A new robust adaptive control algorithm for linear time-varying plants

Robustness is an important property of a control system. Robust adaptive control has been an active research area for more than a decade. Since it was shown that un-modelled dynamics or even a small bounded disturbance can cause most adaptive control algorithms to go unstable, various modifications of the adaptive control algorithms have been developed to counteract instability and improve robustness with respect to unmodelled dynamics and bounded disturbances. However, we know that most of the modified approaches to achieve robustness require knowledge of either the parameter of bounding function on the unmodelled dynamics, or the upper bound on the disturbances, or the bound on the norm of unknown matching controller/plant parameters, and such knowledge can hardly be obtained in practice. A new indirect adaptive control algorithm for linear time-varying plants is proposed to achieve robustness to a class of unmodelled dynamics, bounded disturbances and plant parameter time variations. A modified relative dead zone technique is used, so that knowledge of the parameters of the upper bounding function on the unmodelled dynamics and the disturbances is not required. The stability analysis and the robust performance of adoptively controlled time-varying systems are provided for the new scheme. A simulation example is given to show the effectiveness of the proposed algorithm.     

Robust consensus tracking for a class of high‐order multi‐agent systems

In this paper, we study the robust consensus tracking problem for a class of high‐order multi‐agent systems with unmodelled dynamics and unknown disturbances. A continuous robust state feedback control algorithm is proposed to enable the agents to achieve robust consensus tracking of a desired trajectory. By utilizing Lyapunov analysis methods and an invariance‐like theorem, sufficient conditions for semi‐global asymptotic consensus tracking are established. A robust output feedback control algorithm is designed to obtain a uniformly ultimately bounded consensus tracking result. Numerical simulations are provided to show the effectiveness of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

Parameter estimation in systems with binary-valued observations and structural uncertainties

This paper studies identification of linear systems with binary-valued observations generated via fixed thresholds. In addition to stochastic measurement noises, the systems are also subject to structural uncertainties, including deterministic unmodelled dynamics, nonlinear model mismatch, and sensor observation bias. Since binary-valued observations can supply only limited information on the signals, truncated empirical measures are introduced to extract further information for system identification. An effective identification algorithm is constructed based on the proposed empirical measures. Optimal identification errors, time complexity, optimal input design, and impact of disturbances, unmodelled dynamics, observation bias, and nonlinear model mismatch are thoroughly investigated in a stochastic information framework. Asymptotic upper and lower bounds are established on identification errors. Numerical experiments are presented to demonstrate the effectiveness of the algorithms and the main results.     

Robust adaptive control of strict-feedback nonlinear systems with unmodelled dynamics and time-varying delays

This paper presents a novel robust adaptive neural control scheme which can be taken as a robustification of the adaptive backstepping design. The considered class of uncertainties contains unknown non-symmetric dead-zone inputs, time-varying delay uncertainties, unknown dynamic disturbances and unmodelled dynamics. The radial basis function neural networks (RBFNNs) are employed to approximate the unknown nonlinear functions obtained by Young’s inequality. By constructing exponential Lyapunov-Krasovskii functionals, the upper bound functions of the time-varying delay uncertainties are compensated for. Using Young’s inequality and RBFNNs, the assumptions with respect to unmodelled dynamics are relaxed. It is demonstrated that the proposed controller guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error eventually converges to a neighbourhood of zero.     

一类时变系统鲁棒自适应状态反馈控制的稳定性分析

针对一类离散线性时变参数系统,给出了一种自适应状态反馈控制器,系统的时变参数是已知有界实函数和未知常数的线性组合,该控制器由带有死区的最小二乘辨识算法,状态反馈控制算法和状态观测器构成,文中详细地分析了闭环系统在有界外部干扰和小未建模不确定性影响下的全局稳定性和鲁棒性。     

Robust noise attenuation under stochastic noises and worst-case unmodelled dynamics

This paper investigates noise attenuation problems for systems with unmodelled dynamics and unknown noise characteristics. A unique methodology is introduced that employs signal estimation in one phase, followed by control design for noise rejection. The methodology enjoys certain advantages in its simple control design process, accommodation of unmodelled dynamics, and non-conservative noise rejection performance. Under mild information on unmodelled dynamics, we first derive robust performance bounds on noise attenuation with respect to unmodelled dynamics without noise estimation errors. Then more general results are presented for systems that are subject to both stochastic signal estimation errors and unmodelled dynamics. Examples are also presented to demonstrate our findings.     

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.     

具有未知负载扰动的水井钻机电液伺服系统无模型自适应控制

针对电液伺服系统在水井钻机推进工况下存在的参数不确定以及未知负载扰动突变等非线性因素,提出了基于径向基(RBF)神经网络扰动观测器的无模型自适应控制方法.首先,通过改进的无模型自适应控制动态线性化方法,将被控系统线性化为与输入输出相关的增量形式,并将未知负载扰动合并到一个非线性项中;然后,设计了径向基神经网络扰动观测器对含有未知负载扰动的非线性项进行估计,作为对未知扰动的补偿;最后,设计了时变参数估计律,通过在线调整伪偏导数,给出了电液伺服系统的控制更新律.仿真结果表明,所设计的控制器能够对未知负载扰动突变进行补偿,并能确保跟踪误差有界收敛.     

Observers of External Deterministic Disturbances. I. Objects with Known Parameters

A new design for observers of external deterministic disturbances is developed, in which parametrized disturbance models for wide classes of linear and nonlinear objects can be derived on a unified basis. The possible parametric uncertainty of the controlled system and external disturbance generator has no influence on the observer structure and parameters, and is manifested in the uncertainty of the parametrized disturbance model. Therefore, our observers are convenient for designing adaptive control algorithms for parametrically uncertain systems under external disturbances or adaptive compensation algorithms for unknown external deterministic disturbances.     

Output feedback tracking control by additive state decomposition for a class of uncertain systems

Besides parametric uncertainties and disturbances, unmodelled dynamics and time delay at the input are often present in practical systems, and cannot always be ignored. This paper aims to solve the problem of output feedback tracking control for a class of non-linear uncertain systems subject to unmodelled high-frequency gains and time delay in the input. By additive state decomposition, the uncertain system is transformed to an uncertainty-free system, in which the uncertainties, disturbances and effects of unmodelled dynamics along with time delay are lumped into a new disturbance at the output. Subsequently, additive state decomposition is used to decompose the transformed system to simplify the tracking controller design. The proposed control scheme is applied to three benchmark examples to demonstrate its effectiveness.     

Model reference robust control of systems with significant unmodelled dynamics

In this paper, a recently proposed control design technique, model reference robust control (MRRC), is generalized to provide input–output robust control for a much wider class of SISO systems. A system under consideration may contain not only parametric uncertainties, disturbances, uncertain high-order nonlinearities associated with system output (including stable unmodelled dynamics of the output), but also multiplicative unmodelled dynamics of the input of the system. Input unmodelled dynamics may be unstable and of infinite dimension. Common assumptions such as the order of the system, or bounds on system parameters, or coefficients in size-bounding functions on uncertainties and unmodelled dynamics are not needed in this paper. The a priori information required to apply the proposed design procedure includes the relative degree of the overall system, closed-form expressions of bounding functions, and, for arbitrarily small error in tracking the output of any given reference model, the minimum phase condition. Under the proposed control, the output tracking error can be made arbitrarily small to achieve any specified tracking accuracy. The distinct feature of MRRC is that neither uncertainties nor unmodelled dynamics are required to be small. © 1997 by John Wiley & Sons, Ltd.     

新型多变量鲁棒自校正解耦控制直接算法

本文提出了一种新型多变量鲁棒自校正解耦控制直接算法，由于在算法中采用了一种新的控制律，所以较彻底地克服了系统未建模动态和不可测干扰的影响，在系统具有较强的未建动态和有界不可测干扰的情况下，本文算法不仅可以保证系统的稳定性，而且实现了鲁棒自校正解耦控制，在算法中采用一种新的方法确定正则化系数和死区界，这种方法保证了系统跟踪特性不受死区和正则化的影响，本文还给出了所提出算法的鲁棒性分析和仿真结果。     

New approach to robust model reference adaptive control for a class of plants

Motivated by recent advances in designing robust adaptive controllers and in dealing with uncertain dynamical systems, a new model reference adaptive control which is robust to a class of unmodelled dynamics and bounded output disturbances in the case of relative degree one is presented. The implementation of the controllers includes a switching mechanism which plays a crucially important role in functions of stabilizing as well as tracking. It is shown that global stability of the overall system is achieved under no assumption of persistency of excitation, and tracking errors will converge to a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances explicitly. In the ideal case, the residual set degenerates to a single null point and convergence can be achieved in finite time without any requirement of persistency of excitation.     

Practical issues in the implementation of self-tuning control

Implementation aspects of self-tuning regulators are discussed in the paper. There is a large discrepancy between simulation or academic algorithms and practical algorithms. In the idealized environment of simulations it is easy to get different types of adaptive algorithms to perform well. In practice the situation is quite opposite. The adaptive or self-tuning controller must be able to handle nonlinearities, unmodelled dynamics and unmodelled disturbances over a wide range of operating conditions. Some aspects of how to implement self-tuning controllers are discussed in the paper. This includes robustness, signal conditioning, parameter tracking, estimator wind-up, reset action and start-up. Different ways to use the prior knowledge about the process are also discussed.     

Optimality in discrete model-following systems in the presence of unmodelled dynamics.

The problem of optimal model-following linear control of discrete stochastic adaptive systems is studied in the presence of unmodelled dynamics. The controller complexity is restricted to that corresponding to the perfectly modelled situation. The key for a control design to be robust in the presence of unmodelled dynamics is closely related to some parametrical conditions that ensure a certain linear filter (involving parametrical uncertainties related to unmodelled dynamics) maintains the output stationarity of any stationary random input signal, as in the nominal situation. Partial results concerning robustness are obtained from stability considerations. In any case, a priori knowledge on the unmodelled dynamics is not available for the implementation of the control law.     

Adaptive tracking with external force disturbance rejection for uncertain robotic systems

This paper is concerned with the tracking control problem of robotic systems perturbed by time-varying parameters, unmodelled dynamics and external force (and moment) disturbances. The upper bound of system uncertainties and disturbances is not required for controller design. Also, no limitations are assumed on the speed of variation and the magnitude of unknown parameters and perturbations. An adaptive algorithm with simplicity and universality properties is proposed to ensure robust tracking. Presenting the closed loop stability proof analytically, the tracking controller is applied to a two-link robot manipulator and the simulation results are demonstrated to show the effectiveness of the method.     

A modified direct adaptive robust motion trajectory tracking controller of a pneumatic system

In this study, we developed and tested a high-precision motion trajectory tracking controller of a pneumatic cylinder driven by four costless on/off solenoid valves rather than by a proportional directional control valve. The relationship between the pulse width modulation （PWM） of a signal＇s duty cycle and control law was determined experimentally, and a mathematical model of the whole system established. Owing to unknown disturbances and unmodeled dynamics, there are considerable uncertain nonlinearities and parametric uncertainties in this pneumatic system. A modified direct adaptive robust controller （DARC） was constructed to cope with these issues. The controller employs a gradient type adaptation law based on discontinuous projection mapping to guarantee that estimated unknown model parameters stay within a known bounded region, and uses a deterministic robust control strategy to weaken the effects of unmodeled dynamics, disturbances, and parameter estimation errors. By using discontinuous projection mapping, the parameter adaptation law and the robust control law can be synthesized separately. A recursive backstepping technology is applied to account for unmatched model uncertainties. Kalman filters were designed sepa- rately to estimate the motion states and the derivative of the intermediate control law in synthesizing the deterministic robust control law. Experimental results illustrate the effectiveness of the proposed controller.     

A novel continuous fractional sliding mode control

A new fractional-order controller is proposed, whose novelty is twofold: (i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodelled dynamics, and (ii) based on a principle of dynamic memory resetting of the differintegral operator, it is enforced an invariant sliding mode in finite time. Both (i) and (ii) account for exponential convergence of tracking errors, where such principle is instrumental to demonstrate the closed-loop stability, robustness and a sustained sliding motion, as well as that high frequencies are filtered out from the control signal. The proposed methodology is illustrated with a representative simulation study.     

广义预测鲁棒自适应控制

本文指出自校正控制中广泛采用的CARMA模型会导致控制系统对确定性扰动和非平稳随机扰动缺乏鲁棒性;在CARMA模型中引入相应于上述扰动的不可控模态,给出了一种广义的CARMA模型;基于内模原理,提出一种新的广义预测鲁棒自适应控制器;并从理论上揭示其鲁棒性机理;给出了数字仿真。理论分析和数字仿真结果表明:这种广义预测自适应控制器对各类扰动和对象参数变化具有很强的鲁棒性。     

Iterative identification and control redesign via unfalsified sets of models: A basic scheme

A new worst-case iterative identification and control scheme is introduced which is based on the use of unfalsified model sets in parameter space. No a priori bounds are assumed on the norm of the 'unmodelled dynamics' or on the size of disturbances. In spite of the weak assumptions, the scheme converges close to an 'ideal' performance, which could be achieved only with perfect knowledge of the size of the unmodelled dynamics and the disturbances. An interesting feature of the scheme is that the model structure of the parametric part of the models does not have to be known a priori either. A finite set of alternative parametric models can be hypothesized, and structure selection is part of the iterative identification and control design scheme proposed. Finally, simulations are shown and numerical implementations are discussed.