Luenberger-type Observer Research Articles

Dynamic Boundary Estimation of Suspended Sediment Plume Benefit by the Autonomous Underwater Vehicle Sensing.

The suspended sediment plume generated in the deep-sea mining process significantly impacts the marine environment and seabed ecosystem. Accurate boundary estimation can effectively monitor the scope of environmental impact, guiding mining operations to prevent ecological damage. In this paper, we propose a dynamic boundary estimation approach for the suspended sediment plume, leveraging the sensing capability of the Autonomous Underwater Vehicles (AUVs). Based on the plume model and the point-by-point sensor measurements, a Luenberger-type observer is established for designing the AUV control algorithm. To address the challenge of unknown and time-varying environmental parameters, the estimation errors are reduced by using the projection modification unit. Rigorous convergence and stability analyses of the proposed control algorithm are provided by the Lyapunov method. Numerical simulations demonstrate that the improved algorithm enhances the estimation accuracy of unknown parameters and enables the AUV to patrol along the dynamic boundary in a shorter time, thereby verifying the effectiveness of the boundary estimation algorithm based on AUV sensing.

Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview

Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.

Deep variational Luenberger-type observer with dynamic objects channel-attention for stochastic video prediction

Considering the inherent stochasticity and uncertainty, predicting future video frames is exceptionally challenging. In this work, we study the problem of video prediction by combining interpretability of stochastic state space models and representation learning of deep neural networks with channel-attention. Our model which based on a variational encoder introduces a novel channel-attention block to enhance the ability to capture dynamic objects in video frames and a Luenberger-type observer which catches the dynamic evolution of the latent features. These enable the features of moving objects more conspicuous and decomposition of videos into static features and dynamics in an unsupervised manner. By deriving the stability theory of the nonlinear Luenberger-type observer, the hidden states in the feature space become insensitive with respect to the initial values, which improves the robustness of the overall model. Furthermore, the variational lower bound on the data log-likelihood can be derived to obtain the tractable posterior prediction distribution based on the variational principle. Finally, the experiments including the Rotaton Numbers dataset and the Kth dataset are provided to demonstrate the proposed model outperforms concurrent works.

Estimation of Process Variables in a Steam Distillation Plant

The on-line supervision of the process variables in a steam distillation plant is the main objective of this work. For this end, a nonlinear observer is designed based on the mathematical model proposed by Cerpa et al. (2008). The model has three differential equations, which reproduce the dynamics of the oil mass throughout the three stages of the process: (i) Loss of oil from plant material, (ii) Biphasic (oil-water) layer, (iii) Colected essential oil. The purpose of this work is to estimate the mass flow of oil lost by the plant material and the mass flow in the two-phase layer called the aqueous layer. Both process variables are difficult to measure physically, but it is important to know them because they can have an impact on the performance of the process. However, the mass of oil collected is considered to be an available variable to measure. By taking this consideration into account, a nonlinear Luenberger type observer is designed that takes as available output the mass of oil collected, and from this variable is able to estimate the dynamics of the unavailable variables.

Composite Observer-Based Optimal Attitude-Tracking Control With Reinforcement Learning for Hypersonic Vehicles.

This article proposes an observer-based reinforcement learning (RL) control approach to address the optimal attitude-tracking problem and application for hypersonic vehicles in the reentry phase. Due to the unknown uncertainty and nonlinearity caused by parameter perturbation and external disturbance, accurate model information of hypersonic vehicles in the reentry phase is generally unavailable. For this reason, a novel synchronous estimation is proposed to construct a composite observer for hypersonic vehicles, which consists of a neural-network (NN)-based Luenberger-type observer and a synchronous disturbance observer. This solves the identification problem of nonlinear dynamics in the reference control and realizes the estimation of the system state when unknown nonlinear dynamics and unknown disturbance exist at the same time. By synthesizing the information from the composite observer, an RL tracking controller is developed to solve the optimal attitude-tracking control problem. To improve the convergence performance of critic network weights, concurrent learning is employed to replace the traditional persistent excitation condition with a historical experience replay manner. In addition, this article proves that the weight estimation error is bounded when the learning rate satisfies the given sufficient condition. Finally, the numerical simulation demonstrates the effectiveness and superiority of the proposed approaches to attitude-tracking control systems for hypersonic vehicles.

The Rotary Flexible Joint – A Holistic View from Modeling and Control to Observer Design and Experiments

A two degrees of freedom (2DOF) control for a lab-scale vertically-mounted rotary flexible joint is addressed to realize a benchmark example for nonlinear control education and experimentation. To this end, the mathematical model is derived based on the Euler-Lagrange equations. Further insight into the model is given by addressing the relationship between the two translational springs and their approximation as a single torsion spring. The model is known to be differentially flat, which facilitates a feedforward control design by means of the flat parameterization. Furthermore, a state-feedback controller is introduced to stabilize the desired trajectory. State information is reconstructed using a Luenberger-type observer. Both the state-feedback controller and the Luenberger-type observer are designed based on a linear time-varying (LTV) approximation obtained using a linearization around the flat state parameterization of the system. The 2DOF design is illustrated using experimental results.

Filter-Based Fault Detection and Isolation in Distributed Parameter Systems Modeled by Parabolic Partial Differential Equations

This paper covers model-based fault detection and isolation for linear and nonlinear distributed parameter systems (DPS). The first part mainly deals with actuator, sensor and state fault detection and isolation for a class of DPS represented by a set of coupled linear partial differential equations (PDE). A filter based observer is designed based on the linear PDE representation using which a detection residual is generated. A fault is detected when the magnitude of the detection residual exceeds a detection threshold. Upon detection, several isolation estimators are designed using filters whose output residuals are compared with predefined isolation thresholds. A fault on a linear DPS is declared to be of certain type if the corresponding isolation estimator output residual is below its isolation threshold while the other fault isolation estimator output residual is above its threshold. Next, the fault location is determined when a state fault is identified. The second part of this paper focuses on fault detection and isolation of nonlinear DPS by using a Luenberger type observer. Here fault isolation framework is introduced to isolate actuator, sensor and state faults with isolability condition by using additional boundary measurements and without filters. Finally, the effectiveness of the proposed fault detection and isolation schemes for both linear and nonlinear DPS are demonstrated through simulation.

Robust asymptotic observer of motion states with nonlinear friction

This paper revisits the previously proposed linear asymptotic observer of the motion state variables with nonlinear friction and provides a robust design suitable for both, transient presliding and steady-state sliding phases of the relative motion. The class of motion systems with the only measurable output displacement is considered. The reduced-order Luenberger-type observer is designed based on the obtained simplified state-space representation with a time-varying system matrix. The resulted observation error dynamics proves to be robust and appropriate for all variations of the system matrix, which are due to the nonlinear spatially-varying friction. A specially designed tribological setup to accurately monitor the relative motion between two contacting friction surfaces is used to collect the experimental data of the deceleration trajectories when excited by a series of impulses. The performance of the state estimation using the proposed observer is shown based on the collected experimental data.

Model-Free Observer for Speed and Acceleration Estimations for Speed Servo System Applications

This brief presents a speed and acceleration estimation mechanism combining a Luenberger-type observer and a nonlinear second-order disturbance observer (DOB) using servo system angle measurements without system parameters and load information. The resultant observer has the following two contributions: (a) the inclusion of a system parameter information-free nonlinear DOB as a subsystem to ensure improved robustness and (b) the capability of performance assignment by tuning the scalar design factor without involving any matrix calculation processes. An experimental study validates the practical advantage of the proposed solution using a prototype 500 W dynamo system as a speed servo system.

Stabilizing Output-Feedback Control Law for Hyperbolic Systems Using a Fredholm Transformation

For most networked systems found in the literature, the actuated boundary is usually located at one end. In this article, we first consider the stabilization of a chain of two interconnected subsystems, actuated at the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-between</i> boundary. Each subsystem corresponds to coupled hyperbolic partial differential equations. Such in-domain actuation leads to higher complexity, and represents a significant difference with existing results. Then, starting from a classical controllability condition, we design a state feedback control law for the considered class of systems. The proposed approach is based on the backstepping methodology. However, to deal with the complex structure of the system, we use Fredholm integral transforms instead of classical Volterra transforms. We prove the invertibility of such transforms using an original operator framework. The well posedness of the backstepping kernel equations defining the transformations is also shown with the same arguments. By using a similar procedure, we are then able to design a Luenberger-type observer. Finally, we use the state estimation in the stabilizing controller to obtain an output-feedback law. Some test cases complete the paper.

Newton-series-based observer–predictor control for disturbed input-delayed discrete-time systems

This paper deals with the problem of predicting the future state of discrete-time input-delayed systems in the presence of unknown disturbances that can affect both the state and the output equations of the plant. Since the disturbance is unknown, computing an exact prediction of the future plant states is not possible. To circumvent this problem, we propose using a high-order extended Luenberger-type observer for the plant states, disturbances, and their finite difference variables, combined with a new equation for computing the prediction based on Newton’s series from the calculus of finite differences. Detailed performance analysis is carried out to show that, under certain assumptions, both enhanced prediction and improved attenuation of the unknown disturbances are achieved. Linear matrix inequalities (LMIs) are employed for the observer design to minimize the prediction errors. A stabilization procedure based on an iterative design algorithm is also presented for the case where the plant is affected by time-varying uncertainties. Examples from the literature illustrate the advantages of the scheme.

Cascade Takagi–Sugeno fuzzy observer design for nonlinear uncertain systems with unknown inputs: A sliding mode approach

This article investigates the design of Takagi–Sugeno (TS) fuzzy model-based observers for nonlinear systems with parametric uncertainties and unknown inputs. To address this challenging problem, two observers are constructed in cascade. Based on the sliding mode technique, the first observer allows to examine a new system whose both state and output equations are subject to uncertainties but without unknown inputs. The second Luenberger-type observer is designed for the new system where the effects of uncertainties on the estimation error can be canceled. The TS fuzzy observer design is recast as optimization problems under linear matrix inequalities, which can be effectively solved using convex optimization technique. The new cascade observer structure enables a simultaneous estimation of the system states, the unknown inputs and the uncertainties of the original nonlinear system. The effectiveness and advantage of the proposed estimation method is demonstrated via two numerical examples including a nonlinear vehicle application.

Performance-Boosting Attitude Control for 2-DOF Helicopter Applications via Surface Stabilization Approach

This study solves the attitude stabilization problem of 2-degree-of-freedom (2-DOF) helicopters by robustly assigning the variable-performance to the closed-loop system in the presence of the model-plant mismatches and load variations. The proposed approach reformulates the original problem to a surface stabilization one which yields three contributions: a) the proposed attitude velocity observer forms a conventional Luenberger-type observer incorporating the parameter-independence and estimation gains specifically designed for causing the pole-zero cancellation, b) the pole-zero cancellation velocity control loop makes it possible to accomplish the surface stabilization task with the first-order closed-loop order, and c) the closed-loop analysis results demonstrate the attractive properties of the exponential performance recovery and convergence. The effectiveness of the proposed technique is verified using the experimental platform provided by the Quanser AERO.

Interval estimation for nabla fractional order linear time-invariant systems

In this paper, we provide a framework to achieve interval estimation for nabla Caputo fractional order linear time-invariant (LTI) systems in the presence of bounded model uncertainties. Interval observers based on fractional order positive systems theory are designed by possessing desired stable and positive error dynamics. Specifically, the basic concepts and conditions for guaranteeing stability and positivity of the considered systems are derived systematically by finding the system responses. Using the developed criteria and the structure of Luenberger-type observers, a classic interval observer is designed directly which further extends the system classes of interval estimation. Besides, due to the possible absence of a gain matrix which ensures positivity requirement, a more general interval observer design scheme is given by exploiting the coordinate transformation technique. Finally, some simulated cases including fault detection and fractional order circuits related scenarios are developed to validate the usefulness and practicality of the framework.

Robust H∞ Network Observer-Based Attack-Tolerant Path Tracking Control of Autonomous Ground Vehicle

In this study, a robust H&#x221E; network observer-based attack-tolerant path tracking control design is proposed for the autonomous ground vehicle (AGV) under the effect of external disturbance, measurement noise and actuator/sensor attack signals. At first, a more practical AGV system is applied to describe the interaction among the longitudinal speed, lateral speed and yaw rate. Based on Controller Area Network (CAN), the information of local AGV is transmitted to remote control center through wireless channel and then the control command can be calculated from remote control center. To avoid the corruption of actuator/sensor attack signal from insecure CAN, two novel smoothed signal models are introduced to describe these attack signals and are embedded with the AGV dynamics system as an augmented system. Subsequently these attack signals can be simultaneously estimated with the AGV system state by the conventional Luenberger-type observer of the augmented system. By using the estimated state and attack signals, a robust H&#x221E; network observer-based attack-tolerant path tracking controller is constructed to attenuate the effect of unknown disturbance on the energy of path tracking error and eliminate the influence of attacks signals. With the help of convex Lyapunov function, the design conditions of robust H&#x221E; network observer-based attack-tolerant path tracking control design for AGV are derived in terms of a set of nonlinear difference inequalities. To reduce the difficulties in solving these nonlinear difference inequalities, Takagi-Sugeno fuzzy interpolation method is applied to approximate the nonlinear AGV system and the design can be simplified to a set of LMIs, which can be easily solved via LMI TOOLBOX in MATLAB. A double lance change task of AGV in CAN is provided as a simulation example to illustrate the design procedure and validate the effectiveness of proposed design method in comparison with the conventional steering control method.

An algorithm for the robust estimation of the COVID-19 pandemic’s population by considering undetected individuals.

Due to the current COVID-19 pandemic, much effort has been put on studying the spread of infectious diseases to propose more adequate health politics. The most effective surveillance system consists of doing massive tests. Nonetheless, many countries cannot afford this class of health campaigns due to limited resources. Thus, a transmission model is a viable alternative to study the dynamics of the pandemic. The most used are the Susceptible, Infected and Removed type models (SIR). In this study, we tackle the population estimation problem of the A-SIR model, which takes into account asymptomatic or undetected individuals. By means of an algebraic differential approach, we design a model-free (no copy system) reduced-order estimation algorithm (observer) to determine the different non-measured population groups. We study two types of estimation algorithms: Proportional and Proportional-Integral. Both shown fast convergence speed, as well as a minimal estimation error. Additionally, we introduce random fluctuations in our analysis to represent changes in the external conditions and which result in poor measurements. The numerical results reveal that both model-free estimators are robust despite the presence of these fluctuations. As a point of reference, we apply the classical Luenberger type observer to our estimation problem and compare the results. Finally, we consider real data of infected individuals in Mexico City, reported from February 2020 to March 2021, and estimate the non-measured populations. Our work’s main goal is to proportionate a simple and therefore, an accessible methodology to estimate the behavior of the COVID-19 pandemic from the available data, such that the competent authorities can propose more adequate health politics.

Robust non-fragile memory feedback control for multi-weighted complex dynamical networks with randomly occurring gain fluctuations

This paper deals with the robust observer-based synchronisation problem for a class of complex dynamic networks subject to multi-weights, time-varying coupling delay and external disturbance. Specifically, the gain fluctuation appears in the proposed controller and is represented in terms of a random variable obeying the Bernoulli distribution. The main objective of this paper is to design a non-fragile memory state feedback controller such that the resulting error system is stochastically synchronised under a prescribed performance level . First, a Luenberger-type state observer is constructed to estimate the state variables of the addressed system. Second, by constructing an appropriate Lyapunov–Krasovskii functional and using Wirtinger-based integral inequality techniques, the required set of sufficient conditions for the synchronisation of the proposed system is established in the form of linear matrix inequalities. In the end, two numerical examples are provided to demonstrate the validity and feasibility of the developed theoretical results.

Robust State/Fault Estimation and Fault-Tolerant Control in Discrete-Time T-S Fuzzy Systems: An Embedded Smoothing Signal Model Approach.

This study investigates a simple design method of the robust state/fault estimation and fault-tolerant control (FTC) of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To avoid the corruption of the fault signal on state estimation, a novel smoothing signal model of fault signal is embedded in the T-S fuzzy model for the robust H∞ state/fault estimation of the discrete-time nonlinear system with external disturbance by the traditional fuzzy observer. When the component and sensor faults are generated from different fault sources, two smoothing signal models for component and sensor faults are both embedded in the T-S fuzzy system for robust state/fault estimation. Since the nonsingular smoothing signal model and T-S fuzzy model are augmented together for signal reconstruction, the traditional fuzzy Luenberger-type observer can be employed to robustly estimate state/fault signal simultaneously from the H∞ estimation perspective. By utilizing the estimated state and fault signal, a traditional H∞ observer-based controller is also introduced for the FTC with powerful disturbance attenuation capability of the effect caused by the smoothing model error and external disturbance. Moreover, the robust H∞ observer-based FTC design is transformed into a linear matrix inequality (LMI) -constrained optimization problem by the proposed two-step design procedure. With the help of LMI TOOLBOX in MATLAB, we can easily design the fuzzy Luenberger-type observer for efficient robust H∞ state/fault estimation and solve the H∞ observer-based FTC design problem of discrete nonlinear systems. Two simulation examples are given to validate the performance of state/fault estimation and FTC of the proposed methods.

Output Feedback Energy Control of the Sine-Gordon PDE Model Using Collocated Spatially Sampled Sensing and Actuation

The present investigation focuses on the output energy control of the nonlinear sine-Gordon model in a practical situation where only spatially sampled sensing and actuation are available. The speed-gradient method that has corroborated its utility for the sine-Gordon model, controlled through the manipulable parameters of the external field and boundary actuation, is now generalized to the spatially sampled sensing and actuation, aiming to pump/dissipate the energy of the model to a desired level. Luenberger-type observers are additionally developed in the present nonlinear PDE setting to be involved into the output feedback synthesis over collocated state (position and/or velocity) measurements. Capabilities of the proposed synthesis are illustrated in numerical simulations.

Synchronization Control Design Based On Observers For Time-delay Lur’e Systems

This paper researches synchronization control design for chaotic Lur'e systems (CLSs) with time-varying delay. Considering of the unmeasurable state variables, Luenberger-type observers are designed for the master-slave systems. The synchronization has been achieved by using the proposed controller with the estimated system states. Based on Bessel-Legendre inequality, improved reciprocally convex combination approach and a novel double integral inequality, new Lyapunov Krasovskii functionals(LKFs) are tailored and a synchronization control criterion with less conservatism is obtained. Some simulations are given to verify that this control strategy we proposed is effective.