Adaptive control via parameter set estimation

An adaptive control system is examined where the traditional parameter estimator is replaced by a parameter set estimator which provides a measure of uncertainty of the estimated parameters. it is shown how to construct a parameter set estimator with the property that the true system is always in the model set, and furthermore, how to design the estimation experiment so that the set of uncertainty is as small as possible given some a priori information.     

Parameter bounds for a class of discrete bilinear systems from records with bounded output errors

Parameter bounding offers a useful alternative to point parameter estimation methods when either statistical hypotheses on the errors are not met or uncertainties are better characterized in a deterministic way (e.g. systematic, round-off, truncation errors). So far, many efforts have been devoted to the problem of parameter bounding in linear systems, where exact parameter uncertainty intervals can be computed. In contrast, only partial results have been found for general non-linear parametrization, namely either upper or lower bounds on parameter uncertainties can be evaluated. In this paper we derive approximate parameter uncertainty intervals for a class of discrete bilinear systems with bounded output errors. This work is based on a linear input-output parametrization and previous results on bounded errors-in-variables models. For an extensively simulated example, central estimates by means of the bounded errors-in-variables approach and least squares estimates are computed and compared.     

Asymptotic performance guarantees in adaptive control

In this paper we address the problem of improving the asymptotic performance guarantees of a class of model reference adaptive controllers under insufficient excitation and in the presence of perturbations such as non-parametric uncertainty and bounded disturbances. We show that for a class of perturbations whose normalized effect is bounded by an a priori known function of time an estimate of the parametric uncertainty set can be obtained on-line via a set membership estimator. Furthermore, by incorporating this estimate as an additional constraint in the adaptive law generating the controller parameters, we show that the resulting adaptive controller offers dead-zone-like performance guarantees in the lim-sup sense while preserving the desirable root-mean-square performance guarantees of gradient-based algorithms.     

Use of prior bounds on time constants and steady‐state gain in recursive parameter bounding

Computation of parameter bounds of a linear dynamical system, given input–output observations and bounds on model‐output error, has been developed as an alternative to classical parameter estimation using least squares, maximum likelihood or the prediction error method. When bounds on time‐domain plant behaviour are known in advance, they can be used to develop prior parameter bounds for discrete‐time rational transfer‐function parameters. These bounds can be used to initialize standard parameter‐bounding algorithms which process input–output observations to update the exact polytope feasible set or one of its outer bounding approximations such as an ellipsoid, orthotope or parallelotope. This paper presents a method to compute such prior bounds from bounds on time constants and steady‐state (dc) gain, often available from the physics of the system or from previous experience. The method finds subsets making up the prior feasible parameter set, recursively in model order, for any configuration of the pole ranges. An analysis leading to measures of the value of prior bounds, in terms of their chances of remaining active when new bounds derived from observations are imposed, is presented. A simulation study compares polytope updating with and without such initial bounds. The simulations investigate the influence of the tightness of time‐constant and steady‐state‐gain bounds in reducing the volume of the feasible sets obtained as observations are processed. The effects of initial bound tightness and signal‐to‐noise ratio on survival time of the prior bounds are also examined. Copyright © 2002 John Wiley & Sons, Ltd.     

Decentralized indirect adaptive control of interconnected systems

Continuous time decentralized indirect adaptive controllers are proposed for a large-scale system composed of N interconnected linear subsystems with unknown parameters. Each local adaptive law utilizes a normalizing signal which is generated using the local input and the outputs of all the subsystems. This requires the exchange of output signals between the different subsystems, so that the scheme is no longer totally decentralized. Nevertheless, the degree of computational complexity is about the same as that of a totally decentralized scheme and this makes the scheme very attractive.     

Concurrent learning adaptive control of linear systems with exponentially convergent bounds

Concurrent learning adaptive controllers, which use recorded and current data concurrently for adaptation, are developed for model reference adaptive control of uncertain linear dynamical systems. We show that a verifiable condition on the linear independence of the recorded data is sufficient to guarantee global exponential stability. We use this fact to develop exponentially decaying bounds on the tracking error and weight error, and estimate upper bounds on the control signal. These results allow the development of adaptive controllers that ensure good tracking without relying on high adaptation gains, and can be designed to avoid actuator saturation. Simulations and hardware experiments show improved performance. Copyright © 2012 John Wiley & Sons, Ltd.     

An adaptive nonlinear output feedback controller using dynamic bounding with an aircraft control application

An adaptive output feedback control scheme is developed for a class of nonlinear systems with uncertain nonlinearities, which are bounded by both static and dynamic functions of the system output, and with actuator failures whose failure time instants, patterns and values are unknown, as motivated from an aircraft flight control application. An adaptive backstepping control law using dynamic bounding is constructed to deal with unknown actuator failures as well as system parameter and dynamics uncertainties to guarantee desired system performance. Complete stability and performance analysis and illustrative simulation results of an application to aircraft flight control are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Model reference adaptive control with unknown relative degree

This work presents an indirect, model reference adaptive control for minimum phase linear systems of arbitrary relative degree. Global stability of the closed-loop system is proved in spite of bounded disturbances and asympotic tracking is achieved in the ideal case.     

UUV推进电机在线参数辨识自适应控制方法研究

针对水下无人航行器(UUV)的推进电机矢量控制系统中电流控制器性能因参数变化而下降的问题,提出一种基于智能在线参数辨识的电流环自适应控制方法。以离散型永磁同步推进电机动态模型作为被控对象,采用动态惯性权重粒子群算法对永磁同步推进电机的定子电阻和dq轴电感进行在线辨识,根据电流控制器工程设计方法,将辨识所得的电机参数实时用于计算电流控制器的PI值,实现电流环的自适应控制。最后,通过仿真实验验证所提方法的有效性,结果表明该方法可以有效地克服水下快速洋流对推进电机的负载扰动,进而实现永磁同步推进电机的快速、高精确度电流控制性能。     

Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence

This paper provides a modified model reference adaptive control (MRAC) scheme to achieve better transient control performance for systems with unknown unmatched dynamics, where an adaptive law with guaranteed convergence is introduced. We first revisit the standard MRAC system and analyze the tracking error bound by using L₂‐norm and Cauchy‐Schwartz inequality. Based on this analysis, we suggest a feasible way to compensate the undesired transient dynamics induced by the gradient descent–based adaptive laws subject to sluggish convergence or even parameter drift. Then, a modified adaptive law with an alternative leakage term containing the parameter estimation error is developed. With this adaptive law, the convergence of both the estimation error and tracking error can be proved simultaneously. This enhanced convergence property can contribute to deriving smoother control signal and improved control response. Moreover, this paper provides a simple and numerically feasible approach to online verify the well‐known persistent excitation condition by testing the positive definiteness of an introduced auxiliary matrix. Comparative simulations based on a benchmark 3‐DOF helicopter model are given to validate the effectiveness of the proposed MRAC approach and show the improved performance over several other MRAC schemes.     

Transient bounds of dynamic certainty equivalent adaptive controllers

In this paper we show that the transient bounds of Morse's dynamic certainty equivalent adaptive controller established previously by us can be considerably strengthened. Specifically, we derive a computable bound on the ??_∞-norm of the tracking error which, in contrast with the local bound obtained previously by us, holds for all system initial conditions. Also, we add an ‘adaptation gain’ in the high-order estimator to prove that, by increasing this gain, the ??_∞-norm of the tracking error can be made arbitrarily small without increasing its ??_∞ norm. This is an improvement over the results obtained with backstepping designs, where these performance measures must be traded off in the selection of the adaptation speed.     

Self‐tuning control for polynomial systems using a receding horizon observer and control strategy

A receding horizon observer and control scheme is introduced for non‐linear systems described by polynomial maps. This control scheme has a natural interpretation as a two‐stage adaptive or self‐tuning control algorithm. The non‐linear feedback that results is defined only on the basis of past input and output measurements. The computational complexity aspects of this approach to adaptive or self‐tuning control are briefly discussed. A linear system and a Hénon map example are used to illustrate the ideas. Copyright © 2004 John Wiley & Sons, Ltd.     

Model-system parameter mismatch in GPC control

This paper considers a linear discrete-time system controlled by a GPC regulator. However the parameters and dynamic order of the system assumed for the regulator design differ from the true parameters. Hence there is a model-system parameter mismatch. For this case it is shown how to determine the stability of the system and then how to calculate the mean values and variances of input and output signals. The formulae presented give some insight to the robustness of the stochastic GPC controller.     

Consistent parameter estimation for deterministic mimo systems with overparametrized models

In this paper the parameter estimation problem for deterministic MIMO systems with overparametrized models will be addressed. In SISO systems overparametrized signal models might arise if the order of the plant model is set too high. For MIMO systems this problem will arise whenever its observability indices are different or, as in SISO systems, the order of the system is set too high. With a proper definition of persistent excitation it is shown that the estimated parameters will converge to a set of parameters. Each point of this set will result in the same transfer function as that of the system under consideration. A very efficient correction algorithm will be used to remove the greatest left common divisor of the estimated system parameters. Hence adaptive control algorithms, which may not be suitable if the estimated system parameters are not left coprime, can then be implemented.     

时空混沌的自适应模糊控制

对模型不确定的子系统是多维的耦合Henon映射链提出用离散自适应模糊的方法控制混沌,该方法综合了自适应模糊逻辑系统的逼近能力和带有域变结构控制策略的优点。仿真结果证明了所提方法的有效性。     

A weighted voltage model predictive control method for a virtual synchronous generator with enhanced parameter robustness

To address the problem of insufficient system inertia and improve the power quality of grid-connected inverters, and to enhance the stability of the power system, a method to control a virtual synchronous generator (VSG) output voltage based on model predictive control (MPC) is proposed. Parameters of the inductors, capacitors and other components of the VSG can vary as the temperature and current changes. Consequently the VSG output voltage and power control accuracy using the conventional MPC method may be reduced. In this paper, to improve the parameter robustness of the MPC method, a new weighted predictive capacitor voltage control method is proposed. Through detailed theoretical analysis, the principle of the proposed method to reduce the influence of parameter errors on voltage tracking accuracy is analyzed. Finally, the effectiveness and feasibility of the proposed method are verified by experimental tests using the Typhoon control hardware-in-the-loop experimental platform.     

改进模型参考自适应控制及其在解耦控制中的应用

提出了一种基于扩张状态观测器(extended state observer,ESO)的任意参考模型自适应控制方法,解决了被控对象状态信息不可测以及存在不确定因素导致模型参考自适应控制(model reference adaptive control,MRAC)效果变差甚至使系统不稳定的问题。在简述ESO教学模型的基础上提出了基于ESO的模型参考自适应控制方法并进行了严格的稳定性分析,仿真结果表明所设计方法具有跟踪速度快、稳态误差小、控制量小以及参考模型容易选择等特点。然后,提出基于改进MRAC的解耦控制方法并应用于三输入三输出的四旋翼飞行器姿态控制系统解耦控制,仿真结果表明该解耦控制方法具有鲁棒性好的特点。该方法无需按照通常的做法设计神经网络对不确定因素导致的误差进行补偿,大大简化了控制器设计过程。     

Discrete-time combined model reference adaptive control

The discrete-time version of continuous-time combined model reference adaptive control (CMRAC) is presented in this paper. A global stability proof of the overall adaptive scheme is given using arguments similar to those used in discrete-time direct model reference adaptive control (DMRAC) but properly modified to account for the different structure of CMRAC with respect to DMRAC. © 1997 by John Wiley & Sons, Ltd.     

Two scale high gain adaptive control

Simple adaptive controllers based on high gain output feedback suffer a lack of robustness with respect to bounded disturbances. Existing modifications achieve boundedness of all solutions but introduce solutions that, even in the absence of disturbances, do not achieve regulation. In this paper a new modification that achieves the desired robustness without the side‐effect of undesirable solutions is proposed. The modification features two data‐driven stability indicators. Intuitively, the first indicator drives the ‘closed‐loop poles’ to the closed right half plane while the latter provides fine‐tuning that prevents persistent imaginary axis poles and their associated undesired behaviour. Copyright © 2004 John Wiley & Sons, Ltd.