Observer Design Method Research Articles

Predictor-Based Global Sampled-Data Output Feedback Stabilization for Nonlinear Uncertain Systems Subject to Delayed Output

In this article, we address the problem of global sampled-data output feedback stabilization for a class of nonlinear uncertain systems with delayed output using the continuous-discrete method. Thanks to the prediction technique and feedback domination method, a novel coupled design method of predictor-based continuous-discrete observer and linear controller is proposed when only delayed sampled-data output is accessible. The proposed predictor-based observer can effectively estimate the unknown state by compensating the influences of sampling and output delay. The main advantage of the proposed control method is that the full state information and accurate model nonlinearities do not need to be known any more. The global exponential stability of the overall hybrid control system can be ensured when there hold some sufficient conditions with respect to the maximum allowable sampling period and output delay.

Global Versus Local Lyapunov Approach Used in Disturbance Observer-Based Wind Turbine Control

This contribution presents a Lyapunov-based controller and observer design method to achieve an effective design process for more dedicated closed-loop dynamics, i.e., a maximal flexibility in an observer-based controller design with a large consistency in desired and achieved closed-loop system dynamics is intended. The proposed, pragmatic approach enhances the scope for controller and observer design by using local instead of global Lyapunov functions, beneficial for systems with widely spaced pole locations. Within this contribution, the proposed design approach is applied to the complex control design task of wind turbine control. As the mechanical loads that affect the wind turbine components are very sensitive to the closed-loop system dynamic, a maximum flexibility in the control design is necessary for an appropriate wind turbine controller performance. Therefore, the implication of the local Lyapunov approach for an effective control design in the Takagi-Sugeno framework is discussed based on the sensitivity of the closed-loop pole locations and resulting mechanical loads to a variation of the design parameters.

High-Gain Like Observer Design for Nonlinear Systems Applied to Vehicle Motion Estimation

This work investigates the problem of state estimation for nonlinear triangular systems having additional output measurements. The main objective of this paper is to propose observer design strategies that account for the available additional information, which is difficult to consider using the standard high-gain observer methodology. To deal with this challenge, we propose a novel observer design method to handle the additional output measurements. This method can be thought of as an extension of the standard high-gain observer by introducing a weighting matrix as a tuning parameter, which uses both the high-gain methodology and the LPV/LMI technique. The proposed approach was applied to a nonlinear longitudinal dynamic model that uses extra measurement information, in addition to the measured longitudinal position of the vehicle.

Observer-Based Event-Triggered Containment Control for MASs Under DoS Attacks.

This article studies the observer-based event-triggered containment control problem for linear multiagent systems (MASs) under denial-of-service (DoS) attacks. In order to deal with situations where MASs states are unmeasurable, an improved separation method-based observer design method with less conservativeness is proposed to estimate MASs states. To save communication resources and achieve the containment control objective, a novel observer-based event-triggered containment controller design method based on observer states is proposed for MASs under the influence of DoS attacks, which can make the MASs resilient to DoS attacks. In addition, the Zeno behavior can be eliminated effectively by introducing a positive constant into the designed event-triggered mechanism. Finally, a practical example is presented to illustrate the effectiveness of the designed observer and the event-triggered containment controller.

Linear matrix inequality–based observer design methods for a class of nonlinear systems with delayed output measurements

This article deals with observer design for a class of nonlinear systems subject to delayed output measurements. Using an observer structure borrowed from Targui et al., we propose novel linear matrix inequality conditions ensuring the asymptotic convergence of the estimation error towards zero. We demonstrate analytically that the established linear matrix inequalities are less conservative than that of Targui et al., from a feasibility viewpoint, in the sense that they tolerate larger values of the upper bounds of the delay while guaranteeing the asymptotic convergence of the observer. Such linear matrix inequality conditions are obtained due to the use of a specific Lyapunov–Krasovskii functional, the Young inequality in a judicious way and a reformulation of the Lipschitz condition in a convenient way. We provide two illustrative examples to support the efficiency and superiority of the proposed linear matrix inequality–based techniques.

Robust observer design for LPV systems using Kronecker sum and direct searching

This paper addresses a robust Luenberger observer for an uncertain linear parameter varying (LPV) system based on the concepts of direct searching, Kronecker sum, and small gain theorem. An algorithm is proposed to investigate the situation of the different parts of the initial observer design space, in terms of suitability for being selected as the observer gain or needing elimination due to being an undesirable part. To find the undesirable parts of the design space, the singularity of the Kronecker sum matrix of the estimation error is checked by employing the small gain theorem concept. By excluding undesired parts from the entire design space and checking the remaining parts’ feasibility, a suitable solution can be found, appropriately. The performance of the proposed observer design method is illustrated by using numerical examples and an electric ground vehicle (EGV) system for the estimation of the vehicle sideslip angle and the yaw rate. The results prove the appropriateness of the designed observer using the proposed approach.

On sliding mode observers for non-infinitely observable descriptor systems

This paper presents a sliding mode observer (SMO) design method to estimate the states and unknown inputs (UIs) in a class of non-infinitely observable (NIO) descriptor systems that contain UIs in both the state and output equations. Existing works on SMO design for NIO systems did not consider UIs in the output equation. In order to overcome the difficulty caused by UIs in output channels and the NIO condition, we reformulated the original system and introduced new UIs to replace the original UIs to obtain an equivalent infinitely observable descriptor system whose output does not contain any UI. Based on the developed equivalent system, a new SMO method is proposed to estimate both the states and the UIs. Subsequently, the necessary and sufficient conditions for the existence of the SMO are derived in terms of the original system matrices, which thus makes the conditions easy to be examined. Finally, an example is used to verify the effectiveness of the proposed method.

GEOTECHNICAL SUPPORT FOR THE CONSTRUCTION OF A UNIQUE BUILDING THROUGH THE OBSERVATIONAL DESIGN METHOD

Introduction . In geotechnical design practice, it is common to find objects whose underground structure behavior is difficult to predict based on calculation or experimental work. Such cases permit the use of the observational method allowing for design adjustments during construction according to the results of geotechnical monitoring. The paper describes a practical example of applying the observational method at the construction site of a unique building in the center of Moscow. Aim : to evaluate the actual performance of underground structures and, if necessary, to develop and apply corrective measures within the observational design method using the results of geotechnical monitoring. The subject matter of the study is a unique unfinished building with a five-story underground part exhibiting an uncertain mechanical performance of the foundation at the interface with the retaining wall of the foundation pit due to the long-term suspension of the construction site. The behavior of the underground structures, including their interaction with the bearing soil and the slurry wall, was controlled using a comprehensive system of geotechnical monitoring implemented at the site. Results . The adopted design solutions and the use of corrective actions within the observational design method reduced the effect of existing adverse geotechnical conditions at the site in question, specifically increasing the stiffness of the underground part and minimizing the settlement difference between the central and edge parts of the foundation slab. Conclusions . It is established that geotechnical monitoring provides a means to evaluate the behavior of the building exhibiting an uncertain mechanical performance of structures within the observational design method.

A harmonic suppression strategy for grid-connected inverters based on quadrature sinewave extractor

Grid-connected inverters need to reduce current harmonics as much as possible. After introducing the input signal’s fundamental and main harmonic quadrature components, a discrete state model is created, and the discrete observer design method is used to propose a harmonic extraction algorithm called quadrature sinewave extractor (QSE). The QSE is a stable recursive operator with the advantages of no phase displacement and the ability to eliminate mutual influence between harmonic components. Compared to the widely used proportional multi-resonant controller, QSE can reduce current harmonics and improve system stable performance by using it in the current control of grid-connected inverters. Finally, comparative experiments on a three-phase grid-connected inverter are used to verify the proposed method’s effectiveness.

State estimation of the time–space propagation of COVID-19 using a distributed parameter observer based on a SEIR-type model

The real-time prediction and estimation of the spread of diseases, such as COVID-19 is of paramount importance as evidenced by the recent pandemic. This work is concerned with the distributed parameter estimation of the time–space propagation of such diseases using a diffusion–reaction epidemiological model of the susceptible–exposed–infected–recovered (SEIR) type. State estimation is based on continuous measurements of the number of infections and deaths per unit of time and of the host spatial domain. The observer design method is based on positive definite matrices to parameterize a class of Lyapunov functionals, in order to stabilize the estimation error dynamics. Thus, the stability conditions can be expressed as a set of matrix inequality constraints which can be solved numerically using sum of squares (SOS) and standard semi-definite programming (SDP) tools. The observer performance is analyzed based on a simplified case study corresponding to the situation in France in March 2020 and shows promising results.

Improved Adaptive Fuzzy Control for Non-Strict Feedback Nonlinear Systems: a Dynamic Compensation System Approach

This paper investigates the tracking control problem for uncertain nonlinear non-strict feedback systems (NSFSs) in the presence of full-state constraints and unmeasured disturbances. It is of great practical significance to realize the full-state constraint under disturbed conditions. In view of the non-strict feedback problem, a novel design framework of the state feedback control is given based on the newly proposed dynamic compensation system (DCS). Different from the traditional backstepping, the estimated signal based on the adaptive fuzzy system is indirectly introduced into the virtual and actual control laws through the DCS, which has the advantage of avoiding the algebraic-loop problem in NSFSs. Accordingly, the disturbance observer (DO) design method is improved based on this framework. Integrating the DCS into the DO design avoids the coupling problem between the disturbance and the unknown nonlinear function. An improved barrier Lyapunov function (BLF) is designed by introducing the concept of the inducible factor, and full-state constraints can be guaranteed after a transitional period for any initial state. By combining the DCS, the DO and the improved BLF, a novel adaptive fuzzy tracking control law is constructed, and all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. Finally, the theoretical analysis and simulation results show that all states meet the corresponding constraints while meeting the stability.

Design of a joint adaptive high‐gain observer for a class of nonlinear sampled‐output system with unknown states and parameters

AbstractIn this article, a joint adaptive high‐gain observer design method is proposed for a class of nonlinear systems subject to sampled output data measurements. The considered class of system is characterized by a nonlinear term coupled with an unknown parameter that enters the system in both the outputs and the states equations. The fact that the considered system involves an output sampling process and an unknown parameter renders the design of the nonlinear adaptive observer more difficult. To overcome this difficulty, a novel closed‐loop output predictor is proposed. Based on the well‐known decoupling method between the state and unknown parameters, a joint adaptive high‐gain observer which can simultaneously guarantee the exponential convergence of the estimation of the unknown state and the unknown parameter is proposed in this article. The structure of the designed observer has been extended to the case of sampled and delayed data measurements. The effectiveness of our proposed observer is demonstrated through numerical simulations and performance comparison with another observer structure proposed in the literature.

Consensus for Second-Order Multiagent Systems Under Two Types of Sampling Mechanisms: A Time-Varying Gain Observer Method.

This article considers the consensus of second-order multiagent systems (MASs) under a directed communication topology. By introducing time-varying gains into observers, two types of novel continuous-discrete-time observers are presented to estimate state information of agents under two sampling mechanisms, respectively, namely: 1) a synchronous nonuniform sampling (SNS) mechanism and 2) an asynchronous nonuniform sampling (ANS) mechanism. A new design method of the time-varying gain observer is proposed, in that it can allow for one to select a consensus protocol with lower cost observers to attain the consensus task. Only sampled position information needs to be transmitted in designing consensus protocols for the MSAs, and neither velocity information nor control input information is required. Under the SNS mechanism, a consensus condition is obtained and it is shown that the introduction of time-varying gains in the observers indeed can improve their convergence. Under the ANS mechanism, the corresponding consensus protocol allows the sampling and transmission of different agents to be asynchronous and aperiodic, which means that each agent may sample and transmit its information in line with its own sampling requirements. Furthermore, each sampling period can be arbitrarily selected within a certain range while ensuring the consensus of the MASs. Finally, numerical examples are given to illustrate the effectiveness of the obtained results.

Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment

This paper is a contribution to the modeling–methodological development of the application of mathematical systems theory in population biology. A discrete-time nonlinear Leslie-type model is considered, where both the reproduction and survival rates decrease as the total population size increases. In this context, the monitoring problem means that, from the observation of the size of certain age classes as a function of time, we want to recover (estimate) the whole state process (i.e., the time-dependent size of the rest of the classes). First, for the linearization approach, conditions for the existence and asymptotic stability of a positive equilibrium are obtained, then the discrete-time observer design method is applied to estimate an unknown state trajectory near the equilibrium, where we could observe a single age class. It is also shown how the observer design can be used to detect an unknown change in the environment that affects the population dynamics. The environmental change is supposed to be generated by additional dynamics (exosystem). Now, the Leslie-type model is extended with this exosystem, and the observer design is applied to this extended system. In this way, an estimation can be obtained for different (constant or periodic) environmental changes as well.

Specified QoS based networked observer and PI controller design with disturbance and noise rejection under random packet dropout

In this paper, a novel observer based networked PI controller has been designed by considering bounded disturbance and measurement noise under specified probability of random packet dropouts in networked control systems (NCSs). Lyapunov stability condition of the NCS with an observer and PI controller has been derived using an asynchronous dynamical system (ADS) approach as a linear matrix inequality (LMI) with nonconvex constraints to improve its quality-of-service (QoS) and quality-of-control (QoC). In order to improve QoC and QoS for NCS under process and measurement disturbance, we have used H∞ norm bound, and random packet drop rate in the NCS design. The algorithm has been tested and validated on four test-bench models of energy conversion systems. Confidence intervals and the mean responses of the state variables, state estimation errors of the observer and control signals have been reported using 100 Monte Carlo simulations. Our proposed NCS with PI controller and observer design method can be employed on a wide range of state space models of energy conversion systems. The specified probability of packet dropouts in the communication network between the sensor, observer, PI controller and actuator has been considered in the design which allows design of the NCS with guaranteed Lyapunov stability. We consider a switched linear dynamical system structure of the NCS with bounded noise and disturbance inputs while jointly searching for PI controller and observer gains. Using the controller and observer designed with 90% packet drop rate, we show the system performance degradation at 97%–99% QoS using phase portraits of the error dynamical system around the equilibrium as well as through univariate and multivariate hypothesis tests for equal dispersion around the equilibrium of the error dynamical system.

Actuator fault detection for a PEMFC system based on delta operator approach

This paper proposes an actuator fault detection observer design method for a proton exchange membrane fuel cell (PEMFC) system described by delta operator form. In the first, a nonlinear mathematical model for the PEMFC system is proposed by using the mechanism analysis method, which includes the time delay, external disturbance and uncertainty to reduce the conservatism of the design. Then, in order to detect the actuator fault, the functional observer is constructed as the residual generator, and sufficient conditions for the stability of the error system are obtained by using the Lyapunov-krasovsky functional theory in terms of linear matrix inequalities (LMIs), so as to ensure the design of the required functional observer. Finally, simulation results are provided to show the effectiveness of the approach.

Adaptive event-triggered scheme for load frequency control of smart grid under DoS attacks

This paper studies the load frequency control (LFC) problem of smart grids under aperiodic denial-of-service (DoS) attacks. First, a switching observer model is constructed to deal with the unavailability of system status. Second, an adaptive event-triggered LFC scheme is proposed, which effectively reduces the update frequency of control signals and reduces the impact of aperiodic DoS attacks simultaneously. Third, by considering the impact of DoS attacks and event-triggered mechanisms at the same time, the system is modelled as a switching model. Then, by constructing a suitable piecewise Lyapunov functional, sufficient conditions are derived to ensure the exponential stability of the system with performance. In addition, the joint design method of observer and controller is also developed. Finally, a single-area power system is taken as an example to verify the effectiveness of the proposed method.

Adaptive adjustable dimension observer based fault estimation for switched fuzzy systems with unmeasurable premise variables

This paper focuses on the sensor fault estimation problem for a kind of switched nonlinear systems. A novel fault estimation observer design method is proposed, which can reconstruct the sensor fault and system state, simultaneously. T-S fuzzy model is considered to describe the nonlinear dynamics in switched systems, and the premise variables of the fuzzy models are assumed to be dependent on the unmeasurable system state rather than the measurable variables, which leads to that there is a Lipschitz nonlinear term in the error dynamics. The Lipschitz nonlinear term is divided into two parts, and their influence on estimation result is decoupled and canceled by selecting appropriate observer parameter matrices and adding adaptive compensator, respectively. Compared with the existing results, the proposed method does not require the Lipschitz constant information. Thus, it avoids calculating the Lipschitz constant and reduces the conservatism caused by introducing the Lipschitz constant into LMIs. Besides, the order of the designed observer is not fixed, and can be selected in a certain range, which implies that the proposed method is with more design freedom for different conditions. At last, two examples are listed to verify the proposed fault estimation approach.

Reduced-order intermediate variable observer based fault estimation and fault-tolerant control for fuzzy stochastic systems with exogenous disturbance

This paper studies fault estimation and fault-tolerant control problems for fuzzy systems with exogenous disturbance and stochastic noise. The fuzzy reduced-order intermediate variable observers and the disturbance observers are proposed to reconstruct the sensor fault, the actuator fault and the disturbance. According to the estimated results, the observer based fault-tolerant controllers are devised. Compared with the full-order observer design method, the designed reduced-order observers are with lower dimensions and less cost. Different from the classic intermediate observer, the feedback term of the output estimation error is introduced into our observers, which increases the design freedom. And the obtained linear matrix inequality conditions can ensure that the whole closed-loop systems are mean-square exponentially stable. Finally, two examples are offered to verify the feasibility of the proposed method.

Lower triangle factor based sliding mode observers design for T–S fuzzy systems with faults

The paper mainly focuses on the fault estimation for a class of Takagi–Sugeno (T–S) fuzzy systems with faults. A synthetic estimation observer design method is proposed. The synthetic estimation observer can cover the robust observer, adaptive observer and intermediate estimation observer in the existing study work. Based on the observer design method, an LTF-based sliding mode observer (SMO) is designed for the T–S fuzzy system in consideration. Under the observer, the fault occurring in the system can be well estimated. The obtained LMI-based conditions guarantee the states of the error dynamics to be uniformly ultimately bounded. A numerical example tests the proposed method.