Adaptive Observer Design Research Articles

A Note on Adaptive Observer Design Method for One-Sided Lipschitz Systems

The design problem of adaptive observer for one-sided Lipschitz systems with unknown parameters is addressed. The research focuses on the nonlinear system dynamics which only satisfies one-sided Lipschitz, but not quadratic inner-boundedness. Firstly, an adaptive full-order observer is constructed. Specially, when the one-sided Lipschitz constant is negative, this observer can also be designed. By using the decomposition method, a reduced-order observer is constructed under the same assumptions. The validity of designed observers is illustrated via two examples at last.

Adaptive Full-Order Observer Analysis and Design for Sensorless Interior Permanent Magnet Synchronous Motors Drives

This article proposes a straightforward design guideline and analysis of adaptive full-order observers for rotor position and speed estimation of interior permanent magnet synchronous motors (IPMSM) sensorless drives. The adaptive observer is built upon the IPMSM extended electromotive force model in the stationary reference frame. The design of the adaptation and feedback gains is performed by a cascade approach, where state observer and adaptive law operate at distinct frequencies. Since speed estimation error impacts the system stability, this issue is the focus of the high-bandwidth state observer design. On the other hand, the adaptive feedback loop, which operates at lower frequencies, ensures good rotor speed estimation performance. The effect of synchronous inductances and stator resistance variation on the estimation of the mechanical variables is investigated and analytically described. Experimental results validate the adaptive observer design method and the parameter variation analysis under sensorless vector control.

Output Control by Linear Time-Varying Systems using Parametric Identification Methods

In this paper the problem of control for time-varying linear systems by the output (i.e. without measuring the vector of state variables or derivatives of the output signal) was considered. For the control design, the well-known online procedure for solving the Riccati matrix differential equation is chosen. This procedure involves the synthesis of linear static feedbacks on state variables in the case of known parameters of the plant. If state variables are not measured, then for the observer design using the matrix Riccati differential equation, using the dual scheme, which provides for the transposition of the state matrix and the replacement of the input matrix by the output matrix. It is well known that an observer of state variables built on the basis of a solution of the Riccati matrix differential equation ensures the exponential stability of a closed loop system in the case of uniform observability. Despite the fact that this type of observer can be classified as universal, its have a number of significant drawbacks. The main problem of such observers is the need for accurate knowledge of the parameters and the requirement for uniform observability, which in practice cannot always be realized. Thus, the problem of the new methods design for constructing observers of state variables of linear non-stationary systems is still relevant. Some time ago, a number of methods for the adaptive observers design of state variables for nonlinear systems were proposed. The main idea of the synthesis of observers was based on the transformation of the original dynamic system to a linear regression model containing unknown parameters, which in turn were functions of the initial conditions of the state variables of the control object. This approach in the English language literature is called PEBO. This paper, based on the PEBO method, proposes a new approach for the observers design of state for non-stationary systems. This approach provides the possibility of obtaining monotonic convergence estimates with transient time tuning.

Adaptive Sampled-Data Observer Design for a Class of Nonlinear Systems with Unknown Hysteresis

In this paper, a novel adaptive sampled-data observer design is studied for a class of nonlinear systems with unknown Prandtl–Ishlinskii hysteresis and unknown unmatched disturbances based on radial basis function neural networks (RBFNNs). To begin with, we investigate a sampled-data nonlinear system and present sufficient conditions such that the sampled-data nonlinear system is ultimately uniformly bounded (UUB). Then, an adaptive sampled-data observer is designed to estimate the unknown states of the nonlinear system. The unknown hysteresis and the unknown disturbances are approximated by RBFNNs. We also give the learning laws of the weights of RBFNNs, and prove that the estimation errors of the states and the weights are UUB, based on the obtained sufficient conditions and a special constructing Lyapunov–Krasovskii function. Finally, the effectiveness of the proposed design method is verified by numerical simulations.

Fault Detection of Areo-engine Actuator Based on Adaptive Radial Basic Function Observer

Aiming at the fault detection problem of aero-engine actuators, a fault diagnosis method for aero-engine actuators based on adaptive RBF network observer is proposed. Firstly, the system model is established for the faulty actuator, and then the observer-based actuator fault diagnosis principle is established. Secondly, for the problem that the traditional observer is not sensitive to the gradual fault, the nonlinear approximation characteristics of the RBF network are used. The adaptive fault observer design method based on RBF network is applied. At the same time, the sufficient conditions for the convergence of the observer error system are given by using the Lyapunov stability analysis method. Finally, the simulation experiments of different types of actuators for a turbofan engine are carried out. The results show that the adaptive RBF observer designed in this paper is more effective in detecting faults and has certain fault estimation ability.

Output based bilateral adaptive control of partially known robotic systems

This paper describes the design and implementation of a robust adaptive bilateral observer based control to solve the trajectory tracking problem for a class of master–slave robotic systems. The output-based bilateral control uses an adaptive observer to estimate the force and the unmeasurable velocity state considering only the master–slave system order as well as the position measurements. The stability of the observer and controller is simultaneously proved via the second method of Lyapunov. A set of experimental tests proved the performance of the presented algorithm for a manipulation task in a bilateral teleoperated system based on two delta robots.

Adaptive disturbance observer for trajectory tracking control of underwater vehicles

Complex and highly coupled dynamics, time-variance, unpredictable disturbances and lack of knowledge of hydrodynamic parameters, complicate the control of underwater vehicles. This paper deals with the adaptive disturbance observer design for the robust trajectory tracking problem for underwater vehicles in presence of unknown external disturbances and parametric uncertainties. First, the dynamics of the vehicle is transformed into the so-called regular form. Then, based on the Extended State Observer technique and High Order Sliding Modes Control, a disturbance observer is proposed. Furthermore, the gains of the observer are automatically adjusted by the introduction of an adaption law. The stability of the whole controller/observer scheme is proven using Lyapunov’s arguments. The adaptive disturbance observer aims to improve the Backstepping and nonlinear PD controllers. Real-Time experiments demonstrate the effectiveness of the proposed algorithm for the trajectory tracking task under several scenarios.

Switched adaptive observers design for a class of switched uncertain nonlinear systems

In this paper, a switched adaptive observer for a class of switched uncertain nonlinear systems is designed by using an average dwell time (ADT) method. Due to that switching unknown parameters lead to different coordinates transformation for different subsystems, some new dwell-time conditions are provided by an improved ADT method. Also, the boundedness of all signals is ensured by a well defined persistent excitation condition under a class of switching signals with ADT. Finally, the effectiveness of the theoretical results in this paper is demonstrated through a simulation example.

Adaptive boundary observer design for linear hyperbolic systems; Application to estimation in heat exchangers

In this work, we consider the estimation of temperature along the pipes of concentric heat exchanger tubes in which CO2 is the working fluid. The transport phenomenon is modeled using (2x2) linear hyperbolic partial differential equations, with one rightward equation for the hot flow and one leftward equation for the cold flow. Both flows exchange energy through the wall interface, which physically induces a coupling between the two dynamics. Our objective is to estimate the temperature distribution along the flows from measurements at the tubes boundaries only. In this framework, we propose an adaptive boundary observer that can estimate not only the full state of the system, but also unknown in-domain parameters. The design is based on transforming the error system via a finite-dimensional backstepping-like transformation into a desired filter-based system, for which standard backstepping observer techniques and adaptation laws can be used. The theoretical results are evaluated against the temperature measurements taken from a CO2 refrigeration apparatus built at CERN, Switzerland.

Adaptive Nonlinear Observer Design via a Polytopic Split of Signals

Abstract This paper provides a novel solution for adaptive observer design based on a polytopic representation of the error system. Thanks to a recently appeared factorisation, the proposal is able to deal with fully nonlinear system matrices and nonlinear outputs while dropping conditions on Lipschitz bounds and persistence of excitation. Examples are provided that illustrate the effectiveness and advantages of the new methodology over former approaches.

Adaptive Boundary Observer Design for coupled ODEs-Hyperbolic PDEs systems

We consider the state estimation of ηξ hyperbolic PDEs coupled with ηX ordinary differential equations at the boundary. The hyperbolic system is linear and propagates in the positive x-axis direction. The ODE system is linear time varying (LTV) and includes a set of ηθ unknown constant parameters, which are to be estimated simultaneously with the PDE and the ODE states using boundary sensing. We design a Luenberger state observer, and our method is mainly based on the decoupling of the PDE estimation error states from that of the ODEs via swapping design. We then derive the observer gains through the Lyapunov analysis of the decoupled system. Furthermore, we give sufficient conditions of the exponential convergence of the adaptive observer through differential Lyapunov inequalities (DLIs) and we illustrate the theoretical results by numerical simulations.

Robust adaptive unknown input observer design for a class of disturbed systems

This paper proposes a novel approach for designing a robust adaptive unknown input observer (UIO) for a class of nonlinear system. The system is composed of nonlinear terms and exogenous disturbance and fault signals which are considered to be unknown. The main contribution of the paper is to present the UIO system that uses adaptive law and linear matrix inequality (LMI). Adaptive law is used for system current fault estimation and LMI is used to provide the feasible set of responses while ensuring system stability. The effectiveness of the proposed method is shown by applying to the numerical examples. The simulation results show the validity of this method for a nonlinear system with unknown upper bound disturbance.

A Continuous-discrete Adaptive Observer Design for Nonlinear Systems Subject to Sensor Nonlinearities

In this paper, we address the problem of nonlinear continuous-discrete adaptive observer design for a class of system with sampled data measurements subject to sensor nonlinearities. The main difficulty of the considered class of system is coming from the fact that the output equation contains unknown parameters which renders the design of a classical sampled data observer difficult. To overcome this difficulty, we propose a new online continuous-discrete adaptive observer which ensures a simultaneous exponential convergence of both states and parameters. Comparing to other observer structures, our design is characterized by a simpler structure thanks to the introduction of a parametric adaptation law. To show the efficiency of our proposed approach, numerical simulations have been performed for different values of sampling time. In addition, the delayed-sampled measurements case is also illustrated.

Application of Adaptive Observer to Sensorless Induction Motor via Parameter-Dependent Transformation

This brief addresses the adaptive observer design problem for sensorless induction motor (IM) drives with unknown resistances. In the literature, difficulty is found when applying several well-developed adaptive observer designs to IM dynamics. Hence, by introducing a parameter-dependent transformation, in the new coordinate, the IM dynamics manifest the attributes that facilitate the adaptive observer design. Although the classic designs that require linear-in-parameters result in overparameterization, the proposed nonlinearly parameterized adaptive observer demonstrates a good performance, as illustrated by the simulation and experimental results.

Pole Placement Design Methodology of Back-EMF Adaptive Observer for Sensorless PMSM Drives

This paper proposes a gain design methodology for adaptive observers applied to the estimation of rotor speed of permanent magnet synchronous machines (PMSM). First, a disturbance observer is used for estimation of the back-electromotive force (back-EMF) and avoid undesired nonlinearities in the adaptive observer design. The rotor speed is estimated by a back-EMF adaptive observer based on the PMSM linear model in stationary frame. Both feedback and adaptive gains are analyzed considering the full system in state space form. A pole placement technique is used to design the adaptive and feedback gains, and the mathematical behavior of the speed estimator is obtained. The desired pole locations of the observer are discussed aiming the implementation of a sensorless control scheme. Simulation and experimental results are presented to validate the proposed gain design method.

Lyapunov Theory Based Adaptive Neural Observers Design for Aircraft Sensors Fault Detection and Isolation

In this research, two novel online fault detection algorithms are proposed for sensor faults in aircraft. Radial basis function neural network (RBFNN) is used as a fault detection technique, for weight updating parameters adaptive learning rates are used instead of fixed learning rates, two different adaptive learning rate strategies are proposed based on Lyapunov functions which are compared to Extended Kalman Filter (EKF) algorithm. Boeing 747–100/200 aircraft is used for testing and validation of these algorithms. All algorithms have the ability to detect various types of faults such as simultaneous, intermittent, abrupt and incipient with high preciseness and accuracy occur in aircraft sensors. The capability of sensors fault detection of all algorithms are compared, it is proved that all algorithms have the ability to detect faults but Lyapunov function theory II based algorithm is more efficient and having a fast response in faults detection as compared to Lyapunov function theory I and EKF based algorithms. It is also proved that the Lyapunov function theory II based algorithm is more effective in reducing the computational time and computation load.

Adaptive Observer Design for Sensor Fault Detection and Reconstruction

A new approach is presented for sensor fault detection reconstruction and state estimation. The system considered is linear polytopic parameter-vary ing (LPV) system. The main idea is the design of a novel robust adaptive observer based on and polyquadratic formulation with a new set of relaxation. Sufficient conditions are given by a set of Linear Matrix Inequalities (LMI) in order to guarantee the stability of the system and the asymptotic convergence of the fault error. A simulation example has been studied to illustrate the proposed methods by detecting constant and variable sensor fault.

Adaptive state-dependent impulsive observer design for nonlinear deterministic and stochastic dynamics with time-delays

The present research has introduced a novel adaptive state-dependent impulsive observer (ASDIO) used to control diverse nonlinear systems with time-varying delay. This designed ASDIO is in conformity with the approach of extended pseudo-linearization for the purpose of parametrizing a nonlinear system with time-delay to a pseudo-linear time-delay structure having state-dependent coefficients. This technique makes the ASDIO applicable to nonlinear systems with distributed, multiple, and time-varying delays. The time-varying and delay-independent Lyapunov functional approach, coupled with the comparison method for impulsive systems, was used to confirm the stability of ASDIO. This new theorem affirmed the state and parameter estimation error to approach zero asymptotically through distinct and less-conservative adequate conditions with respect to practical linear matrix inequalities. Furthermore, the maximum impulse time was specified via the presented stability theorem. The ASDIO has also been offered for a special set of stochastic nonlinear systems with time-delay. An investigation of the asymptotic stability for the intended ASDIO was performed via a new theorem employing the comparison principle for stochastic impulsive systems. Accordingly, this observer was simulated on an epidemic system with time-delay nonlinear features to affirm its performance.

Adaptive Sliding Mode Observer Design for a Class of T–S Fuzzy Descriptor Fractional Order Systems

This paper investigates the problem of sliding mode observer (SMO) design for Takagi-Sugeno (T-S) fuzzy descriptor fractional order systems (FOSs) with fractional order $0<; \alpha <; 1$. First, an SMO is designed for the T-S fuzzy descriptor FOS. Then, a fuzzy fractional order integral-type sliding surface is constructed. By utilizing the fuzzy sliding surface, the assumption that all local input matrices are identical in most existing results about sliding mode control (SMC) for T-S fuzzy systems, can be removed. Then, a new sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the admissibility of the sliding mode dynamics. Moreover, adaptive SMC strategy is used such that the reachability condition can be guaranteed. Finally, three examples are given to verify the effectiveness of our results.

Adaptive State Observers for Incrementally Quadratic Nonlinear Systems with Application to Chaos Synchronization

This paper is concerned with the problem of adaptive state observer design for a class of incrementally quadratic nonlinear systems with parameter uncertainty. Its nonlinearity satisfies the condition of incremental quadratic constraints which contains many commonly encountered nonlinearities in existing literature as some special cases. A circle criterion-based adaptive observer is first designed to expand the freedom of observer design. Based on the incremental quadratic constraint condition, sufficient conditions ensuring asymptotic stability of estimation error dynamics are established in terms of linear matrix inequalities. Finally, the adaptive observer is applied to the synchronization design of chaotic systems with parameter uncertainty, which fully demonstrates the effectiveness of the proposed observer.