Observer Design Scheme Research Articles

Nonfragile [formula omitted] observer-based fuzzy control for nonlinear networked control systems with multipath packet dropouts

This work considers the design of nonfragile H∞ observer-based controller for nonlinear networked control systems (NCSs) subject to multipath packet dropouts. The nonlinear NCSs are modeled through the Takagi–Sugeno (T–S) fuzzy model. The occurrences of packet dropouts in the measurable output and the control input indicate the multipath packet dropouts. Two random sequences which are mutually independent and obey the Bernoulli distribution are adopted to represent the multipath packet dropouts. Unlike most existing works about the observer-based controller design, a novel observer design scheme is developed in this paper for the T–S fuzzy NCSs with packet dropouts, which does not require the observer to be designed to share the same local system parameters “Al” as the fuzzy plant. Then, by means of the Lyapunov function approach, sufficient conditions are developed to make certain that the controlled T–S fuzzy NCSs are stochastically stable with a H∞ performance index. Through adopting a two-step design method, the search for the local system parameters and gains of the observer and the controller gains is formulated as a feasibility problem of linear matrix inequalities (LMIs). Eventually, the effectiveness of the derived results is verified by an example.

Fault Estimation and Tolerant Control of a Class of Nonlinear Systems and Its Application in High-Speed Trains

This brief investigates the problem of fault estimation and tolerant control for a class of large-scale systems composed of multiple subsystems of second-order nonlinear dynamics. In particular, there is no growth rate condition on system nonlinearities or bounded constraints on faults or their derivatives. Technically, a novel representation of a fault based on its structural information is used for the problem formulation, which facilitates the design of a distributed fault estimation observer (DFEO) with the fault estimation error globally asymptotically approaching zero. Based on the observer, a distributed fault tolerance controller (DFTC) can be designed for asymptotical reference trajectory tracking. The overall observer and controller design scheme are applied to high-speed trains in the presence of actuator faults, which illustrates the effectiveness of the scheme in a practical application.

Distributed Observer-Based Robust Fault Estimation Design for Discrete-Time Interconnected Systems With Disturbances.

This article focuses on the distributed robust fault estimation problem for a kind of discrete-time interconnected systems with input and output disturbances. For each subsystem, by letting the fault as a special state, an augmented system is constructed. Particularly, the dimensions of system matrices after augmentation are lower than some existing related results, which may help to reduce calculation amount, especially, for linear matrix inequality-based conditions. Then, a distributed fault estimation observer design scheme that utilizes the associated information among subsystems is presented to not only reconstruct faults, but also suppress disturbances in the sense of robust H∞ optimization. Besides, to improve the fault estimation performance, a common Lyapunov matrix-based multiconstrained design method is first given to solve the observer gain, which is further extended to the different Lyapunov matrices-based multiconstrained calculation method. Thus, the conservatism is reduced. Finally, simulation experiments are shown to verify the validity of our distributed fault estimation scheme.

A novel H∞ memory observer design for uncertain switched nonlinear systems using past output measurements

AbstractThis paper tackles the problem of robust memory observer design problem for discrete‐time switched nonlinear systems by using past output measurements. Different from traditional design strategies of Luenberger‐type observers using the current output measurements, the memory Luenberger‐type observer design strategy introduces the past output measurements of switched systems and observers simultaneously. In addition, in order to better describe the observer error systems, a novel augmented state variable framework of the observer error systems is developed. The highlight of this paper lies that the memory observer design strategy is developed by considering past output measurements and state error values of memory observers, whose performance can be improved by increasing the number of past output measurements used in the observer design, which is an important discovery and significant novelty of this work. By combining the multiple Lyapunov functions approach and average dwell time technique, and introducing matrix variables with free structure, new sufficient conditions for weighted performance analysis of observer error systems are derived. Then, the memory observer synthesis conditions are obtained in the form of linear matrix inequality (LMI), and the memory observers can be obtained by solving these LMIs. Lastly, two examples are presented to show the advantages and effectiveness of the derived results.

Flat input based canonical form observers for non‐integrable nonlinear discrete‐time systems

AbstractWe define flat inputs for discrete‐time systems and carry over a flat input based observer design strategy for non‐integrable nonlinear continuous‐time systems to the discrete‐time case. This approach allows to design observers for nonlinear discrete‐time systems that cannot be transformed into observer canonical form, i.e., conventional observer design strategies fail. This approach is illustrated by two examples.

A New Method of Fault Estimation Observer Design for T-S Fuzzy Singular Systems With Disturbances Using Dissipativity Theory

This brief dedicates to addressing the robust fault estimation (FE) problem for a class of T-S fuzzy singular systems (TSFSSs) subject to faults and disturbances. A dissipativity-based FE observer design scheme is proposed to realize fault reconstruction, by which the FE performance can be improved in contrast to the existing one. With the help of the Lyapunov approach, dissipativity theory and matrix transformation technique, a brand-new condition is established to ensure observation error dynamics to be strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\mathscr {Q}, \mathscr {U}, \mathscr {R})-\iota -$ </tex-math></inline-formula> dissipative. It is worth mentioning that different from some previous studies, our method can solve observer gains simultaneously in a strict linear matrix inequality (LMI) framework rather than determine some of them artificially. Moreover, to bring extra degrees of freedom, slack scalars and matrices are added in FE observer design. The superiority of our method is fully illustrated via simulations.

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.

Formula omitted] observer design for networked Hamiltonian systems with sensor saturations and missing measurements

In this paper, the H∞ observer design problem is investigated for discrete-time Hamiltonian systems subject to missing measurement and sensor saturations governed by Bernoulli distributed random variables. Our purpose is to design an observer such that the error dynamics of the state estimation is exponentially mean-square stable with prescribed H∞ performance. By resorting to the Lyapunov function and the Hamiltonian system property, sufficient conditions are derived to guarantee the existence of the desired observer. Moreover, observer gains are designed in forms of the solutions to certain matrix inequalities. Finally, an illustrative example is utilized to testify the effectiveness of our observer design scheme.

Adaptive Fuzzy Observer-Based Fault Estimation for a Class of Nonlinear Stochastic Hybrid Systems

This article studies the fault estimation problem for a class of continuous-time nonlinear Markovian jump systems with unmeasured states, unknown bounded sensor faults, and unknown nonlinearities simultaneously. In this article, a new adaptive fuzzy observer design scheme is developed, where the completely unknown nonlinear terms are approximated by adaptive fuzzy logic systems. By means of a novel online adaptive mechanism, the asymptotic stability of the error dynamic system is guaranteed despite of sensor faults and unknown nonlinear terms. Moreover, the sliding surface switching problem in the traditional sliding mode observer techniques can be avoided for Markovian jump systems. Finally, two practical examples are given to demonstrate the effectiveness of the proposed approach.

Event-Triggered Diagnostic Observer Design Using the Performance Tradeoff Approach

This paper presents an optimal diagnostic observer design scheme to deal with the remote fault detection problem for a local closed-loop system with unknown external disturbances and faults. To utilize limited network shared resources efficiently, an event-triggered generator is employed in the local closed-loop system to determine whether to transmit the current output measurement for fault detection. By constructing the error system that contains event-triggered transmission errors and evaluating the composition of the residual under the constraint of Luenberger conditions, the diagnostic observer which has optional order and flexible structure is designed by the use of factorization techniques to achieve the optimal performance tradeoff between disturbance robustness and fault sensitivity. Next, the inevitable influence of reference input on the residual is taken into account in the residual evaluation to deliver a time-varying threshold. Finally, a vehicle lateral dynamic system is presented to illustrate the validity of the proposed optimal diagnostic observer design scheme.

A novel approach for event-triggered state-estimation of one-sided Lipschitz systems for efficient bandwidth utilization

This paper proposes a robust event-triggered observer design scheme for the systems fulfilling the one-sided Lipschitz and quadratic inner-boundedness conditions. The suggested observer scheme differs from the traditional methods because it deals with a less conservative and a more generalized class of nonlinear systems while utilizing fewer resources and meeting performance requirements. In contrast to the conventional Lipschitz methods, the proposed method considers a broader class of OSL systems, and it can avoid a high-gain observer, which can be sensitive to the measurement noise. The proposed linear matrix inequalities-based observer design guarantees the uniformly ultimately bounded convergence of the observation error with an exponential decay under disturbances. Also, several scenarios selecting a threshold for event-triggering schemes from an observer design perspective are addressed along with their advantages and issues. Simulation results are provided to validate the established results.

Fast Parameter Estimation for Adaptive Maximum Torque Per Ampere Control of Interior Permanent Magnet Synchronous Motor Drives

This paper proposes a fast adaptive parameter estimation method for maximum torque per ampere control (MTPA) of interior permanent magnet synchronous motor (IPMSM) drives. The adaptive features that enable fast parameter estimation are investigated, and an adaptive observer with a structure capable of achieving fast estimation is proposed. A cascade adaptive observer design strategy is presented in order to obtain the benefit of fast estimation from the proposed adaptive scheme. The MTPA is achieved through the solution of the stator current optimization problem combined with the IPMSM estimated parameters. Simulation and experimental results are provided in order to validate the proposed fast estimation adaptive MTPA algorithm.

Control Design for Uncertain Switched Nonlinear Systems: Adaptive Neural Approach

This paper addresses adaptive neural output feedback control for uncertain nonlinear switched systems. The main difficulty for control design comes from the loss of the precise information on those virtual coefficients of each subsystem. To overcome this difficulty, we give a robust observer design scheme by using convex combination approach. Furthermore, develop an observer-based output feedback control strategy. During the procedure of control design, adaptive neural control approach is used to deal with the unknown nonlinear functions and backstepping technique is employed to construct the ideal control laws. It is shown that the presented control law achieves the control issue of getting small tracking error, meanwhile, ensuring boundedness of all the closed-loop signals. Finally, a simulation example is used to test our results.

Anti‐disturbance adaptive sampled‐data observers for a class of nonlinear systems with unknown hysteresis

AbstractIn this article, based on radial basis function neural network (RBFNN) and disturbance estimator (DE), an adaptive sampled‐data observer design scheme is proposed for a class of nonlinear systems with unknown Prandtl–Ishlinskii (PI) hysteresis and unknown multiple disturbances. To begin with, we investigate a class of sampled‐data nonlinear systems and present corresponding sufficient conditions ensuring ultimate uniform boundedness (UUB). Subsequently, a sampled‐data observer and a DE are designed to estimate the unknown states and compounded disturbances, respectively. Additionally, the unknown hysteresis and the unknown unmatched disturbances are approximated by RBFNNs. Meanwhile, we also give the learning laws of the weights of RBFNNs. The estimation errors of the states and the weights are verified to be UUB in the light of the obtained sufficient conditions and a special constructing Lyapunov–Krasovskii function. Finally, the effectiveness of the proposed design method is verified by numerical simulations.

State-estimation-based adaptive sliding mode control of uncertain switched systems: A novel linear sliding manifold approach

A new sliding mode observer design scheme is developed with a novel linear sliding manifold for the exponential stabilization problem of a class of uncertain switched systems in this note. Firstly, the linear sliding manifold is constructed based on a modified observer, through which a new technical approach of the underlying system analysis is exploited to devise a novel exponential stability criteria. Moreover, an associated adaptive switching controller is presented, by which the arrival condition of the designated sliding manifold is fulfilled. Ultimately, illustrative examples are conducted to confirm the feasibility of the proposed scheme.

A Novel Approach to State and Unknown Input Estimation for Takagi–Sugeno Fuzzy Models With Applications to Fault Detection

In this paper, a novel approach is proposed for state and unknown input estimation of Takagi-Sugeno fuzzy systems. By introducing an augmented state vector, containing both system state and the unknown input, a functional observer is proposed to estimate this vector, and the proposed observer provides a highly flexible estimation output. Through casting the observer design problem into an equivalent solvability problem of a linear matrix equation with respect to the observer gains, the existence condition for the proposed observer is explicitly derived in terms of matrix rank. Furthermore, a parameterization methodology of the observer gain matrices is provided as well, which avoids directly solving the Sylvester equation. The proposed observer design scheme is further applied to the $H\_{}/H_\infty $ fault detection problem, and the effectiveness of the proposed approach is demonstrated by state and unknown input estimation for a tunnel diode circuit and fault detection for a continuously stirred tank reactor system.

Robust Observer Design for Two-Dimensional Discrete Positive Switched Systems With Delays

The design problem of the robust positive observer for a class of two-dimensional (2-D) positive discrete switched systems in the presence of delays and uncertainties is considered in this brief. The delays and uncertainties in this brief are assumed to be time-varying and polytopic type, respectively. Firstly, the multiple Lyapunov functional (MLF) approach has been used to formulate some sufficient asymptotical stability conditions for 2-D switched systems with uncertainties, by choosing a suitable co-positive Lyapunov-Krasovskii functional (CPLKF). Secondly, under the assumption that the system states are not measurable, a robust observer design scheme is formulated that helps in the approximation of the corresponding non-negative states. It also ensures the asymptotic convergence of the associated error system. Finally, an appropriate example is discussed to show the usefulness of the proposed results.

Space-sampling-based fault detection for nonlinear spatiotemporal dynamic systems with Markovian switching channel

This technical note is devoted to investigating the fault detection problem for a class of nonlinear spatiotemporal dynamic systems. Initially, by using sector nonlinearity approach, the considered nonlinear systems are represented by an Takagi–Sugeno fuzzy model. Second, a new measure method, piecewise measure, is introduced to save the cost of system design. Furthermore, taking into account the switching network transmission channel, a mode-dependent asynchronous fuzzy diagnostic observer is constructed. Then, the sufficient conditions that guarantee the disturbance/control-inputs robustness and fault sensitivity are established to optimize the fault detection system’s performance. Finally, a practical application (cooling fin of a high-speed aerospace vehicle) is given to illustrate the effectiveness of the developed diagnostic observer design strategy.

Complex-Coefficient Adaptive Disturbance Observer for Position Estimation of IPMSMs With Robustness to DC Errors

Model-based position-sensorless control of interior permanent magnet synchronous motors (IPMSMs) is promising for high-speed operation, besides the fact that the estimation accuracy degrades by dc errors from integration, measurements, and parameter uncertainties. In this article, a new complex-coefficient adaptive disturbance (CCAD) observer based on the back electromotive force estimation is proposed. The proposed CCAD observer has a bandpass characteristic and possesses resonating peak response at the corner frequency which is adapted to the synchronous rotor frequency. This adaptive resonant frequency effectively improves the robustness to dc errors, without magnitude loss and phase delay. The proposed observer is also compact and has lower order as compared to the other bandpass observers, and that substantially benefits in the embedded implementation. To configure the proposed CCAD observer, a reverse observer design scheme is analyzed. The stability of the observer is guaranteed based on a speed adaptation law, and small-signal approximation is then applied to linearize the proposed observer for parameter design and dynamic analyses, which have not been well discussed in literature. The proposed method is verified by experiments for a 15 kW IPMSM drive.

A New Switched State Jump Observer for Traffic Density Estimation in Expressways Based on Hybrid-Dynamic-Traffic-Network-Model.

When faced with problems such as traffic state estimation, state prediction, and congestion identification for the expressway network, a novel switched observer design strategy with jump states is required to reconstruct the traffic scene more realistically. In this study, the expressway network is firstly modeled as the special discrete switched system, which is called the piecewise affine system model, a partition of state subspace is introduced, and the convex polytopes are utilized to describe the combination modes of cells. Secondly, based on the hybrid dynamic traffic network model, the corresponding switched observer (including state jumps) is designed. Furthermore, by applying multiple Lyapunov functions and S-procedure theory, the observer design problem can be converted into the existence issue of the solutions to the linear matrix inequality. As a result, a set of gain matrices can be obtained. The estimated states start to jump when the mode changes occur, and the updated value of the estimated state mainly depends on the estimated and the measured values at the previous time. Lastly, the designed state jump observer is applied to the Beijing Jingkai expressway, and the superiority and the feasibility are demonstrated in the application results.