入动态信号,有效地处理了由状态未建模动态引起的动态不确定性.通过在总的李雅普诺夫函数中引入非负正则化信号,并利用稳定性分析中引入的紧集,证明了闭环控制系统是半全局一致终结有界的.数值仿真验证了所提方案的有效性.     

具有未建模动态系统的自适应动态面输出反馈控制

针对一类具有未建模动态和动态扰动且状态不可量测的非线性系统,利用神经网络逼近未知函数设计K-滤波器重构系统状态,提出一种自适应输出反馈控制策略。通过对未建模动态的新刻画,避免动态信号的引入。采用动态面设计方法,取消理论分析中产生的未知连续函数的估计,降低设计的复杂性。利用Lyapunov方法证明了闭环系统的所有信号是半全局一致终结有界的,并通过仿真结果验证了所提出方案的有效性。     

具有动态不确定性的自适应动态面控制

针对一类具有未建模动态的纯反馈非线性系统,提出一种自适应动态面控制方法。利用神经网络逼近未知连续函数,通过引入一种动态信号克服未建模动态。与现有结果相比,提出的设计方案简化了对未建模动态的处理过程,取消了神经网络逼近误差有界的假设。理论分析证明了该自适应控制方法能够保证闭环系统是半全局一致终结有界的,仿真结果验证了该方案的有效性。     

Robust adaptive quantized DSC of uncertain pure‐feedback nonlinear systems with time‐varying output and state constraints

In this paper, the problem of neural adaptive dynamic surface quantized control is studied the first time for a class of pure‐feedback nonlinear systems in the presence of state and output constraint and unmodeled dynamics. The considered system is under the control of a hysteretic quantized input signal. Two types of one‐to‐one nonlinear mapping are adopted to transform the pure‐feedback system with different output and state constraints into an equivalent unconstrained pure‐feedback system. By designing a novel control law based on modified dynamic surface control technique, many assumptions of the quantized system in early literary works are removed. The unmodeled dynamics is estimated by a dynamic signal and approximated based on neural networks. The stability analysis indicates that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the output and all the states remain in the prescribed time‐varying or constant constraints. Two numerical examples with a coarse quantizer show that the proposed approach is effective for the considered system.     

具有未建模动态及输入输出约束的单相全桥逆变器动态面事件触发控制

全桥逆变器是一类典型的开关型非线性系统,系统中存在很多非线性和不确定因素,易导致系统性能下降,甚至造成不稳定.对于具有未建模动态和时变输出约束的单相全桥逆变器系统,利用动态信号处理未建模动态,设计辅助动态系统补偿控制信号,提出一种事件触发的自适应动态面跟踪控制策略;引入跟踪误差变换,解决输出约束问题;对控制输入进行约束,使用模糊系统调节参数向量的欧氏范数作为自适应参数,设计事件触发控制,这些技术的采用可有效降低控制器计算量,保证实际系统的可实现性,完善了具有输入约束条件下动态面控制方法的稳定性分析和证明.逆变器精确模型无需已知,实际控制系统具有较好的稳定性和鲁棒性.理论分析表明,闭环系统的所有信号半全局一致终结有界,所提出方案的有效性通过仿真实验得到进一步验证.     

基于未建模动态补偿的一类MIMO非线性系统的自适应广义预测解耦切换控制

针对一类不确定的多输入多输出(MIMO)离散时间零动态不稳定非线性系统, 提出了一种基于未建模动态补偿的非线性广义预测解耦切换控制方法. 该控制方法要求系统的未建模动态满足线性增长条件, 放宽了未建模动态全局有界的限制. 建立了所提的自适应控制方法的稳定性和收敛性分析. 而且, 在设计广义预测解耦控制器时, 把“一一映射”与ANFIS的训练相结合来估计系统的未建模动态, 保证了ANFIS的万能逼近特性. 最后, 仿真结果验 证了所提方法的优越性.     

具有未建模动态和输出约束的耦合系统的分散自适应控制

针对一类具有输入、状态未建模动态和非线性输入的耦合系统,提出一种自适应神经网络控制方案.利用径向基函数神经网络逼近未知非线性连续函数;引入动态信号和正则化信号处理状态及输入未建模动态;通过引入非线性映射,将具有时变输出约束的严格反馈系统化为不含约束的严格反馈系统.最后,通过理论分析验证闭环系统中所有信号是半全局一致最终有界的,仿真结果进一步验证了所提出控制方案的有效性.     

具有输入及状态未建模动态系统的输出反馈自适应控制

针对一类具有输入及状态未建模动态的非线性系统, 设计K滤波器来估计系统不可量测状态, 基于动态面控制技术并利用径向基函数神经网络的逼近能力, 提出一种输出反馈自适应跟踪控制方案. 利用Nussbaum 函数性质, 有效地解决了高频增益符号未知问题. 在控制器设计中引入规范化信号来约束输入未建模动态, 从而有效地抑制其产生的扰动. 通过理论分析证明了闭环控制系统是半全局一致终结有界的.

     

Robust adaptive DSC of directly input‐coupled nonlinear systems with input unmodeled dynamics and time‐varying output constraints

In this paper, an adaptive robust dynamic surface control is proposed for a class of uncertain nonlinear interconnected systems with time‐varying output constraints and dynamic input and output coupling. The directly coupled inputs and control inputs are both of nonlinear input unmodeled dynamics. To counteract the instable impact of the nonlinear input unmodeled dynamics, normalization signals are designed on the basis of the convergence rates of their Lyapunov functions. With new state variables and control variables being defined, the real control inputs are obtained through solving the equations of intermediate control laws. The time‐varying constraints on output signals are implemented by introducing asymmetric barrier Lyapunov functions. In addition, dynamic signals and decentralized K‐filters are used to deal with the state unmodeled dynamics and to estimate the unmeasurable states, respectively. By the theoretical analysis, the signals in the closed‐loop system are proved to be semi‐globally uniformly ultimately bounded, and the output constraints are guaranteed simultaneously. A numerical example is provided to show the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics

A neural network-based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unmodeled dynamics. By on-line approximating the unknown nonlinear functions and unmodeled dynamics by radial basis function (RBF) networks, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. It is proved that with the proposed control law, the closed-loop system is stable and the tracking error converges to zero in the presence of unmodeled dynamics and unknown nonlinearity. A simulation example is presented to demonstrate the method.     

Robust adaptive control: Conditions for global stability

An input-output approach is presented for analyzing the global stability and robustness properties of adaptive controllers to unmodeled dynamics. The concept of a tuned system is introduced, i.e., the control system that could be obtained if the plant were known. Comparing the adaptive system to the tuned system results in the development of a generic adaptive error system. Passivity theory is used to derive conditions which guarantee global stability of the error system associated with the adaptive controller, and ensure boundedness of the adaptive gains. Specific bounds are presented for certain significant signals in the control systems. Limitations of these global results are discussed, particularly the requirement that a certain operator be strictly positive real (SPR)-a condition that is unlikely to hold due to unmodeled dynamics.     

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     

Adaptive architectures for control of uncertain dynamical systems with actuator and unmodeled dynamics

In adaptive control of uncertain dynamical systems, it is well known that the presence of actuator and/or unmodeled dynamics in feedback loops can yield to unstable closed‐loop system trajectories. Motivated by this standpoint, this paper focuses on the analysis and synthesis of multiple adaptive architectures for control of uncertain dynamical systems with both actuator and unmodeled dynamics. Specifically, we first analyze model reference adaptive control architectures with standard, hedging‐based, and expanded reference models for this class of uncertain dynamical systems and develop sufficient stability conditions. We then synthesize a robustifying term for the latter architecture and analytically show that this term can allow for a relaxed sufficient stability condition. The proposed theoretical treatments involve Lyapunov stability theory, linear matrix inequalities, and matrix mathematics. Finally, we compare the resulting sufficient stability conditions of the considered adaptive control architectures on a benchmark mechanical system subject to actuator and unmodeled dynamics.