An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

In this paper, the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A nonlinear adaptive sliding‐mode observer is proposed based on a nonlinear parameter estimation algorithm. It is shown that such a nonlinear algorithm provides a rate of convergence faster than exponential, ie, faster than the classic linear algorithm. Then, the proposed parameter estimation algorithm is included in the structure of a sliding‐mode state observer, providing an ultimate bound for the full estimation error and attenuating the effects of the external disturbances. Moreover, the synthesis of the observer is given in terms of linear matrix inequalities. The corresponding proofs of convergence are developed based on the Lyapunov function approach and input‐to‐state stability theory. Some simulation results illustrate the efficiency of the proposed adaptive sliding‐mode observer.     

A disturbance‐decoupled adaptive observer and its application to faulty parameters estimation of a hydraulically driven elevator

In this paper, a disturbance‐decoupled adaptive observer is designed for the joint state‐parameter estimation of a system with unknown disturbance inputs. The proposed Robust Adaptive Observer (RAO) integrates an Unknown Input Observer (UIO) to the parameter estimation process, where the unknown parameters are estimated as extended states of the system. An auxiliary input is added to the UIO in coping with the estimation errors so that the exponential stability and convergence of the observer are guaranteed. The proposed observer is applied to a hydraulically driven elevator for the faulty parameter estimation. The simulation results show the accuracy of the observer and its robustness to both disturbances and measurement noises. Copyright © 2010 John Wiley & Sons, Ltd.     

一类非线性系统模糊自适应鲁棒控制

针对一类不确定性非线性系统的传统模糊自适应控制方案存在的缺陷,利用第一类模糊逻辑系统直接作为非线性系统控制器,提出了一种模糊自适应鲁棒控制策略.在传统方案的基础上加入鲁棒补偿项,取消监督控制项,进一步放宽稳定条件到最小近似误差有界,利用Lyapunov稳定性理论证明了系统的全局稳定性.通过对二阶混沌对象仿真结果表明,鲁棒控制有效地补偿了稳态误差,解决了单一模糊自适应控制寻优空间有限问题.     

An adaptive observer for joint estimation of states and parameters in both state and output equations

An adaptive observer is a recursive algorithm for joint state–parameter estimation of parameterized state‐space systems. Previous works on globally convergent adaptive observers consider unknown parameters either in state equations or in output equations, but not in both of them. In this paper, a new adaptive observer is designed for linear time‐varying systems with unknown parameters in both state and output equations. Its global convergence for simultaneous estimation of states and parameters is formally established under appropriate assumptions. A numerical example is presented to illustrate the performance of this adaptive observer. Copyright © 2011 John Wiley & Sons, Ltd.     

Globally asymptotic adaptive controller/observer for tracking in robots without velocity measurement

In this work, we present an adaptive observer/controller for a multiple degree of freedom robotic plant without velocity measurement and without knowledge of plant parameter values. For this considered plant, we propose and present an adaptive observer/controller that estimates or observes the velocity and drives the position tracking error to zero. We prove that the combined tracking error and observer error converges to zero globally asymptotically and that all closed‐loop signals remain bounded. A contribution of the present paper, as compared with previous work for this same plant, can be deemed to be the fact that, to the best of our knowledge, the present paper is the first proven globally asymptotic result for this plant for which the size of the control torque does not increase exponentially with respect to the size of the tracking error. The control torque is discontinuous, however, only at isolated time instants. No sliding modes are used. Copyright © 2011 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.     

Hamilton‐based adaptive robust control for the speed and tension system of reversible cold strip rolling mill

The adaptive robust control problem for the speed and tension system of reversible cold strip rolling mill is studied based on the Hamilton theory in this paper. First, the dissipative Hamilton model of the rolling mill system's speed and tension outside loop is built through pre‐feedback control, and then, dissipative Hamilton controllers are designed by utilizing the interconnection and damping assignment and the energy shaping method. Second, in order to realize tensiometer‐free control and adaptive robust control for the perturbation parameters and load disturbance, full‐order state observers and adaptive robust controllers are designed for the rolling mill system's speed and tension outside loop by using the “extended system + feedback” method. Third, robust controllers for the rolling mill system's current inside loop are designed based on the cascade control thought, so as to realize the tracking control for the speed and tension of reversible cold strip rolling mill. Theoretical analyses show that the resulting closed‐loop system is stable. Finally, simulation research is carried out on the speed and tension system of a 1422‐mm reversible cold strip rolling mill, and simulation results verify the validity of the proposed control strategy in comparison with the decentralized overlapping control strategy.     

Finite‐model adaptive control using an LS‐like algorithm

Adaptive control problem of a class of discrete‐time nonlinear uncertain systems, of which the internal uncertainty can be characterized by a finite set of functions, is formulated and studied by using an least squares (LS)‐like algorithm to design the feedback control law. For the finite‐model adaptive control problem, this algorithm is proposed as an extension of counterpart of traditional LS algorithm. Stability in sense of pth mean for the closed‐loop system is proved under a so‐called linear growth assumption, which is shown to be necessary in general by a counter‐example constructed in this paper. The main results have been also applied to parametric cases, which demonstrate how to bridge the non‐parametric case and parametric case. Copyright © 2006 John Wiley & Sons, Ltd.     

A study on higher‐order disturbance observer and robust stability

In earlier papers, it has been reported that a fast and precise servo system, which has low sensitivity to parameter variation and disturbance, can be realized with simple structure by using a high‐order disturbance observer. However, no clear and simple design method satisfying specifications for robust stability, the influence of measurement noise, and relative stability (damping characteristics) for large parameter variation has been proposed. In this paper, we clarify the class of robust servo systems realized by adjusting the order of the disturbance observer and the control parameters. We apply this strategy to the design of a second delay system, such as a position servo system, and realize a high‐performance robust servo system using a high‐order disturbance observer. © 1999 Scripta Technica, Electr Eng Jpn, 128(1): 37–44, 1999     

Adaptive observer for nonlinear fractional‐order systems

In this paper, an adaptive observer is proposed for the joint estimation of states and parameters of a fractional nonlinear system with external perturbations. The convergence of the proposed observer is derived in terms of linear matrix inequalities (LMIs) by using an indirect Lyapunov method.The proposed adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü's systems. Copyright © 2016 John Wiley & Sons, Ltd.     

LMI‐based adaptive output feedback fault‐tolerant controller design for nonlinear systems

This paper presents 2‐novel linear matrix inequality (LMI)‐based adaptive output feedback fault‐tolerant control strategies for the class of nonlinear Lipschitz systems in the presence of bounded matched or mismatched disturbances and simultaneous occurrence of actuator faults, including failure, loss of effectiveness, and stuck. The constructive algorithms based on LMI with creatively using Lyapunov stability theory and without the need for an explicit information about mode of actuator faults or fault detection and isolation mechanism are developed for online tuning of adaptive and fixed output‐feedback gains to stabilize the closed‐loop control system asymptotically. The proposed controllers guarantee to compensate actuator faults effects and to attenuate disturbance effects. The resulting control methods have simpler structure, as compared with most existing recent methods and more suitable for practical systems. The merits of the proposed fault‐tolerant control scheme have been verified by the simulation on nonlinear Boeing 747 lateral motion dynamic model subjected to actuator faults.     

Robust adaptive estimation of nonlinear system with time‐varying parameters

The vast majority of available parameter estimation methods assume that the parameters to be estimated are constant or slowly time‐varying and mainly depend on a predictor or observer design so that a large adaptive gain must be used to achieve fast adaptation; this may result in high‐frequency oscillations when the system subjects to a large source of uncertainties or disturbances. This paper is concerned with adaptive online estimation of time‐varying parameters for two kinds of linearly parameterized nonlinear systems. By dividing the time into small intervals, the time‐varying parameters are approximated in terms of polynomials with unknown coefficients. Then a novel adaptive law design methodology is developed to estimate those constant coefficients, for which the parameter estimation error information is explicitly derived and used to drive the adaptations. To guarantee the continuity of the parameter estimation for all time, a parameter resetting scheme is introduced at the beginning of each interval. Finite‐time estimation convergence and the robustness against disturbances are all proved. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms for estimating time‐varying parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

Performance improvement of induction motor speed sensor‐less vector control system using an adaptive observer with an estimated flux feedback in low‐speed range

Because of various errors caused by the dead time of an inverter, temperature variation of resistances, and so on, speed estimation error is inevitable in speed sensor‐less vector control of an induction motor. In particular, the speed control loop becomes unstable at near‐zero frequencies. In order to solve these problems, this paper proposes a novel design of an adaptive observer for speed estimation. By adding a feedback loop of the error between the estimated flux and the flux command, the sensitivity of speed estimation and primary resistance identification is improved. The proposed system is analyzed and appropriate feedback gains are derived. Experimental results showed good performance in the low‐speed range. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 169(3): 33–46, 2009; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/eej.20909     

Adaptive observer for a class of nonlinear systems with time‐varying delays

The adaptive observer design problems have been extensively studied in literature for both linear and nonlinear systems. Some researches have also been carried out on adaptive observer design for linear time‐delay systems, but there is no significant work on adaptive observer design for nonlinear time‐delay systems. In this work, the adaptive observer design problem for a class of nonlinear time‐delay systems is considered. The observer is designed for the nonlinear systems whose nonlinear functions satisfy Lipschitz condition. Like conventional adaptive observers for the systems without time delays, this observer also estimates both states and unknown parameters simultaneously. For this property, it will be very much useful for many real‐time systems where time delays cannot be avoided. The sufficient conditions for existence of the observer are derived using the linear matrix inequality approach. With the help of a numerical example, effectiveness of the proposed observer is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiple‐model adaptive robust dynamic surface control with estimator resetting

A multiple‐model adaptive robust dynamic surface control with estimator resetting is investigated for a class of semi‐strict feedback nonlinear systems in this paper. The transient performance is mainly considered. The multiple models are composed of fixed models, one adaptive model, and one identification model that can be obtained when the persistent exciting condition is satisfied. The transient performance of the final tracking system can be improved significantly by designing proper switching mechanism during the parameter tuning procedure. The semi‐globally uniformly ultimately bounded stability of the closed‐loop system can be easily achieved because of the framework of adaptive robust dynamic surface control. Numerical examples are provided to demonstrate the effectiveness of the proposed multiple‐model controller. Copyright © 2014 John Wiley & Sons, Ltd.     

Less conservative criteria for fault accommodation of time‐varying delay systems using adaptive fault diagnosis observer

This paper studies the problem of fault accommodation of time‐varying delay systems using adaptive fault diagnosis observer. Based on the proposed fast adaptive fault estimation (FAFE) algorithm using only a measured output, a delay‐dependent criteria is first established to reduce the conservatism of the design procedure, and the FAFE algorithm can enhance the performance of fault estimation. On the basis of fault estimation, the observer‐based fault‐tolerant tracking control is then designed to guarantee tracking performance of the closed‐loop systems. Furthermore, comprehensive analysis is presented to discuss the calculation steps using linear matrix inequality technique. Finally, simulation results of a stirred tank reactor model are presented to illustrate the efficiency of the proposed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Extended disturbance observer for nonlinear system with time-varying disturbance gain

In control engineering, the disturbance is a major problem that deteriorates system robustness. To address this problem, a disturbance observer (DOB) has been proposed and developed. In particular, a general method of estimating high-order disturbance, expressed as a time series expansion, was studied (H-DOB). However, systems to which H-DOB are applicable are limited to those in which disturbance gain is constant. This constraint degrades the generality of H-DOB because applicable systems are limited. Therefore, by expanding to a system with a time-varying disturbance gain, we propose a more general H-DOB. The DOB proposed in this paper redesigns the dynamics of the observer based on the structure of the H-DOB. The proposed DOB is applicable even if the system is highly nonlinear. This paper verifies the convergence of the proposed DOB through proof. Using this proof, the same characteristic error dynamics can be obtained, so the same design method can be applied. The simulation for the verification of the proposed method performs disturbance estimation of the extension system. This simulation proves that, compared to H-DOB, the proposed DOB has good disturbance estimation performance.     

Reduced‐order robust adaptive control design of uncertain SISO linear systems

In this paper, a stability and robustness preserving adaptive controller order‐reduction method is developed for a class of uncertain linear systems affected by system and measurement noises. In this method, we immediately start the integrator backstepping procedure of the controller design without first stabilizing a filtered dynamics of the output. This relieves us from generating the reference trajectory for the filtered dynamics of the output and thus reducing the controller order by n, n being the dimension of the system state. The stability of the filtered dynamics is indirectly proved via an existing state signal. The trade‐off for this order reduction is that the worst‐case estimate for the expanded state vector has to be chosen as a suboptimal choice rather than the optimal choice. It is shown that the resulting reduced‐order adaptive controller preserves the stability and robustness properties of the full‐order adaptive controller in disturbance attenuation, boundedness of closed‐loop signals, and output tracking. The proposed order‐reduction scheme is also applied to a class of single‐input single‐output linear systems with partly measured disturbances. Two examples are presented to illustrate the performance of the reduced‐order controller in this paper. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust adaptive control for non‐linear systems in generalized output‐feedback canonical form

Design of global robust adaptive output‐feedback dynamic compensators for stabilization and tracking of a class of systems that are globally diffeomorphic into systems in generalized output‐feedback canonical form is investigated. This form includes as special cases the standard output‐feedback canonical form and various other forms considered previously in the literature. Output‐dependent non‐linearities are allowed to enter both additively and multiplicatively. The system is allowed to contain unknown parameters multiplying output‐dependent non‐linearities and, also, unknown non‐linearities satisfying certain bounds. Under the assumption that a constant matrix can be found to achieve a certain property, it is shown that a reduced‐order observer and a backstepping controller can be designed to achieve practical stabilization of the tracking error. If this assumption is not satisfied, it is shown that the control objective can be achieved by introducing additional dynamics in the observer. Sufficient conditions under which asymptotic tracking and stabilization can be achieved are also given. This represents the first robust adaptive output‐feedback tracking results for this class of systems. Copyright © 2003 John Wiley & Sons, Ltd.     

Low‐complexity robust adaptive generalized sidelobe canceller detector for DS/CDMA systems

A novel low computational complexity robust adaptive blind multiuser detector, based on the minimum output energy (MOE) detector with multiple constraints and a quadratic inequality (QI) constraint is developed in this paper. Quadratic constraint has been a widespread approach to improve robustness against mismatch errors, uncertainties in estimating the data covariance matrix, and random perturbations in detector parameters. A diagonal loading technique is compulsory to achieve the quadratic constraint where the diagonal loading level is adjusted to satisfy the constrained value. Integrating the quadratic constraint into recursive algorithms seems to be a moot point since there is no closed‐form solution for the diagonal loading term. In this paper, the MOE detector of DS/CDMA system is implemented using a fast recursive steepest descent adaptive algorithm anchored in the generalized sidelobe canceller (GSC) structure with multiple constraints and a QI constraint on the adaptive portion of the GSC structure. The Lagrange multiplier method is exploited to solve the QI constraint. An optimal variable loading technique, which is capable of providing robustness against uncertainties and mismatch errors with low computational complexity is adopted. Simulations for several mismatch and random perturbations scenarios are conducted in a rich multipath environment with near–far effect to explore the robustness of the proposed detector. Copyright © 2008 John Wiley & Sons, Ltd.