A set-theoretic model reference adaptive control architecture for disturbance rejection and uncertainty suppression with strict performance guarantees

Research in adaptive control algorithms for safety-critical applications is primarily motivated by the fact that these algorithms have the capability to suppress the effects of adverse conditions resulting from exogenous disturbances, imperfect dynamical system modelling, degraded modes of operation, and changes in system dynamics. Although government and industry agree on the potential of these algorithms in providing safety and reducing vehicle development costs, a major issue is the inability to achieve a-priori, user-defined performance guarantees with adaptive control algorithms. In this paper, a new model reference adaptive control architecture for uncertain dynamical systems is presented to address disturbance rejection and uncertainty suppression. The proposed framework is predicated on a set-theoretic adaptive controller construction using generalised restricted potential functions.The key feature of this framework allows the system error bound between the state of an uncertain dynamical system and the state of a reference model, which captures a desired closed-loop system performance, to be less than a-priori, user-defined worst-case performance bound, and hence, it has the capability to enforce strict performance guarantees. Examples are provided to demonstrate the efficacy of the proposed set-theoretic model reference adaptive control architecture.     

Direct fuzzy model‐reference adaptive control

Intelligent systems may be viewed as a framework for solving the problems of nonlinear system control. The intelligence of the system in the nonlinear or changing environment is used to recognize in which environment the system currently resides and to service it appropriately. This paper presents a general methodology of adaptive control based on multiple models in fuzzy form to deal with plants with unknown parameters which depend on known plant variables. We introduce a novel model‐reference fuzzy adaptive control system which is based on the fuzzy basis function expansion. The generality of the proposed algorithm is substantiated by the Stone‐Weierstrass theorem which indicates that any continuous function can be approximated by fuzzy basis function expansion. In the sense of adaptive control this implies the adaptive law with fuzzified adaptive parameters which are obtained using Lyapunov stability criterion. The combination of adaptive control theory based on models obtained by fuzzy basis function expansion results in fuzzy direct model‐reference adaptive control which provides higher adaptation ability than basic adaptive‐control systems. The proposed control algorithm is the extension of direct model‐reference fuzzy adaptive‐control to nonlinear plants. The direct fuzzy adaptive controller directly adjusts the parameter of the fuzzy controller to achieve approximate asymptotic tracking of the model‐reference input. The main advantage of the proposed approach is simplicity together with high performance, and it has been shown that the closed‐loop system using the direct fuzzy adaptive controller is globally stable and the tracking error converges to the residual set which depends on fuzzification properties. The proposed approach can be implemented on a wide range of industrial processes. In the paper the foundation of the proposed algorithm are given and some simulation examples are shown and discussed. © 2002 Wiley Periodicals, Inc.     

具有Preisach类型磁滞输入的不确定非线性系统 自适应神经网络控制

本文针对一类执行器受Preisach磁滞约束的不确定非线性系统, 提出一种基于神经网络的直接自适应控制 方案, 旨在解决系统的预定精度轨迹跟踪问题. 由于Preisach算子与系统动态发生耦合, 导致算子输出信号不可测 量, 给磁滞的逆补偿造成了困难. 为解决此问题, 本文首先将Preisach模型进行分解, 以提取出控制命令信号用于 Backstepping递归设计, 并在此基础上融合一类降阶光滑函数与直接自适应神经网络控制策略, 形成对磁滞非线性 和被控对象非线性的强鲁棒性能, 且所设计方案仅包含一个需要在线更新的自适应参数, 同时可保证Lyapunov函数 时间导数的半负定性. 通过严格数学分析, 已证明该方案不仅保证闭环系统所有信号均有界, 而且输出跟踪误差随 时间渐近收敛到用户预定区间. 基于压电定位平台的半物理仿真实验进一步验证了所提出控制方案的有效性.     

Robust model reference adaptive control for transient performance enhancement

To circumvent the potentially poor transient response induced by nonlinear uncertain dynamics in the adaptive control system, this article proposes a new model reference adaptive control design scheme to improve its transient control response. We first construct a compensator to online extract the undesired dynamics in the online learning, which is incorporated into the reference model and control simultaneously. Then, an error feedback term is incorporated into the reference model to speed up the convergence of both the compensator and tracking error. Moreover, a new leakage term containing the estimation error is constructed and then added in the adaptive law to guarantee the convergence of both the estimation error and tracking error. To further reveal the mechanisms behind these proposed methods, a new methodology to analyze the transient error bounds based on L₂‐norm and Cauchy‐Schwartz inequality is also developed. Based on the analysis results, we find that the proposed methods can effectively reduce the bound of the tracking error and thus achieve an improved transient control performance without violating the system stability even with high‐gain adaptation. In addition, the frequency‐domain analysis is resorted to show the comparative responses of different adaptive laws, which indicate that the proposed adaptive law can maintain the stability margin even with a high‐gain learning rate. A numerical example is given to demonstrate improved control responses of these proposed schemes.     

An Adaptive Neural Sliding Mode Controller for MIMO Systems

Here, a novel adaptive neural sliding mode controller (ANSMC) is proposed to handle the coupling and dynamic uncertainty of MIMO systems. The structure of this model-free new controller is based on a radial basis function neural network (RBFNN) which is derived from Lyapunov stability theory and relaxing Kalman–Yacubovich lemma to monitor the system for tracking a user-defined reference model. The weights of RBFNN can be initialized at zero, then, a novel online tuning algorithm is developed based on Lyapunov stability theory. A boundary layer function is introduced into the updating law to cover the parameter errors and modeling errors, and to guarantee the state errors converge into a specified error bound. An e-modification is added into the updating law to release the assumption of persistent excitation and obtain the appropriate values of the connecting weights of a RBFNN. To evaluate the control performance of the proposed controller, a two-link robot system is chosen as the simulation case. The numerical simulations results show that this novel controller has very good tracking accuracy, stability and robustness.     

On fractional order composite model reference adaptive control

This paper presents a novel composite model reference adaptive control approach for a class of fractional order linear systems with unknown constant parameters. The method is extended from the model reference adaptive control. The parameter estimation error of our method depends on both the tracking error and the prediction error, whereas the existing method only depends on the tracking error, which makes our method has better transient performance in the sense of generating smooth system output. By the aid of the continuous frequency distributed model, stability of the proposed approach is established in the Lyapunov sense. Furthermore, the convergence property of the model parameters estimation is presented, on the premise that the closed-loop control system is stable. Finally, numerical simulation examples are given to demonstrate the effectiveness of the proposed schemes.     

Improving transient performance of adaptive control architectures using frequency-limited system error dynamics

Although adaptive control theory offers mathematical tools to achieve system performance without excessive reliance on dynamical system models, its applications to safety-critical systems can be limited due to poor transient performance and robustness. In this paper, we develop an adaptive control architecture to achieve stabilisation and command following of uncertain dynamical systems with improved transient performance. Our framework consists of a new reference system and an adaptive controller. The proposed reference system captures a desired closed-loop dynamical system behaviour modified by a mismatch term representing the high-frequency content between the uncertain dynamical system and this reference system, i.e., the system error. In particular, this mismatch term allows the frequency content of the system error dynamics to be limited, which is used to drive the adaptive controller. It is shown that this key feature of our framework yields fast adaptation without incurring high-frequency oscillations in the transient performance. We further show the effects of design parameters on the system performance, analyse closeness of the uncertain dynamical system to the unmodified (ideal) reference system, discuss robustness of the proposed approach with respect to time-varying uncertainties and disturbances, and make connections to gradient minimisation and classical control theory. A numerical example is provided to demonstrate the efficacy of the proposed architecture.     

Robust adaptive fault-tolerant control for time delay uncertain nonlinear systems with time-varying performance bounds

In this paper, a robust adaptive fault tolerant controller guaranteeing with time-varying performance bounds is designed for a class of time delay uncertain nonlinear systems subject to actuator failures and external disturbance. The influence of time delay on the system is mitigated and the system performance can be guaranteed by introducing a positive nonlinear control gain function and the generalised restricted potential function. A new method with more design degrees of freedom is developed to ensure the norm of the system state within a-priori, user-defined time varying performance bounds. Using the online estimation information provided by adaptive mechanism, a robust adaptive fault-tolerant control method guaranteeing time varying performance bounds is proposed. It is shown that all the signals of the resulting closed-loop system are bounded and the system state less than a-priori, user-defined performance bounds. Finally, simulation results are given to demonstrate the efficacy of the proposed fault-tolerant control method.     

Particle swarm optimisers for the designing of parametric adjustment laws in discrete-time adaptive systems

A large variety of linear/nonlinear adaptive systems in continuous/discrete time can be represented by using error models, which facilitates their analysis. In addition, a solution found for a particular error model constitutes an universal strategy which can be applied to any system represented through that error model. In this paper, we present a novel methodology based on particle swarm optimisers for online parametric adjustment in discrete-time adaptive systems represented by type 1, 2, and 3 error models, which provides stability properties and high performance compared with traditional techniques. Successful applications in combined and direct model reference adaptive control via detailed simulations are provided.     

Model reference adaptive control of a solenoid valve controlled hydraulic system

The MRAC is applied to the control of an electrohydraulic system controlled by a solenoid valve. The adaptive algorithms proposed in this paper guarantee the asymptotic stability of the error between the plant output and that of the reference model. The robustness properties of the adaptive control system are examined based on the concept of a tuned system—an ideal converged (non-adaptive) closed-loop system when the gain of the valve is varying non-linearly. A modified adaptive law that guarantees the tracking error will be bounded in a residual region is proposed. The performance improvement is also studied by implementing the ternary mode solenoid valve. To illustrate the validity, the simulation results of a gun turret position control system are also included.     

GA-based decoupled adaptive FSMC for nonlinear systems by a singular perturbation scheme

Generally, the difficulty with multivariable system control is how to overcome the coupling effects for each degree of freedom. The computational burden and dynamic uncertainty of multivariable systems makes the model-based decoupling approach hard to implement in a real-time control system. In this study, an intelligent adaptive controller is proposed to handle these behaviors. The structure of these model-free new controllers is based on fuzzy systems for which the initial parameter vector values are found based on the genetic algorithm. One modified adaptive law is derived based on Lyapunov stability theory to control the system for tracking a user-defined reference model. The requirement of the Kalman–Yacubovich lemma is fulfilled. In addition, a non-square multivariable system can be decoupled into several isolated reduced-order square multivariable subsystems by using the singular perturbation scheme for different time-scale stability analysis. The adjustable parameters for the intelligent system can be initialized using a genetic algorithm. Novel online parameter tuning algorithms are developed based on the Lyapunov stability theory. A boundary-layer function is introduced into these updating laws to cover parameter and modeling errors and to guarantee that the state errors converge into a specified error bound. Finally, a numerical simulation is carried out to demonstrate the control methodology that can rapidly and efficiently control nonlinear multivariable systems.     

Decentralised adaptive architectures for control of large-scale active–passive modular systems with stability and performance guarantees

ABSTRACT

Decentralised control of large-scale active–passive modular systems is considered in this paper. The considered class of large-scale systems consist of physically interconnected and generally heterogeneous modules, where local control signals can only be applied to a subset of these modules (i.e. active modules) and the rest do not admit any control signals (i.e. passive modules). Specifically, based on a set-theoretic model reference adaptive control approach predicated on restricted potential functions, we design and analyse decentralised command following control laws for each active module such that they can effectively perform their tasks in the presence of unknown physical interconnections between modules and module-level system uncertainties. The key feature of our framework allows the system error trajectories of the active modules to be contained within a-priori, user-defined compact sets. Thus, they are guaranteed to achieve strict performance guarantees, where this is of paramount importance for practical applications. In addition to our theoretical findings and research contributions, the efficacy of the proposed decentralised adaptive control architecture is demonstrated in an illustrative numerical example.     

具有时滞的柔性关节多机械臂协同自适应位置/力控制

由于关节机械臂长期运行后,齿轮间隙扩大产生的时间滞后将使得系统跟踪性能降低.针对此问题,本文提出了一种自适应位置/力控制策略来保证闭环系统稳定性以及位置/力跟踪性能.首先,对多机械臂和物体系统进行任务空间动力学建模.随后,利用Pade理论将时间滞后近似为二阶有理分式.同时,利用神经网络自适应算法克服模型建模误差对系统稳定性的影响,利用同时包含位置误差和力误差的线性滑模项,设计位置/力控制器.通过李雅普诺夫稳定性理论,证明控制策略能实现位置误差和内力误差的渐近收敛.最后,仿真验证证明所设计控制策略的有效性.     

Computing actuator bandwidth limits for model reference adaptive control

Although model reference adaptive control theory has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, a linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that is not affected by the presence of actuator dynamics. Specifically, we first generalise the hedging approach to cover a variety of cases in which actuator output and the control effectiveness matrix of the uncertain dynamical system are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov-based stability analysis tools and propose a linear matrix inequality-based framework for the computation of the minimum allowable actuator bandwidth limits such that the closed-loop dynamical system remains stable. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.     

Globally stable model reference adaptive control based on fuzzy description of the plant

A novel fuzzy adaptive control algorithm is presented that belongs to direct model reference adaptive techniques based on a fuzzy (Takagi-Sugeno) model of the plant. The global stability of the overall system is proven, namely all the signals in the system remain bounded while the tracking error and estimated parameters converge to some residual set that depends on the size of disturbance and high-order parasitic dynamics. The hallmarks of the approach are its simplicity and transparency. The proposed algorithm is a straightforward extension of classical model reference adaptive control (MRAC) with a robust adaptive law to nonlinear systems described by fuzzy models. The performance of the approach was tested on a simulated plant and compared with the performance of a PI controller and a classical MRAC.     

输出约束的有限时间自适应区间二型模糊输出反馈PMSM伺服控制

针对永磁同步电机驱动的伺服系统在不确定性摩擦和未知负载的影响下难以达到高精度的控制效果,提出一种基于区间二型模糊系统的带有输出约束的有限时间自适应输出反馈控制方案.首先,构建一个基于非线性扰动观测器的区间二型模糊状态观测器,分别完成对于未知扰动和速度的估计,区间二型模糊系统完成对于非线性摩擦的逼近;然后,在此基础上,结合滤波误差补偿机制和有限时间技术,引入障碍Lyapunov函数和反步控制技术设计输出约束的自适应区间二型模糊输出反馈控制器;最后,根据Lyapunov稳定性理论提出严格的稳定性分析,保证闭环系统的所有信号均是有限时间内有界的,并通过数值仿真和实验验证了所提出方法的有效性.     

Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

An adaptive fixed‐time trajectory tracking controller is proposed for uncertain mechanical systems in this study. The polynomial reference trajectory is planned for trajectory tracking error. Fractional power of linear sliding mode is applied to design the nonlinear controller, adaptive laws are used to adjust controller parameters. Trajectory planning and fractional power are combined to ensure the tracking‐error convergence in a fixed time. The boundary layer technique is used to suppress the model uncertainties and decrease the chattering phenomenon. The closed‐loop system stability is proved strictly in the Lyapunov framework to show that the trajectory tracking errors and adaptive parameters tend to zero in a fixed time set in advance. Numerical simulation results of robotic manipulators illustrate the effectiveness of the proposed controller.     

液压釜温度自适应预测控制1)

This paper introduces the details of the adaptive control scheme,error analysis and field adjustment of a hydraulic cauldron control system.A kind of new adaptive predictive control scheme is designed based on the all-coefficient adaptive control theory and model predictive control theory.The stability of this control algorithm is proved,and the analysis of error in stable stage and analysis of dynamic performance in the closed loop system are given.The actual application shows that the method proposed in this paper has good robustness to model error,system delay and measure noise.     

液压釜温度自适应预测控制

详细介绍了液压釜温度系统自适应控制方案、误差分析及实际应用调试情况.应用全系数自适应控制理论及模型预测控制原理设计了一种新的自适应预测控制方案,并给出了控制算法的稳定性证明及闭环系统稳态误差和动态特性分析.实际应用表明,该方法对建模误差、系统延时及测量噪声具有较好的鲁棒性.     

液压釜温度自适应预测控制

详细介绍了液压釜温度系统自适应控制方案、误差分析及实际应用调试情况．应用全系数自适应控制理论及模型预测控制原理设计了一种新的自适应预测控制方案,并给出了控制算法的稳定性证明及闭环系统稳态误差和动态特性分析．实际应用表明,该方法对建模误差、系统延时及测量噪声具有较好的鲁棒性．