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.     

Adaptive robust control of a class of nonlinear systems in semi‐strict feedback form with non‐uniformly detectable unmeasured internal states

This paper proposes a novel control method for a special class of nonlinear systems in semi‐strict feedback form. The main characteristic of this class of systems is that the unmeasured internal states are non‐uniformly detectable, which means that no observer for these states can be designed to make the observation error exponentially converge to zero. In view of this, a projection‐based adaptive robust control law is developed in this paper for this kind of system. This method uses a projection‐type adaptation algorithm for the estimation of both the unknown parameters and the internal states. Robust feedback term is synthesized to make the system robust to uncertain nonlinearities and disturbances. Although the estimation error for both the unknown parameters and the internal states may not converge to zero, the tracking error of the closed‐loop system is proved to converge to zero asymptotically if the system has only parametric uncertainties. Furthermore, it is theoretically proved that all the signals are bounded, and the control algorithm is robust to bounded disturbances and uncertain nonlinearities with guaranteed output tracking transient performance and steady‐state accuracy in general. The class of system considered here has wide engineering applications, and a practical example—control of mechanical systems with dynamic friction—is used as a case study. Simulation results are obtained to demonstrate the applicability of the proposed control methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Adaptive fuzzy output feedback backstepping control of pure‐feedback nonlinear systems via dynamic surface control technique

In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure‐feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Passivity‐based control for stabilization,regulation and tracking purposes of a class of nonlinear systems

In this paper, a new passivity‐based control (PBC) scheme based on state feedback is proposed in order to solve tracking, regulation and stabilization problems for a class of multi‐input multi‐output (MIMO) nonlinear systems expressed in the normal form, with time‐invariant parameters and locally bounded reference weakly minimum phase. For the proposed control scheme two new different state feedbacks, one non‐adaptive for the case when the system parameters are assumed to be known and the other adaptive for the case of unknown parameters, are developed. For the adaptive case it is assumed that the unknown parameters appear linearly in the equations. Analysis of the transient behaviour of the proposed control schemes is presented through the simulation of two examples. Copyright © 2006 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.     

Robust stabilization of a class of non‐minimum‐phase nonlinear systems in a generalized output feedback canonical form

In this paper, a globally robust stabilizer for a class of uncertain non‐minimum‐phase nonlinear systems in generalized output feedback canonical form is designed. The system contains unknown parameters multiplied by output‐dependent nonlinearities and output‐dependent nonlinearities enter such a system both additively and multiplicatively. The proposed method relies on a recently developed novel parameter estimator and state observer design methodology together with a combination of backstepping and small‐gain approach. Our design has three distinct features. First, the parameter estimator and state observer do not necessarily follow the classical certainty‐equivalent principle any more. Second, the design treats unknown parameters and unmeasured states in a unified way. Third, the technique by combining standard backstepping and small‐gain theorem ensures robustness with respect to dynamic uncertainties. Finally, two numerical examples are given to show that the proposed method is effective, and that it can be applied to more general systems that do not satisfy the cascading upper diagonal dominance conditions developed in recent papers, respectively. Copyright © 2008 John Wiley & Sons, Ltd.     

Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

This paper investigates the adaptive quasi‐passification‐based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasi‐passification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi‐passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods.     

Distributed output estimation error observer-based adaptive fault-tolerant consensus tracking control of multi-agent systems

The purpose of this study is to discuss the fully distributed design of output estimation error observer and fault-tolerant consensus tracking control for a class of multi-agent systems with Lipschitz nonlinear dynamics and actuator faults. Firstly, based on the relative output measurements of neighboring agents, the distributed output estimation error observer is developed to adaptively estimate the state and fault information of each agent, and further overcome the difficulties of online updating the adaptive estimations of unknown hyper-parameters. Secondly, to achieve the state consensus tracking goal and compensate for the negative effects of actuator faults, the distributed fault-tolerant consensus tracking control scheme is proposed on the basis of the state estimation and adaptive fault estimation information, and has excellent robustness and consensus tracking control performance. Moreover, sufficient criteria can ensure that consensus tracking error of each agent converges to a small set near the origin. Finally, numerical simulations are provided to show the effectiveness of the proposed fully distributed algorithm.     

Robust adaptive output‐feedback control for a class of nonlinear systems with hysteresis compensation controller

In this paper, a robust adaptive output‐feedback dynamic surface control scheme is proposed for a class of single‐input single‐output nonlinear systems preceded by unknown hysteresis with the following features: (1) a hysteresis compensator is designed in the control signal to compensate the hysteresis nonlinearities with only the availability of the output of the control system; (2) by estimating the norm of the unknown parameter vector and the maximum value of the hysteresis density function, the number of the estimated parameters is reduced, which implies that the computational burden is greatly reduced; (3) by introducing the initializing technique, the initial conditions of the state observer and adaptive laws of unknown parameters can be properly chosen, and the arbitrarily small norm of the tracking error is achieved. It is proved that all the signals in the closed‐loop system are ultimately uniformly bounded and can be arbitrarily small. Simulation results show the validity of the proposed scheme.     

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.     

State estimation and simultaneous unknown input and measurement noise reconstruction based on associated observers

This paper considers the problems of the state estimation and the simultaneous unknown input and measurement noise reconstruction when the observer matching condition is not satisfied. A new augmented system is constructed by introducing a new augmented state vector. An auxiliary output vector is proposed to deal with the observer matching condition issues, and a high‐order sliding mode observer is considered to get the exact estimates of both the auxiliary outputs and their derivatives in a finite time. A reduced‐order observer is developed to asymptotically estimate the system states, and a kind of reconstruction method of the new system's unknown inputs is proposed to reach the goal of reconstructing the original system's unknown input and measurement noise. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Extremum seeking-based observer design for reduced order models of coupled thermal and fluid systems

We present an extremum seeking (ES)-based robust observer design for thermal-fluid systems, pursuing an application to efficient energy management in buildings. The model is originally described by Boussinesq equations which is given by a system of two coupled partial differential equations (PDEs) for the velocity field and temperature profile constrained to incompressible flow. Using proper orthogonal decomposition, the PDEs are reduced to a set of nonlinear ordinary differential equations. Given a set of temperature and velocity point measurements, a nonlinear state observer is designed to reconstruct the entire state under the error of initial states, and model parametric uncertainties. We prove that the closed loop system for the observer error state satisfies an estimate of L₂ norm in a sense of locally input-to-state stability with respect to parameter uncertainties. Moreover, the uncertain parameters estimate used in the designed observer are optimized through iterations of a data-driven ES algorithm. Numerical simulation of a two-dimensional Boussinesq PDE illustrates the performance of the proposed adaptive estimation method.     

Fault estimation and accommodation for networked control systems with nonuniform sampling periods

This paper deals with the problem of fault estimation and accommodation for a class of networked control systems with nonuniform uncertain sampling periods. Firstly, the reason why the adaptive fault diagnosis observer cannot be applied to networked control systems is analyzed. Based on this analysis, a novel robust fault estimation observer is constructed to estimate both continuous‐time fault and system states by using nonuniformly discrete‐time sampled outputs. Furthermore, using the obtained states and fault information, a nonuniformly sampled‐data fault tolerant control law is designed to preserve the stability of the closed‐loop system. The proposed scheme can not only guarantee the impact of continuous‐time uncertainties and discrete‐time sampled estimation errors on the faulty system to satisfy a H _∞ performance index but also repress the negative effect of the unknown intersample behavior of continuous‐time fault by use of an inequality technique. Finally, simulation results are included to demonstrate the feasibility of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Dual high‐gain‐based adaptive output‐feedback control for a class of nonlinear systems

We propose an adaptive output‐feedback controller for a general class of nonlinear triangular (strict‐feedback‐like) systems. The design is based on our recent results on a new high‐gain control design approach utilizing a dual high‐gain observer and controller architecture with a dynamic scaling. The technique provides strong robustness properties and allows the system class to contain unknown functions dependent on all states and involving unknown parameters (with no magnitude bounds required). Unlike our earlier result on this problem where a time‐varying design of the high‐gain scaling parameter was utilized, the technique proposed here achieves an autonomous dynamic controller by introducing a novel design of the observer, the scaling parameter, and the adaptation parameter. This provides a time‐invariant dynamic output‐feedback globally asymptotically stabilizing solution for the benchmark open problem proposed in our earlier work with no magnitude bounds or sign information on the unknown parameter being necessary. Copyright © 2007 John Wiley & Sons, Ltd.     

Output feedback adaptive command following and disturbance rejection for nonminimum phase uncertain dynamical systems

In this paper, we develop an output feedback adaptive control framework for continuous‐time nonminimum phase multivariable systems for output stabilization, command following, and disturbance rejection. The approach is based on a nonminimal state space realization that generates an expanded set of states using the filtered inputs and filtered outputs and their derivatives of the original system. Specifically, a direct adaptive controller for the nonminimal state space model is constructed using the expanded states of the nonminimal realization and is shown to be effective for multi‐input, multi‐output nonminimum phase systems with unstable dynamics. The adaptive controller does not require any model information nor does it require information of the system poles and system zeros or estimation of the system Markov parameters. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

This paper considers the problem of adaptive fuzzy output‐feedback tracking control for a class of switched stochastic nonlinear systems in pure‐feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states. Based on these methods, an adaptive fuzzy output‐feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method.