Functional Interval Observers Research Articles

State Estimation for a New Battery and Motor Circuit Model of an Electric Vehicle Using Event-Triggered Functional Interval Observers

State Estimation for a New Battery and Motor Circuit Model of an Electric Vehicle Using Event-Triggered Functional Interval Observers

Design of Functional Interval Observer for Discrete Time-Varying Nonlinear Interconnected Systems Based on Coding-Decoding Scheme

In this paper, we design a distributed functional interval observer for discrete time-varying nonlinear interconnected systems. The communication between subsystems adapts the coding-decoding scheme (CDS) to save bandwidth and avoid data conflicts. The state set is described by the ellipsoid which can improve estimation accuracy and reduce conservatism. Besides, we give the conditions for the establishment of the observer and the stability of the error dynamic system. The observer gain matrices are obtained by solving a set of linear matrix inequalities (LMI) and some given conditions. The shape matrix of the ellipsoid is determined by selecting the optimal solution. Finally, we give two simulation examples to prove the designed functional interval observer is effective.

Functional interval observer design for multivariable linear parameter-varying systems

This paper presents a new functional interval observer design methodology for discrete-time multivariable Linear Parameter-Varying (LPV) systems subject to bounded uncertainties. A functional interval observer is designed to estimate the bounds of the functional state using H∞/L∞ formalism to attenuate the effects of the uncertainties and to improve the accuracy of the estimation. The sufficient conditions of the observer design are developed in terms of Linear Matrix Inequalities (LMIs) constraints using the Lyapunov stability theory. Eventually, the effectiveness of the proposed methodology is illustrated by a numerical example.

Functional Interval Observer for Discrete-Time Nonlinear Lipschitz Systems

This paper considers discrete-time nonlinear Lipschitz systems with unknown but bounded disturbances. Thanks to the existence of bounding decomposition functions for mixed monotone mappings and the Lyapunov approach, we present a functional interval observer to achieve stable upper and lower bounds for a linear function of the system state. The simulation on a numerical example is given to illustrate the theoretical results.

Functional interval observer design for linear time-varying systems with additive disturbances

This paper investigates the problem of the functional interval observer design for linear time-varying (LTV) systems with additive disturbances in both input and output channels. First, sufficient conditions for the existence of a functional interval observer for LTV systems are proposed. Based on the solution of a type of Sylvester matrix equations (generalized Sylvester equations, GSEs), completely parameterized expressions of functional interval observer coefficient matrices are established, yielding a simple and effective design approach for solving the interval estimation issue of the LTV system, while the free parameters in the expressions provide the design degrees of freedom that can be utilized to achieve additional system specifications. Furthermore, the developed observer may execute state estimation at the desired convergence rate, considerably improving estimate performance. Finally, a numerical example and a back-to-turn (BTT) aircraft control example are presented, with the results showing that the upper and lower bounds provided by the designed observer provide a better performance of interval estimation of the functional state variables, demonstrating the effectiveness of the proposed method.

Parametric Design of Functional Interval Observer for Time-Delay Systems with Additive Disturbances

Parametric Design of Functional Interval Observer for Time-Delay Systems with Additive Disturbances

Design of distributed functional interval observers for large-scale networks impulsive systems

In this paper, we consider the problem of designing distributed functional interval observers (IOs) for a class of large-scale networks impulsive systems with bounded uncertainties. We first design IOs for linear functions of the state vector of each system of the considered system. We then provide conditions for the existence of such IOs and an effective algorithm for computing unknown observer matrices. Finally, two examples and simulation results are given to illustrate the effectiveness of the proposed design method.

Functional Interval Observer for Discrete-Time Switched Descriptor Systems

This article investigates functional interval observer based estimation methods for discrete-time switched descriptor systems with disturbances. A functional observer is presented using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> formalism, and then a zonotope-based approach is applied to estimate its boundaries with a reduction of observer design constraints. To avoid the wrapping effect brought by the order reduction operations in the zonotope approach, reachability analysis is combined with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> technique to design a switched functional interval observer with a better performance. Moreover, the relationship between the existing method, zonotope approach, and reachability analysis method is discussed in detail. The aforementioned methods are applied to an example for comparisons and to show their performance.

Finite‐time functional interval observer for linear systems with uncertainties

This study investigates the problem of designing a finite-time functional interval observer (FTFIO) for linear systems with uncertainties. A novel structure is proposed to design an FTFIO for uncertain systems. Based on the proposed structure, the sufficient conditions for the existence of such a finite-time observer are established as a set of coefficient matrix equations with a constraint matrix. Meanwhile, using the obtained existence conditions, the parametric expression of an FTFIO is developed by adopting the solutions to a type of first-order Sylvester equations, which provides extra degrees of freedom. Finally, the FTFIO design method is efficiently applied to the estimation problem in two examples, including the simple numerical system and chaotic system.

Functional interval observers for nonlinear fractional-order systems with time-varying delays and disturbances

This article considers the estimation problem for a class of uncertain fractional-order systems with time-varying delays and disturbances, in which the time-varying delays are present in the state, while the disturbances are present in the output. A new design method of functional interval observers is proposed. In contrast to interval observers currently available in the literature, which dealt with integer-order systems or fractional-order systems without time delays, the functional interval observers with fractional-order [Formula: see text] in this article can deal with fractional-order time-delay systems and integer-order time-delay systems (when [Formula: see text]). Existence conditions of functional interval observers for non-linear fractional-order systems with time-varying delays are established and they are formulated in terms of linear programmings. Two algorithms are provided for determining the functional interval observers. Illustrative examples of the functional interval observer application are presented.

Functional interval observer design for singular fractional-order systems with disturbances

In this study, we consider the problem of designing functional interval observers for a class of singular fractional-order systems. The goal of this work is to design not a full state interval observer for singular fractional-order systems, but to design an observer for state functions of this kind of systems. Conditions for the existence of such functional interval observers are given and an effective algorithm for computing unknown observer matrices is provided in this study. Two numerical examples and simulation results are provided to illustrate the effectiveness of the proposed design method.

Distributed Functional Interval Observers for Nonlinear Interconnected Systems With Time-Delays and Additive Disturbances

In this article, a novel distributed functional interval observer design method is developed for nonlinear interconnected time-delay systems with additive disturbances in the outputs. The traditional distributed functional state observer is replaced by two distributed ones corresponding to two bounds (upper and lower bound) of functions of the state variables which need to be estimated. The structures of the functional interval observer for each subsystem are first proposed and then existence conditions are provided and formulated in terms of linear programmings (LPs). Finally, three examples are provided to illustrate the feasibility of the propounded theories.

Functional interval observer for discrete-time systems with disturbances

Abstract This paper further investigates the design problem of the functional interval observer for discrete-time systems with disturbances. Two methods are given to design functional interval observers. Given monotone system theory, a Luenberger-like functional interval observer is constructed and sufficient conditions are achieved by Sylvester equations in the first method. The second approach is known as the two-step method. An H∞ functional observer of the system is presented by the H∞ technique, and then the approach of the zonotope is used to estimate its upper and lower boundaries to improve the estimation accuracy. The above methods are applied to two examples for comparison and to show the correctness.

Design of functional interval observers for nonlinear fractional-order interconnected systems

ABSTRACTIn this paper, we address problem of distributed functional interval observers for a class of nonlinear fractional-order interconnected systems with bounded uncertainties. The system under consideration is formed by N () interconnected subsystems. We first design N stand-alone distributed functional interval observers for the system. The designed interval observer for each subsystem is based on the local outputs, known bounds of the local uncertainty and additional outputs from other subsystems but without the need to exchange the state estimates among the observers. Then, conditions for the existence of such distributed functional interval observers are derived and an effective algorithm for computing unknown observer matrices is provided. Finally, two numerical examples and simulation results are given to illustrate the effectiveness of the proposed design method.

Design of functional interval observers for non‐linear fractional‐order systems

AbstractThis paper considers the problem of designing functional interval observers for a class of non‐linear fractional‐order systems with bounded uncertainties. First, interval observers for linear functions of the state vector of the considered system are designed. Then, conditions for the existence of such interval observers are established and an effective algorithm for computing unknown observer matrices is provided in this paper. Finally, numerical examples and simulation results are given to illustrate the effectiveness of the proposed design method.

Functional interval observer for the linear systems with disturbances

A Luenberger-like functional interval observer for the linear systems with time-varying disturbances is developed in this study. First, as an extension of the definition of the general interval observer, a new definition of the functional interval observer is provided. Then the sufficient conditions for the existence of such an observer are introduced in terms of the properties of positive systems. Simultaneously, on the basis of the proposed existence conditions, the parametric design method of the interval observer for the linear functional of the states in the systems is presented by employing the solution of the Sylvester equations. Eventually, the correctness and efficiency of the obtained results are illustrated by a numerical example.

On Reduced-Order Linear Functional Interval Observers for Nonlinear Uncertain Time-Delay Systems with External Unknown Disturbances

In this paper, we consider the problem of designing reduced-order linear functional interval observers for nonlinear uncertain time-delay systems with external unknown disturbances. Given bounds on the uncertainties, we design two reduced-order linear functional state observers in order to compute two estimates, an upper one and a lower one, which bound the unmeasured linear functions of state variables. Conditions for the existence of a pair of reduced-order linear functional observers are presented, and they are translated into a linear programming problem in which the observers’ matrices can be effectively computed. Finally, the effectiveness of the proposed design method is supported by four examples and simulation results.