Bounded-error estimation using dead zone and bounding ellipsoid

The use of a dead zone and a bounding ellipsoid for parameter estimation when measurement errors are bounded is discussed. the size of the dead zone is set to be exactly equal to the assumed noise bound. The algorithm retains the properties of computing parameter point estimates and allows a bounding ellipsoid to be computed at each iterative step.     

Online data‐driven composite adaptive backstepping control with exact differentiators

This paper presents an online data‐driven composite adaptive backstepping control for a class of parametric strict‐feedback nonlinear systems with mismatched uncertainties, where both tracking errors and prediction errors are utilized to update parametric estimates. Hybrid exact differentiators are applied to obtain the derivatives of virtual control inputs such that the complexity problem of integrator backstepping can be avoided. Closed‐loop tracking error equations are integrated in a moving‐time window to generate prediction errors such that online recorded data can be utilized to improve parameter adaptation. Semiglobal asymptotic stability of the closed‐loop system is rigorously established by the time‐scales separation and Lyapunov synthesis. The proposed composite adaptation can not only avoid the application of identification models and linear filters resulting in a simpler control structure, but also suppress parametric uncertainties and external perturbations via the time‐interval integral. Simulation results have demonstrated that the proposed approach possesses superior control performances under both noise‐free and noisy‐measurement environments. Copyright © 2015 John Wiley & Sons, Ltd.     

Parameter‐dependent Lyapunov function‐based robust iterative learning control for discrete systems with actuator faults

This paper considers iterative learning control for a class of uncertain multiple‐input multiple‐output discrete linear systems with polytopic uncertainties and actuator faults. The stability theory for linear repetitive processes is used to develop control law design algorithms that can be computed using linear matrix inequalities. A class of parameter‐dependent Lyapunov functions is used with the aim of enlarging the allowed polytopic uncertainty range for successful design. The effectiveness and feasibility of the new design algorithms are illustrated by a gantry robot case study. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive robust output‐feedback motion control of hydraulic actuators

Most previous advanced motion control of hydraulic actuators used full‐state feedback control techniques. However, in many cases, only position feedback is available, and thus, there are imperious demands for output‐feedback control for hydraulic systems. This paper firstly transforms a hydraulic model into an output feedback–dependent form. Thus, the K‐filter can be employed, which provides exponentially convergent estimates of the unmeasured states. Furthermore, this observer has an extended filter structure so that online parameter adaptation can be utilized. In addition, it is a well‐known fact that any realistic model of a hydraulic system suffers from significant extent of uncertain nonlinearities and parametric uncertainties. This paper constructs an adaptive robust controller with backstepping techniques, which is able to take into account not only the effect of parameter variations coming from various hydraulic parameters but also the effect of hard‐to‐model nonlinearities such as uncompensated friction forces, modeling errors, and external disturbances. Moreover, estimation errors that come from initial state estimates and uncompensated disturbances are dealt with via certain robust feedback at each step of the adaptive robust backstepping design. After that, a detailed stability analysis for the output‐feedback closed‐loop system is scrupulously checked, which shows that all states are bounded and that the controller achieves a guaranteed transient performance and final tracking accuracy in general and asymptotic output tracking in the presence of parametric uncertainties only. Extensive experimental results are obtained for a hydraulic actuator system and verify the high‐performance nature of the proposed output‐feedback control strategy.     

Improved performance MRAC of linear and non-linear systems

The problem of improved performance adaptive control (IPAC) of a class of linear and non-linear systems is considered. A method for its solution is presented, the main feature of which lies in augmenting the ‘standard’ model reference adaptive controller by a signal properly designed to compensate for the effect of plant parameter uncertainty on the output error. One of the main performance improvement characteristics of the proposed IPAC is that the zero-state output error can be made arbitrarily small under standard model reference adaptive control (MRAC) assumptions in the case of linear systems, while a similar result holds true for a class of linearizable systems as well. the structure of the proposed controller is such that several existing MRAC results, such as exponential convergence of output and parameter errors in the presence of sufficiently rich reference inputs, remain valid. the proposed controller also achieves improved performance in the presence of a class of bounded disturbances and/or unmodelled dynamics as well as in the case of an adaptation switch-off.     

Adaptive guaranteed cost control of a class of uncertain nonlinear systems

This paper proposes an adaptive guaranteed cost control (GCC) method for a class of nonlinear systems with uncertainties, which guarantees the system cost to be bounded by some specified values while adaptively compensating for the effects of uncertainties and nonlinearities in the system dynamics. By Lyapunov's theory and linear matrix inequality techniques, a parameter adaptation law and a sufficient condition for GCC design are derived for a class of uncertain nonlinear systems. Simulation results on a mechanical system with hard nonlinearity show the effectiveness of the proposed method.     

Eigenvalue range determination for interval and parametric matrices

Study of the dynamic behaviour of linear limped parameter circuits or systems under parametric uncertainties is a well‐established research area. The present paper addresses the problem of determining the exact (within rounding errors) ranges for the real and imaginary parts of an eigenvalue of real matrices whose elements are either independent intervals or linear (affine) functions of independent interval parameters. A unified method for solving the above problem is suggested in the paper. It is iterative and reduces to forming and solving, at each iteration, two real (incomplete) quadratic systems to find outer interval bounds on the set of the right and left eigenvectors associated with the eigenvalue considered. The method is applicable if: (i) the solutions of both quadratic systems involved are positive and (ii) the outer interval bounds on the eigenvectors satisfy certain constant sign conditions. It is shown that its numerical complexity is polynomial in the size n of the matrix studied. Numerical examples illustrating the applicability of the new method are provided. Copyright © 2009 John Wiley & Sons, Ltd.     

Parameter estimation for coupled multivariable error models

An adaptive algorithm is developed for estimating the parameters of a linear multivariable error model with coupled dynamics, using estimation errors for coupling inputs. Coupled dynamics in an error equation lead to a new type of error models which have different regressors but the same parameter error. A total cost function is used to derive a desired adaptive law for updating the parameter estimates. As an application, this algorithm is employed for control and identification of multivariable systems with actuator uncertainties. Copyright © 1999 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.     

Adaptive observer design for uncertain nonlinear ODE-PDE cascades

We are revisiting the problem of adaptive observer design for systems that are constituted of an Ordinary Differential Equation (ODE), containing a globally Lipschitz function of the state, and a linear Partial Differential Equation (PDE) of a diffusion–reaction heat type. The ODE and PDE are connected in series and both are subject to parametric uncertainties. In addition to nonlinearity and uncertainty, the system complexity also lies in the fact that no sensor can be implemented at the junction point between the ODE and the PDE. In the absence of parameter uncertainty, nonadaptive state observers are available featuring exponential convergence. However, convergence is guaranteed only under the condition that either the Lipschitz coefficient is sufficiently small or the PDE domain length is sufficiently small. To get around this limitation, and also to account for parameter uncertainty, we develop a design that involves two concatenated adaptive observers, covering the two subintervals of the PDE domain. The proposed design employs one extra sensor, providing the measurement of the PDE state at an inner position close to the ODE-PDE junction point. Both observers are shown to be exponentially convergent, under ad-hoc persistent excitation (PE) conditions, with no limitation on the Lipschitz coefficient and domain length.     

A procedure for designing robust control of systems with bounded uncertain parameters

In recent years, the robust control design problem has drawn considerable attention because it allows one to ensure desirable closed-loop properties in the presence of model uncertainties. As a result, several design methods have been developed. This paper discusses mainly the problem of robust control design of systems with bounded uncertain parameters, and presents a new design method, called “incentive design,” for this design problem. This method is based mainly on such a consideration whereby the designed robust control law can ensure a most favorable value of the cost functional regardless of how the uncertain parameters vary within given bounds. Therefore, in this sense, the existence of the uncertainty in controlled systems has at least no bad effect on the optimal value of the cost functional. This paper gives first the procedure for designing robust control of the systems with bounded uncertain parameters, in general. Then for a class of uncertain linear quadratic systems, a robust control law is designed concretely and a numerical example is presented. It is shown from this derivation and this numerical example that the method proposed in this paper is effective and feasible for some practical control problems with bounded uncertain parameters. The design method developed here may be expected to have some further applications for practical control problems in future.     

A decentralized model following controllers for a class of large‐scale interconnected dynamical systems with uncertainties

The problem of decentralized robust tracking and model following is considered for a class of large‐scale interconnected systems with uncertainties. A class of linear decentralized state feedback controllers are proposed for robust tracking of dynamical signals in such a class of uncertain large‐scale systems. The proposed decentralized tracking controllers can guarantee that the tracking errors between each subsystem and local reference model are uniformly ultimately bounded. Moreover, we modify the linear controllers by introducing some nonlinear parts so that the tracking errors decrease asymptotically to zero in the presence of uncertain parameters and interconnection terms. Finally, an illustrative example is given to demonstrate the validity of our results. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(2): 48–58, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10101     

On‐line parameter estimation for a class of time‐varying continuous systems with bounded disturbances

In this paper, we proposed an on‐line parameter estimation algorithm for a class of time‐varying continuous systems with bounded disturbance. In this method, a novel polynomial approximator with a bounded regressor vector is constructed and utilized to approximate the time‐varying parameters. The direct least‐squares algorithm is employed to acquire the on‐line estimates, so that several useful properties of the direct estimation, such as fast convergence and robustness to the bounded disturbance, are reflected in our method. We have proved that the estimation error of this method is bounded. Furthermore, the bound on the Euclidean norm of the estimation error is derived. The simulation results demonstrate that this method can provide accurate estimates of time‐varying parameters even under the influence of bounded disturbance. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive backstepping control for a class of time delay systems with nonlinear perturbations

The sliding mode control method has been extensively employed to stabilize time delay systems with nonlinear perturbations. Although the resulting closed‐loop systems have good transient and steady‐state performances, the designed controllers are dependent on the time delays. But one knows that it is difficult to obtain the precise delay time in practical systems, especially when it is time varying. In this paper, we revisit the problem and use the backstepping method to construct the state feedback controller. First, a coordinate transformation is used to obtain a cascade time delay system. Then, a linear virtual control law is designed for the first subsystem. The memoryless controller is further constructed based on adaptive method for the second subsystem with the uncertainties bounded by linear function. By choosing new Lyapunov–Krasovskii functional, we show that the system state converges to zero asymptotically. Via the proposed approach, we also discuss the case that the uncertainties are bounded by nonlinear functions. Finally, simulations are done to verify the effectiveness of the main results obtained. Copyright © 2007 John Wiley & Sons, Ltd.     

电力系统非线性鲁棒自适应分散励磁控制设计

利用反步法设计了多机电力系统中的非线性鲁棒自适应励磁控制方案,控制目标是调节发电机功角和频率至稳态运行点的极小领域,并使闭环系统对发电机阻尼系数和电抗参数的不确定性具有自适应能力,且对模型误差和外部有界干扰具备鲁棒性,同时保证各控制器是分散化和本地化的。采用4机系统进行的数字仿真结果表明,实施此方案能有效地提高发电机的功角稳定性。     

Robust quadratic stable dynamic output compensator

In this paper, a new robust quadratic stable dynamic output feedback compensator is introduced and applied to a car steering model subject to parameter uncertainties. Arbitrary-order dynamic output feedback controllers are used together with the robust quadratic stabilization algorithm (RQSA) to attain a family of robust dynamic output compensators. A treatment through solving Lyapunov-like matrix equations and a special state transformation are employed. The RQSA is based only on checking end points of an uncertainty bounding hyperpolyhedron. The combined algorithm is implemented, and the simulations reveal that the new compensator provides more robust, stable and reliable performance under a variety of uncertainties involved in the car steering system model.     

不确定互联电力系统的分散鲁棒控制

针对不确定互联电力系统,提出了一种分散鲁棒输出反馈控制器的设计方法.为了使参数不确定性符合工程实际和简化控制器的求解,引入数值界的形式对不确定性进行描述.该方法将控制器的设计归结为一组矩阵不等式的求解问题,采用同伦迭代算法,通过固定不同的变量,将非线性矩阵不等式转化为两组线性矩阵不等式并交替求解.仿真结果表明所获得的控制器使得互联电力系统鲁棒稳定,阻尼转矩充足,满足给定的性能指标,并且具有良好的抑制大扰动的能力.     

Persistent tracking and identification of regime‐switching systems with structural uncertainties: unmodeled dynamics,observation bias,and nonlinear model mismatch

This work focuses on tracking and system identification of systems with regime‐switching parameters, which are modeled by a Markov process. It introduces a framework for persistent identification problems that encompass many typical system uncertainties, including parameter switching, stochastic observation disturbances, deterministic unmodeled dynamics, sensor observation bias, and nonlinear model mismatch. In accordance with the ‘frequency’ of the parameter switching process, we divide the problems into two classes. For fast‐switching systems, the switching parameters are stochastic processes modeled by irreducible and aperiodic Markov chains. Because accurately tracking real‐time parameters in such systems is not possible because of the uncertainty principles, the effect of parameter switching is evaluated on their average by the stationary distribution of the Markovian chain and estimated by the least squares algorithms. We derive upper and lower bounds on identification errors, which characterize how identification accuracy depends on the earlier uncertainty terms. When the system parameters switch their values infrequently in a probabilistic sense, their values can be tracked based on input/output observations. Stochastic approximation algorithms with adaptive step sizes are used for such systems. Simulation studies are carried out to demonstrate that slowly varying parameters could be tracked with reasonable accuracy.Copyright © 2012 John Wiley & Sons, Ltd.     

Stabilizing SSR oscillations with a shunt reactor controller foruncertain levels of series compensation

The authors demonstrate how frequency-domain techniques based on I. Horowitz et al.'s (1986) quantitative feedback theory can be applied to the design of fixed-parameter controllers in power systems where the plant parameters have large uncertainties. They present the design of a controller for a shunt reactor to eliminate torsional shaft oscillations in a turbogenerator susceptible to subsynchronous resonance (SSR). The considered parameter uncertainty is the series capacitor compensation level, which has been assumed to vary between 12% and 76%. Simulated transients results of the uncontrolled/controlled system are depicted