Adaptive Observer Design Research Articles

A continuous-discrete adaptive observer with a diagonal gain matrix and sigma-modification: applications in chaos synchronization and dynamical state estimation

In this paper, we propose an improved continuous-discrete observer with enhanced convergence properties and reduced sensitivity to persistent excitations. Our approach introduces several key innovations, including a customised diagonal gain matrix which improves the convergence speed, a sigma-modification technique that relaxes the persistent excitation conditions, and a weighting factor tailored to optimise the estimation of unknown parameters. Through comprehensive numerical experiments, we illustrate the effectiveness of our observer in two distinct scenarios. Firstly, we demonstrate its application in synchronising a 4-component chaotic dynamical system. Secondly, we showcase its utility in tracking a reduced 2-component chemical engineering process. Our simulation results reveal that the proposed observer outperforms existing methods by achieving quicker convergence and higher estimation accuracy. This study contributes to the advancement of adaptive observer design, offering valuable insights for its application across diverse fields.

Adaptive Current Observer Design for Single Current Sensor Control in PMSM Drives

Adaptive Current Observer Design for Single Current Sensor Control in PMSM Drives

Adaptive observer design for coupled ODE–hyperbolic PDE systems with application to traffic flow estimation

This paper studies the state estimation problem for a class of coupled linear ODE–hyperbolic PDE systems with unknown in-domain parameters. Based on the swapping transformation and the least squares parameter estimation method, a Luenberger-type adaptive boundary observer is designed to estimate the ODE–PDE states under the unknown parameters. The exponential convergence conditions w.r.t. the observer feedback gains are given by employing the Lyapunov technique. Finally, an application to traffic state estimation of the Aw–Rascle–Zhang (ARZ) model involving the unknown relaxation time and the boundary input speed deviation is provided to validate the theoretical result.

Fault diagnosis of virtually‐coupled trains by adaptive observer with pattern‐matched detection and reinforced identification

SummaryVirtual coupling is gaining in popularity as a promising development direction to maximize the rail‐line efficiency by minimizing the headway distance among trains in the presence of potentially encountered traction engines' faults with unknown amplitude, happening time and probability, which would be huge threat to the safety of trains without proper sensing and handling. This paper considers the fault diagnosis problem for virtually‐coupled multiple trains using adaptive observer design. In order to generate false‐free and timely fault alarming and relieving signals, an adaptive threshold function design is firstly given using a novel pattern‐matched gain technique with explicit consideration of model uncertainty. Then, reinforced regressor‐based fault identification algorithm is proposed to generate precise estimation of unknown fault values, activated and powered‐off by the fault alarming and relieving signals output by fault detection observer, with globally Lipschitz property and fast convergence performance. Finally, comparative and simulation results are given to demonstrate the effectiveness and advantages of proposed fault diagnosis algorithms.

Improvement of real-time state estimation performance in HVDC systems using an adaptive nonlinear observer

This paper proposes a novel adaptive nonlinear observer design for a voltage source converter based on high-voltage direct current (VSC-HVDC) transmission systems. We consider a system consisting of a power grid, and a converter station connected to an unknown load through a long HVDC cable. The primary contribution of this work is the development of a global high-gain observer that facilitates the estimation of all system states. Specifically, it encompasses the estimation of power grid parameters, such as the angular frequency and the voltage at the point of common coupling (PCC), as well as the states of the HVDC cable and the current absorbed by the load. The performance of the proposed observer is assessed through theoretical analysis and simulations. Additionally, we implemented our observer on a digital signal processor (DSP) eZdsp in a processor-in-the-loop (PIL) quasi-real-time setting. Experimental results, coupled with numerical simulations, showcase the outstanding performance of our proposed observer.

Concurrent learning adaptive boundary observer design for linear coupled hyperbolic partial differential equation systems

This paper proposes a novel concurrent learning-based adaptive boundary observer designed to tackle the joint estimation problem of system states and unknown parameters for a class of hyperbolic partial differential equation systems under the circumstance of unsatisfied persistent excitation conditions. By leveraging concurrent learning technique, an adapted data points selection algorithm is employed concurrently with current data to construct the adaptation law of unknown parameters, which overcomes the limitations imposed by persistent excitation conditions and ensures exponential convergence of estimation errors of unknown parameters under finite excitation conditions. Furthermore, combining the ideas of backstepping and swapping filters on the basis of uncertain estimation, a concurrent learning-based adaptive boundary observer is designed, accompanied by rigorous theoretical analysis and proofs to demonstrate its capability of achieving exponential convergence in estimation. Finally, the corresponding illustrative simulations are given to show the effectiveness of the proposed methodology.

Fractional adaptive observer for variable structure high cell density fed-batch cultures

This paper presents the design and application of a fractional order asymptotic adaptive observer coupled to an adaptive controller for the robust operation of high-cell density cultures in fed-batch mode. The control goal is to maximize biomass productivity by controlling the culture’s estimated specific growth rate. Since the specific growth rate cannot be measured, a fractional order asymptotic adaptive observer is proposed, based on the equivalent integer order asymptotic observer proposed before. Simulations are performed to validate the observer and controller, under the assumption that the system is in the oxidative regime under aerobic conditions. Obtained results show that, in close loop operation, the fractional adaptive observer behaves better than the integer order observer in the presence of measurement noise. For fractional orders of the observer in the range α G [0.6,0.8], it was observed a 51.71% increase in biomass concentration, compared to the biomass obtained with the classic integer-order observer. Furthermore, the controlled system reaches very low ethanol concentrations (< 1 grams per liter), which is desirable in this process.

Modeling and Adaptive Observer Design of Buck Power Converter with Transmission Delay

In terms of energy transmission, several phenomena can occur, which can affect the reliability of the network, cause instabilities, and deteriorate the performance of the system, including delay. This work considers a simple energy source presented by a Buck-type DC-DC converter remote by a transmission line, assimilated to a distributed delay that interposes between the source and the considered resistive load. We are interested in the modeling of this system and the design of an adaptive observer that provides accurate estimates of the state and unknown parameters during the transmission of energy along the line.

Adaptive Observer Design for Heat PDEs with Sensor Delay and Parameter Uncertainties

Adaptive Observer Design for Heat PDEs with Sensor Delay and Parameter Uncertainties

Adaptive Observer Design for Sensorless IPMSM Drives With Known Regressors Variant of Extended EMF Model

Adaptive Observer Design for Sensorless IPMSM Drives With Known Regressors Variant of Extended EMF Model

Finite-dimensional adaptive observer design for linear parabolic systems

A new finite-dimensional adaptive observer is proposed for some linear parabolic systems. The observer is based on the modal decomposition approach and uses a classical persistent excitation condition to ensure practical exponential convergence of both states and parameters estimation.

Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs – application to chaos synchronization

Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs – application to chaos synchronization

Neural Network Adaptive Observer design for Nonlinear Systems with Partially and Completely Unknown Dynamics Subject to Variable Sampled and Delay Output Measurement

This paper proposes a novel Neural Network Adaptive Observer (NNAO) for Nonlinear Systems with Partially and Completely Unknown Dynamics (NSPCUD), subject to variable sampled and delayed output. The method involves designing a neural network observer for partially unknown nonlinear systems with sampled and delayed outputs, using a radial basis function (RBF) neural network to approximate the system’s unknown part. A new weight update algorithm is proposed, along with a closed-loop output predictor for coping with variable samples, and a closed-loop integral compensation to handle variable delay. This approach is then extended to cover completely unknown systems as well. Numerical simulations and comparisons between the proposed method and previous methods on autonomous ground vehicle models were conducted to verify the effectiveness of the proposed NNAO.

Adaptive Fuzzy Boundary Observer Design for Uncertain Linear Coupled Hyperbolic Partial Differential Equation Systems

Joint uncertainties and state estimation of a class of linear coupled hyperbolic partial differential equation systems in the presence of unstructured and structured uncertainties are studied in this paper. For unstructured uncertainties which are completely unknown, by employing Takagi-Sugeno fuzzy logic system to approximate the unstructured uncertainties, a novel adaptive fuzzy boundary observer is developed to estimate both unknown system states as well as unknown weights in the fuzzy logic system, and the estimation errors are ultimately bounded. Therein, in the design of the proposed observer, a set of swapping filters and infinite dimensional backstepping technique are combined. On the other hand, for structured uncertainties that can be described in a concrete parameterized form, the proposed method can easily achieve the exact estimation of weights and states to their true values. The rigorous proof is provided to show that the ultimately bounded estimation errors for the case of unstructured uncertainties and the exponential convergent estimation errors for the case of structured uncertainties can be realized. Finally, three illustrative simulations are carried out to show the feasibility and effectiveness of the developed methods in this paper.

Adaptive Neural Network-Based Observer Design for Switched Systems With Quantized Measurements.

This study is concerned with the adaptive neural network (NN) observer design problem for continuous-time switched systems via quantized output signals. A novel NN observer is presented in which the adaptive laws are constructed using quantized measurements. Then, persistent dwell time (PDT) switching is considered in the observer design to describe fast and slow switching in a unified framework. Accurate estimations of state and actuator efficiency factor can be obtained by the proposed observer technique despite actuator degradation. Finally, a simulation example is provided to illustrate the effectiveness of the developed NN observer design approach.

Sensor Fault Detection in A Satellite Launcher Using Adaptive Neuro-fuzzy Observer

Fault detection is performed by estimating the states and comparing them with measured values. A fault is signaled when the difference between the estimated and measured values crosses a threshold value, This paper presents the design of adaptive neuro-fuzzy observer based sensor fault detection and fault tolerant control under sensor failure conditions for a satellite launcher. In this Adaptive Neuro-Fuzzy Inference System (ANFIS), optimal shape and parameters for the membership functions and effective rule base for the fuzzy system are fixed by a neural network. Three such adaptive neuro-fuzzy inference systems act as reduced order observers that estimate the system states. Decision functions are built from estimation errors to detect the fault. If any failure is identified, the control law is modified accordingly using the estimated value replacing the failed sensor output to implement the fault tolerant control. In this work, such fault detector is designed and simulated. The individual failures of three sensors in the satellite launcher are considered and the results are discussed. The results show that the system is able to detect any sensor failure situations perfectly.

Adaptive observer design for a class of nonlinear descriptor systems

This paper concerns the adaptive observer design for a class of nonlinear descriptor systems. It allows the simultaneous estimation of the system states and its parameters. The presented observer is in a general form, generalizing the design for the full order and reduced order observers. The existence conditions for the observer are given and the parameterization of all the observer parameters is provided. The design is obtained in the LMI formulation. The case of the linear descriptor system can be directly obtained from the presented results as a particular case. A numerical example is provided to illustrate the design procedure.

Adaptive observer design for uncertain hyperbolic PDEs coupled with uncertain LTV ODEs; Application to refrigeration systems

The problem of estimating the temperatures and the heat transfer coefficient of a concentric tube heat exchanger coupled with a heater is considered in this work. Measurements collected from the extremities of the exchanger tube are used to estimate the heat distribution over the length of the exchanger, which induces a boundary estimation problem. This system, which is part of any standard cooling plant, is particularly challenging due to the distributed nature of its variables. It is modeled by a system of (2 × 2) hyperbolic PDEs, coupled with an ODE at the boundary. To solve the estimation problem, we consider a general class of systems consisting of a (2 × 2) hyperbolic system coupled with a set of nX linear time-varying (LTV) ODEs at the boundary. Both the PDE and the ODEs have uncertain parameters to be estimated. The objective is to estimate the PDE states, the ODE states, and the parameters simultaneously with no assumption on the ODEs stability. 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 from the Lyapunov analysis of the decoupled system after proving the boundedness of the swapping filters. We give sufficient conditions of the exponential convergence of the adaptive observer through differential Lyapunov inequalities (DLIs). Finally, we apply the developed theory on the coupled heat exchanger–heater model to evaluate the performance of the observer in numerical simulations.

Adaptive observer design for a class of delayed parabolic systems

A new adaptive observer is proposed for a class of uncertain time-delay parabolic systems. The uncertainties are located in both the state equation and the output equation which are also subjected to a distributed delay. Our algorithm is based on backstepping-like transformation and a classical persistent excitation condition. To illustrate the performances of this observer, simulation results are provided.

Sensorless Adaptive Observers for Linearly Parameterized Class of Induction Machine

In this paper a new adaptive flux, speed, load torque and rotor resistance observer is proposed for induction machine drive system. The structure of the proposed observer is simple and it is able to give rise to different observers among which adaptive high gain and adaptive sliding mode. We adopt a mild change of coordinates that allows to easily design of adaptive observer. Computer simulation results verify the validity of the proposed estimation algorithm.