Output Estimation Error Research Articles

Hybrid observer with finite-memory output error correction for linear systems under intrinsic impulsive feedback

A novel hybrid observer that estimates the states of an oscillating system composed of a linear chain structure and an intrinsic pulse-modulated feedback is considered. This particular type of plant model appears in e.g. endocrine systems with pulsatile hormone secretion. The observer reconstructs the continuous states of the model as well as the firing times and weights of the feedback impulses. Since the pulse-modulated feedback is intrinsic, no measurements of the discrete part of the plant are available to the observer. For a periodical plant solution, to reconstruct the hybrid state, the impulses in the observer have to be synchronized with those in the plant. The observer is equipped with two feedback loops driven by the output estimation error. One of these is utilized to correct the estimates of the continuous states. In contrast with previous observer designs, the estimate of the next impulse firing time is implemented by means of a finite-memory convolution operator. A pointwise mapping capturing the propagation of the continuous plant and observer states through the discrete cumulative sequence of the feedback firing instants is derived. Local stability properties of the synchronous mode are related to the spectral radius of the Jacobian of the pointwise mapping. The observer design is based on assigning a guaranteed convergence rate to the local dynamics of a synchronous mode through the output error feedback gains to the continuous and discrete part of the observer. The observation of a stable m-cycle in the plant is treated to establish a general scenario, whereas the special case of 1-cycle is worked out in detail as the most common one. A numerical example illustrates the observer performance in the case of periodic modes of low multiplicity in an impulsive model of testosterone regulation in the male. Despite the local nature of the design approach, convergence to a synchronous mode is observed for a wide range of initial conditions for the discrete state estimate in the observer.

Fixed-Time-Convergent Generalized Extended State Observer Based Motor Control Subject to Multiple Disturbances

Inertia load change, torque disturbance, and sophisticated mechanical nonlinearity impose great challenge on the high-precision control design of motor servo systems. To achieve better tracking and disturbance rejection performance, a practical control scheme, which combines a fixed-time-convergent generalized extended state observer (FGESO) with a fixed-time-convergent state feedback control law, is proposed in this article. First, an FGESO is designed to estimate the lumped disturbance and the fixed-time convergence of the estimation errors can be achieved. In the FGESO, there are three parameters and the correction term is selected as a continuous switching function of the output estimation error, which can facilitate the tuning process and greatly alleviate the chattering problem. Second, a control law based on the bilimit homogeneity technique is provided to regulate the tracking errors within a finite time independent of the initial condition. The fixed-time stability of the closed-loop system can be rigorously proved based on the Lyapunov theory. To facilitate the application of the proposed method, a practical two-step tuning procedure is established. Finally, extensive simulations and experiments are performed on a brushless direct current motor to validate the effectiveness and robustness of the proposed method.

Observer design and stability analysis for a class of PDE chaotic systems

This paper deals with observer design and stability for a class of partial differential equation (PDE) systems governed by one-dimensional wave equations with mixed derivative terms and superlinear boundary conditions, whose dynamics exhibits chaos when the system parameters change within certain ranges. Firstly, a sufficient and necessary condition that guarantees the stability of this class of systems is obtained. Secondly, based on the method of characteristics, an observer is designed by injecting the measurement output estimation error on the boundary, and the observation error dynamics is proved to be stable with a necessary and sufficient criterion, which can identity the range of the feedback gain for the observer. Finally, two numerical examples are provided to illustrate the validity of the theoretical conclusions.

A hybrid metaheuristic algorithm for identification of continuous-time Hammerstein systems

This paper presents a new hybrid identification algorithm called the Average Multi-Verse Optimizer and Sine Cosine Algorithm for identifying the continuous-time Hammerstein system. In this paper, two modifications were employed on the conventional Multi-Verse Optimizer. Our first modification was an average design parameter updating mechanism to solve the local optima issue. The second modification was the hybridization of Multi-Verse Optimizer with Sine Cosine Algorithm that will balance the exploration and exploitation processes and thus improve the poor searching capability. The proposed hybrid method was used for identifying the parameters of linear and nonlinear subsystems in the Hammerstein model using the given input and output data. A continuous-time linear subsystem was considered in this study, while there were a few methods that utilize such models. Furthermore, various nonlinear subsystems such as the quadratic and hyperbolic functions had been used in those experiments. The efficiency of the novel technique is illustrated using a numerical example and two real-world applications, which are a twin rotor system and a flexible manipulator system. The numerical and experimental results analysis were observed with respect to the convergence curve of the fitness function, the parameter deviation index, time-domain and frequency-domain responses of the identified model, and the Wilcoxon's rank test. The results showed that the proposed method was efficient in identifying both the Hammerstein model subsystems in terms of the quadratic output estimation error and parameter deviation index. The proposed hybrid method also achieved better performance in modeling of the twin-rotor system as well as the flexible manipulator system and provided better solutions compared to other optimization methods including Particle Swarm Optimizer, Grey Wolf Optimizer, Multi-Verse Optimizer and Sine Cosine Algorithm.

Robust Output Feedback Sliding Mode State and Disturbance Observer-based Controller Design for Nonlinear Systems

This study uses an output feedback disturbance observer-based proportional derivative (PD) controller with variable damping ratios for a class of single-input, single-output nonlinear systems in the presence of unknown disturbances. The proposed sliding mode state and disturbance observer, in which the switching term of the output estimation error is employed to counteract the effect of external disturbance, ensures that the estimation error is finally bounded in a neighborhood and reconstructs simultaneously the system state and unknown disturbance. Herein, the characteristics of the proposed observer are presented in the frequency domain, followed by the corresponding analysis in the time domain. A nonlinear PD controller with a variable damping ratio designed using the estimation state and disturbances should achieve low overshoot and short settling time. Finally, the simulation results demonstrate the validity of the proposed method.

A fault estimation and fault-tolerant control based sliding mode observer for LPV descriptor systems with time delay

This paper considers the problem of fault-tolerant control (FTC) and fault reconstruction of actuator faults for linear parameter varying (LPV) descriptor systems with time delay. A polytopic sliding mode observer (PSMO) is synthesized to achieve simultaneous reconstruction of LPV polytopic descriptor system states and actuator faults. Exploiting the reconstructed actuator faults and state estimates, a fault-tolerant controller is designed to compensate the impact of actuator faults on system performance by stabilizing the closed-loop LPV delayed descriptor system. Besides, the controller and PSMO gains are obtained throughout the resolution of linear matrix inequalities (LMIs) using convex optimization techniques. The developed PSMO could force the output estimation error to converge to zero in a finite time when the actuators faults are bounded through the reinjection of the output estimation error via a nonlinear switching term. Simulation results applied to a given numerical system are presented to highlight the superiority and effectiveness of the proposed approach.

A rules‐firing strength‐based neuro‐fuzzy observer for information‐poor systems

In this paper, a neuro-fuzzy observer (NFO) is proposed for estimating the unmeasured states of an information-poor system by relaxing the strictly positive real condition (without using filtered fuzzy basis function (FBF) and filtered output estimation error) and without using high-gain terms. To recover the performance of the observer in the absence of high-gain terms, a concept of weighted fuzzy rules (or strengthened FBF) is proposed. The weighted fuzzy rules are then used to propose the concept of weighted function approximation which is then utilized in the design of NFO to estimate the unknown dynamical function. For reducing computational power and avoiding over-tuning of the weights, a concept of relay-switching is also introduced in the design of the NFO. The stability analysis of the proposed NFO is also presented using Lyapunov approach and the effectiveness of the proposed scheme is demonstrated through a simulation example.

Optimal output estimation for infinite-dimensional systems with disturbances

Abstract Often only some aspect of the state needs to be estimated, not the whole state. This problem is referred to as output estimation Also, there may be disturbances other than Gaussian noise. In such situations a Kalman filter may not be the most appropriate estimator. Two alternative approaches are to reduce the H 2 or H ∞ output estimation error. A derivation of both types of estimators for output estimation of linear infinite-dimensional systems is provided. A practical framework for constructing finite-dimensional estimators that provide performance arbitrarily close to optimal is developed.

Prediction‐discrepancy based on innovative particle filter for estimating UAV true position in the presence of the GPS spoofing attacks

In this paper, a novel prediction-discrepancy based on innovative particle filter (PDIPF) is proposed to solve the unmanned aerial vehicle (UAV) positioning problem in the presence of the global positioning system (GPS) spoofing attack, supposing that the GPS spoofing effects are in the form of unknown but bounded errors. To cope with the GPS spoofing attacks as unknown sudden changes of system state variables, the compensation of the GPS spoofing effects is adaptively done in two basic parts of PDIPF algorithm including particle weighting and covariance matrix adaption. In addition, a theorem is developed which verifies that the output estimation error is upper bounded by a given probability with the help of the adapted covariance matrix. Besides, the particle weight calculation in PDIPF is done with respect to the prediction discrepancy of generated particles from the GPS measurements. The proposed PDIPF is used to decrease the effects of any GPS spoofing errors with different probability density functions and estimate true position of UAV in the presence of the GPS spoofing attacks. The algorithm is applied to the inertial navigation system/GPS/Loran-C integration systems. Simulation results demonstrate the effectiveness of the proposed PDIPF algorithm in terms of accuracy and redundancy.

Intermediate Observer-Based Robust Distributed Fault Estimation for Nonlinear Multiagent Systems With Directed Graphs

This article focuses on the problem of robust distributed fault estimation for nonlinear multiagent systems with actuator faults and sensor faults. The communication topology of the multiagent systems is assumed to be directed. A novel intermediate observer design method is proposed to estimate the system states, actuator faults, and sensor faults. For the observer constructed in one agent, the output estimation errors of itself and its neighbors are considered, simultaneously. The observer matching condition is not needed in the observer design process. Based on Schur decomposition, the observer parameter calculation method is presented in terms of solution to one linear matrix inequality, which is with the same order as it is for the single agent system. Thus, the calculated amount remains unchanged even when the number of agents increases, since the inequality dimension is independent of the agent number. At last, simulation results are provided to illustrate the effectiveness of the proposed technique.

Sliding mode observers for a class of linear parameter varying systems

SummaryIn this paper, a new framework for the synthesis of a class of sliding mode observers for affine linear parameter varying (LPV) systems is proposed. The sliding mode observer is synthesized by selecting the design freedom via linear matrix inequalities (LMIs). Posing the problem from a small gain perspective allows existing numerical techniques from the literature to be used for the purpose of synthesizing the observer gains. In particular, the framework allows affine parameter‐dependent Lyapunov functions to be considered for analyzing the stability of the state estimation error dynamics, to help reduce design conservatism. Initially a variable structure observer formulation is proposed, but by imposing further constraints on the LMIs, a stable sliding mode is introduced, which can force and maintain the output estimation error to be zero in finite time. The efficacy of the scheme is demonstrated using an LPV model of the short period dynamics of an aircraft and demonstrates simultaneous asymptotic estimation of the states and disturbances.

Adaptive Fault-Tolerant Output Regulation of Linear Multi-Agent Systems With Sensor Faults

This article studies the problem of cooperative fault-tolerant output regulation of leader-follower multi-agent systems with sensor faults. To compensate for the faults existing in the followers, distributed observers based on relative output estimation errors are firstly designed. Then an adaptive fault-tolerant output regulation framework is built by solving the regulator equation. It is shown that stability of the closed-loop system can be ensured and that all tracking errors will converge to zero under the designed fault-tolerant controller. Finally, simulation results demonstrate the effectiveness of the proposed control law.

Output Feedback Consensus of Multi-agent Systems with Generalized Uniformly Joint-Connected Switching Networks

This paper presents an output feedback synthesis for leader-follower consensus of linear multi-agent systems with switching networks. We first establish uniform global exponential stability (UGES) for a class of cascaded linear switched systems by adopting weak zero-state detectibility (WZSD). Then a distributed output feedback controller is proposed based on the certainty equivalent principle, employing the neighborhood output estimation error only. A generalized uniformly joint-connected condition for switching networks is provided to check WZSD without any dwell-time condition.

Prescribed-Time Observers for Linear Systems in Observer Canonical Form

For linear systems in the observer canonical form, we introduce a state observer with time-varying gains that tend to infinity as time approaches a prescribed convergence time. The observer is shown to exhibit fixed-time stability with an arbitrary convergence time, which is prescribed by the user irrespective of initial conditions. The output estimation error injection terms are also shown to remain uniformly bounded and converge to zero at the prescribed time.

Stubborn State Estimation for Delayed Neural Networks Using Saturating Output Errors.

This paper is concerned with the stubborn state estimation of delayed neural networks that subject to a general class of disturbances in measurements, including outliers and impulsive disturbances as its special cases. This class of disturbances may be unbounded, irregular, and assorted; therefore, they can hardly be suppressed by existing identification-based estimation approaches. In this paper, a stubborn state estimator is constructed by intentionally devising a saturation scheme on the injection of output estimation error. The embedded saturation can effectively resist the influences from these measurement disturbances by saturating them. Moreover, the saturation threshold in the designed scheme is not constant but governed by a dynamic equation with parameters to be designed. Benefiting from this adaptiveness, the estimator obtains more freedom in dealing with various disturbances. By combining a novel Lyapunov functional, the generalized sector condition and two latest integral inequalities, a delay-dependent criterion is derived in a less conservative way to check whether the estimation error system with this dynamic saturation is globally stable. A sufficient condition with two tuning scalars is further provided to codesign the gain of the state estimator and the evolution law of the saturation threshold. Finally, two numerical examples are used to illustrate the stubbornness of this state estimator in the presence of measurement outliers or impulsive disturbances.

$\mathcal {L}_2$ State Estimation With Guaranteed Convergence Speed in the Presence of Sporadic Measurements

This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error at each sampling time. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve global exponential stability with a given decay rate to a set wherein the estimation error is equal to zero. Robustness with respect to external perturbations and $\mathcal{L}_2$-external stability from the plant perturbation to a given performance output are considered. Moreover, computationally efficient algorithms based on the solution to linear matrix inequalities are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in three examples.

Fault Detection of continuous time linear switched systems using combination of Bond Graph method and switching observer

In this paper, a new Fault Detection (FD) scheme based on combination of switching observer and Bond Graph (BG) method for linear continuous time switched systems with Average Dwell Time (ADT) approach is proposed. The proposed scheme is a BG-based two-stage FD system in which the compact state space representation and Global Analytical Redundancy Relations (GARRs) are derived based on the BG model. In the first stage, a switched observer is designed considering disturbance attenuation level, fault sensitivity and rapid fault detection criteria by solving a weighted Linear Matrix Inequality (LMI) optimization problem. Next, a new form of GARRs which is based on output estimation error of the observer and is called Error-based Global Analytical Redundancy Relations (EGARRs) is developed to combine the observer and BG method. The output estimation errors from the observer, which are adequately sensitive to faults and simultaneously the effects of disturbances are attenuated therein, are given to the EGARRs to generate the residuals of the FD system. The proposed method may be used for fault detection of switched linear systems with ADT based on the BG model of the system. Finally, two case studies including a two-tank system and a buck converter-driven DC motor are considered to show the efficiency and real-time implementation of the proposed method.

Sliding mode switching observer-based actuator fault detection and isolation for a class of uncertain systems

This paper proposes a fault detection and isolation (FDI) method for a class of uncertain systems with actuator faults. First, based on the multiple model schemes, a bank of parallel sliding mode switching observers are designed to match the fault-free, stuck and loss of effectiveness fault models. A switching strategy is introduced to maintain a sliding motion even in the presence of actuator faults. Stability analysis of the sliding motions and the reachability conditions are given in various fault models. Without the assumption that all states are available, the residual signals are constructed by using the measurable output estimation errors. Then, the fault detection scheme is designed by comparing the residual evaluation function with the threshold. The fault isolation scheme is derived by looking for the minimum residual evaluation function, which is generated by the observer that matches the current system model well. Finally, an L-1011 aircraft model is presented to illustrate the effectiveness of the FDI method obtained in this paper.

Fault estimation observer design for a class of nonlinear multiagent systems in finite‐frequency domain

SummaryThis paper focuses on the fault estimation observer design problem in the finite‐frequency domain for a class of Lipschitz nonlinear multiagent systems subject to system components or actuator fault. First, the relative output estimation error is defined based on the directed communication topology of multiagent systems, and an observer error system is obtained by connecting adaptive fault estimation observer and the state equation of the original system. Then, sufficient conditions for the existence of the fault estimation observer are obtained by using a generalized Kalman‐Yakubovich‐Popov lemma and properties of the matrix trace, which guarantee that the observer error system satisfies robustness performance in the finite‐frequency domain. Meanwhile, the pole assignment method is used to configure the poles of the observer error system in a certain area. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.

Fault diagnosis based on sliding mode observer for LPV descriptor systems

AbstractThis paper considers the problem of fault detection and reconstruction of actuator faults for linear parameter varying descriptor systems. A polytopic sliding mode observer (PSMO) is constructed to achieve simultaneous reconstruction of LPV polytopic descriptor system states and actuator faults. Sufficient conditions for the existence and design algorithm of the proposed polytopic sliding mode observer are provided. In addition, the design of the PSMO is formulated in terms of linear matrix inequalities that can be suitably solved using convex optimization techniques. This PSMO can force the output estimation error to converge to zero in a finite time when the actuators faults are bounded through the reinjection of the output estimation error via a nonlinear switching term. The effectiveness of the design technique is illustrated through a simulation of an anaerobic bioreactor.