Class Of Continuous-time Nonlinear Systems Research Articles

Set-based adaptive estimation for a class of nonlinear systems with time-varying parameters

In this paper, an adaptive estimation technique is proposed for the estimation of time-varying parameters for a class of continuous-time nonlinear system. A set-based adaptive estimation is used to estimate the time-varying parameters along with an uncertainty set. The proposed method is such that the uncertainty set update is guaranteed to contain the true value of the parameters. Unlike existing techniques that rely on the use of polynomial approximations of the time-varying behaviour of the parameters, the proposed technique does require a functional representation of the time-varying behaviour of the parameter estimates. A simulation example and a building systems estimation example are considered to illustrate the developed procedure and ascertain the theoretical results.

On observer-based controller design for Sugeno systems with unmeasurable premise variables

This paper considers the design of observer-based controller for a class of continuous-time nonlinear systems presented by Takagi–Sugeno (T–S) model with unmeasurable premise variables. This T–S structure can represent a larger class of nonlinear systems as compared to the measurable premise variable case but its analysis is more complicated. To reduce the design complexity, a common output model for subsystems is employed by the use of local nonlinear rules. As a result, the proposed T–S structure reduces the number of rules in the Sugeno model as well as the analysis complexity. The proposed controller guarantees exponential convergence of states based on the fuzzy Lyapunov function analysis and Linear Matrix Inequality (LMI) formulation. Simulation results illustrate effectiveness of the proposed method.

Nonsynchronized Robust Filtering Design for Continuous-Time T–S Fuzzy Affine Dynamic Systems Based on Piecewise Lyapunov Functions

This paper investigates the problem of robust H(∞) state estimation for a class of continuous-time nonlinear systems via Takagi-Sugeno (T-S) fuzzy affine dynamic models. Attention is focused on the analysis and design of an admissible full-order filter such that the resulting filtering error system is asymptotically stable with a guaranteed H(∞) disturbance attenuation level. It is assumed that the plant premise variables, which are often the state variables or their functions, are not measurable so that the filter implementation with state-space partition may not be synchronous with the state trajectories of the plant. Based on piecewise quadratic Lyapunov functions combined with S-procedure and some matrix inequality linearization techniques, some new results are presented for the filtering design of the underlying continuous-time T-S fuzzy affine systems. Illustrative examples are given to validate the effectiveness and application of the proposed design approaches.

Time-varying increasing-gain observers for nonlinear systems

A full-order state observer for a class of nonlinear continuous-time systems is presented as generalization of the high-gain observer for having a time-varying gain that is let to be small in the first time instants, increases over time up to its maximum, and then is kept constant. The global stability of the resulting estimation error is proved by means of a Lyapunov functional via a change of coordinate. The design of such an observer is obtained by solving a nonlinear programming problem and using series expansions to set the time-varying gain.

Interval state estimation for uncertain nonlinear systems

The objective of this work is to develop some design methods of interval observers for a class of nonlinear continuous-time systems. It is assumed that the estimated system can be represented as a superposition of the nominal subsystem (belonged to the class of uniformly observable systems) and a Lipschitz nonlinear perturbation vanishing at the origin. Then it is shown there exists an interval observer for the system that estimates the set of admissible values for the state consistent with the output measurements. An example of the observer application is given with computer simulation results.

H∞Control of Pairwise Distributable Large-Scale TS Fuzzy Systems

The paper presents new conditions suitable in design of the stabilizing state controller for a class of continuous-time nonlinear systems, which are representable by pairwise distributable Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the pairwise subsystems fuzzy control scheme relating to the parallel distributed output compensators, the extended bounded real lemma form and the sufficient design conditions for pairwise decentralized control are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and, using free tuning parameter, provides the way to obtain global stability of such large-scale TS systems and optimizes subsystems interactionH∞norm bounds.

Stabilizing Fuzzy Output Control for a Class of Nonlinear Systems

The paper presents new conditions suitable in design of a stabilizing output controller for a class of continuous-time nonlinear systems, represented by Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the fuzzy control scheme relating to the parallel distributed output compensators, the sufficient design conditions are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and guarantees global stability of the system. Simulation result illustrates the design procedure and demonstrates the performances of the proposed design method.

Analysis and design of robust estimation filter for a class of continuous-time nonlinear systems

This article addresses the design of a multiconstrained robust estimation filter (MREF) for a class of continuous-time nonlinear systems in the presence of input and output disturbances. By constructing an augmented system, the MREF achieves the estimation of both states and faults, under existence conditions that are less restrictive than those associated with existing adaptive fault diagnosis observer (AFDO) and sliding mode observer design. Moreover, a detailed discussion on and comparison with the AFDO design are given. Furthermore, by introducing slack variables, improved results on MREF design are obtained such that different Lyapunov functions can be separately designed for multiple constraints. Simulation results are presented to illustrate our contributions.

Convergence of a parameter switching algorithm for a class of nonlinear continuous systems and a generalization of Parrondo’s paradox

In this paper, we prove the convergence of a numerical algorithm that switches in some deterministic or random manner, the control parameter of a class of continuous-time nonlinear systems while the underlying initial value problem is numerically integrated. The numerically obtained attractor is a good approximation of the attractor obtained when the control parameter is replaced with the average of the switched values. In this way, a generalization of Parrondo’s paradox can be obtained. As an application, the Lorenz and Rabinovich–Fabrikant systems are used for illustration.

Design of Fuzzy Based Virtual Actuator for a Class of Nonlinear Systems

The paper presents new conditions suitable in design of a virtual actuator for a class of continuous-time nonlinear systems represented by Takagi-Sugeno models, and measurable premise variables. Simulation results illustrate the design procedure and demonstrate the basic performances of the proposed control design method.

Robust and Resilient Finite-Time Control of a Class of Continuous-Time Nonlinear Systems

Finite-time state-feedback stabilization of a class of continuous-time nonlinear systems with conic type nonlinearities, bounded feedback control gain perturbations, and additive disturbances is presented. Sufficient conditions for the existence of a robust and resilient linear finite-time state-feedback controller for this class of systems are derived. Then, using linear matrix inequality techniques, solutions for the controller gain and the upper bound on the gain perturbations are obtained. The developed controller is robust for all unknown nonlinearities lying in a hyper-sphere and all admissible disturbances. Furthermore, it is resilient against any bounded perturbations that may modify the controller's gain by at most a prescribed amount. We conclude the paper with a numerical example illustrating the applicability of the main result.

Set-based adaptive estimation for a class of nonlinear systems with time-varying parameters

In this paper, an adaptive estimation technique is proposed for the estimation of time-varying parameters for a class of continuous-time nonlinear system. A set-based adaptive estimation is used to estimate the time-varying parameters along with an uncertainty set. The proposed method is such that the uncertainty set update is guaranteed to contain the true value of the parameters. Unlike existing techniques that rely on the use of polynomial approximations of the time-varying behaviour of the parameters, the proposed technique does require a functional representation of the time-varying behaviour of the parameter estimates. A simulation example is used to illustrate the developed procedure and ascertain the theoretical results.

Optimal Fuzzy Control for a Class of Nonlinear Systems

The paper presents conditions suitable in design giving quadratic performances to stabilizing controllers for given class of continuous‐time nonlinear systems, represented by Takagi‐Sugeno models. Based on extended Lyapunov function and slack matrices, the design conditions are outlined in the terms of linear matrix inequalities to possess a stable structure closest to LQ performance, if premise variables are measurable. Simulation results illustrate the design procedure and demonstrate the performances of the proposed control design method.

Robust Fault Diagnosis based on Constraint Satisfaction and Interval Continuous-time Parity Equations

This paper deals with fault diagnosis for a class of nonlinear continuous-time systems based on an interval extension of continuous-time parity equations. The parity equations are designed based on ordinary differential equations modeling some links between the successive output and input vector derivatives. The noisy inputs and outputs are evaluated through a high-order sliding-mode differentiator. The redundancy relations are formulated as a Constraint Satisfaction Problem (CSP) with faults as unknown variables. In this case, a reliable estimation of the fault magnitude can be performed by solving the CSP using interval techniques. This technique is well suited to deal with actuator faults as well as parametric or sensor faults. However, in this paper, we choose to focus on actuator faults and the performance of the proposed approach is illustrated through simulations on oscillatory failure detection in aircraft surface servo loops. input observer, fault reconstruction, consistency techniques, nonlinear systems.

Non-fragile fuzzy H∞ filter design for nonlinear continuous-time systems with [formula omitted] stability constraints

This paper is concerned with the problem of designing non-fragile H ∞ filters for a class of nonlinear continuous-time systems. The considered nonlinear plant is represented by a Takagi–Sugeno (T–S) fuzzy model. Attention is focused on the design of a filter such that the filtering error system guarantees a prescribed H ∞ performance level with D stability constraints, where the filter to be designed is assumed to be with multiplicative gain variations. A sufficient condition for the non-fragile H ∞ filter design is proposed in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H ∞ fuzzy filter is given. A simulation example will be given to show the efficiency of the proposed design methods.

Interval State Estimation for a Class of Nonlinear Systems

The goal of this technical note is to design interval observers for a class of nonlinear continuous-time systems. The first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time-invariant changes of coordinates even if the system is not cooperative. This result is extended to a class of nonlinear systems using partial exact linearisations. The proposed observers guarantee to enclose the set of system states that is consistent with the model, the disturbances and the measurement noise. Moreover, it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity, uncorrelation or type of distribution. The proposed observer is illustrated through numerical simulations.

Lyapunov-based design of resilient mixed MSE-dissipative-type state observers for a class of nonlinear systems and general performance criteria

A class of continuous-time nonlinear system and measurement equations having locally incrementally conic nonlinearities and finite energy disturbances is considered. A Lyapunov-based resilient mixed mean square error (MSE)-dissipative-type state observer design approach is presented, which guarantees the satisfaction of MSE-type estimation error performance together with a variety of dissipative performance criteria ranging from H∞ to passivity of various types. Linear matrix inequalities are used in the feasibility study of the solution. Some simulation examples are included to illustrate and provide support to the effectiveness of the proposed design methodology.

Stabilising nonlinear systems with time-varying delays by new parametrised method

This paper establishes new robust delay-dependent stability and stabilisation methods for a class of nonlinear continuous-time systems with time-varying delays. The nonlinearities are unknown time-varying perturbations satisfying Lipschitz conditions in the state and the delayed-state. An appropriate Lyapunov functional is constructed and delay-dependent stability analysis is performed to characterise Linear Matrix Inequalities (LMIs)-based conditions under which the nominally-linear delay system is robustly asymptotically stable with an γ-level L 2-gain. Then we design delay-dependent feedback stabilisation schemes: a static one based on state (delayed-satte)-measurements and a dynamic one based on observer-based output feedback. In all schemes, the closed-loop feedback system enjoys the delay-dependent asymptotic stability with a prescribed γ-level L 2-gain. The feedback gains are determined by convex optimisation over LMIs and all the developed results are tested on a representative example.

Stochastically Resilient Observer Design for a Class of Continuous-Time Nonlinear Systems

AbstractThis work addresses the design of stochastically resilient or non-fragile continuous-time Luenberger observers for systems with incrementally conic nonlinearities. Such designs maintain the convergence and/or performance when the observer gain is erroneously implemented due possibly to computational errors i.e. round off errors in computing the observer gain or changes in the observer parameters during operation. The error in the observer gain is modeled as a random process and a common linear matrix inequality formulation is presented to address the stochastically resilient observer design problem for a variety of performance criteria. Numerical examples are given to illustrate the theoretical results.

Stochastic Averaging in Continuous Time and Its Applications to Extremum Seeking

We investigate stochastic averaging theory in continuous time for locally Lipschitz systems and the applications of this theory to stability analysis of stochastic extremum seeking algorithms. First, we establish a general stochastic averaging principle and some related stability theorems for a class of continuous-time nonlinear systems with stochastic perturbations and remove or weaken several significant restrictions present in existing results: global Lipschitzness of the nonlinear vector field, equilibrium preservation under the stochastic perturbation, global exponential stability of the average system, and compactness of the state space of the perturbation process. Then, we propose a continuous-time extremum seeking algorithm with stochastic excitation signals instead of deterministic periodic signals. We analyze the stability of stochastic extremum seeking for static maps and for general nonlinear dynamic systems.