Additive Gain Perturbations Research Articles

A novel non-fragile [formula omitted] fault-tolerant course-keeping control for uncertain unmanned surface vehicles with rudder failures

This paper investigates the problem of non-fragile H∞ fault-tolerant course-keeping control (NFC) for uncertain unmanned surface vehicles (UUSV) with rudder failures. Firstly, due to the inevitable parameter perturbations in practice, the unmanned surface vehicles (USV) is modeled as a kind of uncertain Nomoto model, and an uncertain second-order under-damped system is used to describe the rudder system. Next, considering the distribution characteristic of failures, a distribution-dependent stochastic failure model is established and incorporated into the controller design. In order to investigate the fragile problems of the controller, a new non-fragile fault-tolerant scheme is given against multiplicative and additive controller gain perturbations. Finally, the effectiveness of the proposed methods is verified via two numerical examples.

Non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults

AbstractThis paper investigates the non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults. First, a novel fault model consisting of linear and nonlinear terms is established for the systems. By constructing a stochastic co‐positive Lyapunov function, the non‐fragile reliable controller is designed for the systems with additive gain perturbations using matrix decomposition technique. Then, the proposed design is extended for dealing with multiplicative gain perturbations and variable gain perturbations. Under the designed controllers, the resulting closed‐loop systems are positive and stochastically stable. All presented conditions are solvable in terms of linear programming. Finally, two illustrative examples are provided to verify the effectiveness of the theoretical results.

Fuzzy resilient control for synchronizing chaotic systems with time-variant delay and external disturbance

This paper focuses on the issue of fuzzy resilient control for synchronizing chaotic systems with time-variant delay and external disturbance. The goal is to design a fuzzy resilient controller with additive gain perturbations to guarantee that not only the drive and response systems are asymptotically synchronized in the absence of external disturbance, but also the synchronization error system has a prescribed disturbance attenuation index under the zero initial condition. By utilizing an appropriate Lyapunov–Krasovskii functional, the Bessel–Legendre inequality, and the reciprocally convex combination technique, a criterion on the stability and [Formula: see text] performance of the synchronization error system is derived. Then, by means of some decoupling methods, a design scheme of the fuzzy resilient controller is developed. Finally, one numerical example is provided to examine the effectiveness of the fuzzy resilient controller design scheme.

Non-fragile [formula omitted] filtering for a class of switched neural networks

This paper is devoted to non-fragile L2−L∞ filtering for switched neural networks with time-variant delay. The aim is to design a L2−L∞ filter subject to either additive or multiplicative gain perturbations, such that the filter-error system not only is asymptotically stable when there is no external disturbance but also has a predefined disturbance attenuation index under the zero initial condition. A criterion of the stability and L2−L∞ performance for the filter-error system is proposed by applying mode-dependent Lyapunov functionals, the Bessel–Legendre inequality, as well as the reciprocally convex combination technique. Then, a design method for the non-fragile L2−L∞ filter is developed by getting rid of some nonlinear coupling terms. The method is formulated as a problem of finding a feasible solution to a collection of linear matrix inequalities, which are computationally tractable. At last, two numerical examples are employed to illustrate the applicability of the L2−L∞ filtering design method.

Non‐fragile control of periodic piecewise linear time‐varying systems with time delay

In this study, the stability and stabilisation issues of a class of periodic piecewise linear time-varying systems with time delay are studied. Based on a lemma with respects to the negative definite matrix polynomial, a sufficient delay-dependent exponential stability condition is obtained via constructing a Lyapunov–Krasovskii functional with periodic matrix functions. Then, for two types of norm-bounded uncertainties of time-varying controller gains, the non-fragile stabilising controllers under the multiplicative and additive gain perturbations are designed to stabilise the closed-loop system. The obtained controller gains could be solved with linear matrix inequalities directly instead of using the iterative algorithm. That is valued in engineering applications. Numerical examples are presented to demonstrate the effectiveness of the proposed methods.

Robust partially mode‐dependent H∞ filtering for discrete‐time nonhomogeneous Markovian jump neural networks with additive gain perturbations

This paper studies the robust partially mode‐dependent H∞ filtering for nonhomogeneous Markovian jump neural networks with additive gain perturbations. The discrete time‐varying jump transition probability matrix is considered to be a polytope set. A partially mode‐dependent filter with additive gain perturbations is constructed to increase the robustness of the filter, which is subjects to H∞ performance index. Based on the Lyapunov function approach, sufficient conditions are established such that the filtering error system is robustly stochastically stable. The efficiency of the new technique is illustrated by an illustrative example and a biological network example.

A novel robust non-fragile control approach for a class of uncertain linear systems with input constraints

This paper addresses the non-fragile control problem for a class of uncertain linear systems subject to model uncertainty, controller perturbations, fault signals and input constraints. The controller to be designed is supposed to have additive gain perturbations. A novel state feedback controller is proposed based on the exact available expectation of a Bernoulli random variable, which is introduced to model the feature of the controller gain perturbation that randomly occurs. By using Lyapunov stability theory, new sufficient conditions are derived to design non-fragile controller for a class of uncertain linear systems considering input constraints. Compared with the existing non-fragile state feedback controller methods, the non-fragile property is fully considered to improve the tolerance of uncertainties in the controller, where the conservativeness can be reduced via the Bernoulli random variable. The effectiveness of the proposed control strategy is illustrated by two numerical examples.

Resilient dynamic output feedback control for discrete-time descriptor switching Markov jump systems and its applications

This paper investigates the resilient dynamic output feedback (DOF) control problem for discrete-time descriptor switching Markov jump systems for the first time, where the time-varying transition probabilities are described by a piecewise-constant matrix and a high-level signal subject to average dwell time switching. The controllers to be designed can tolerate additive gain perturbations. Firstly, by constructing a stochastic Lyapunov functional and using an average dwell time method, a sufficient condition is given such that the resultant closed-loop systems are stochastically admissible and have a $$H_{\infty }$$ noise attenuation performance. Then, based on the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition is presented such that the resultant closed-loop systems are stochastically admissible with a $$H_{\infty }$$ noise attenuation performance. When the uncertain parameters exist not only in plant matrices but also in controller gain matrices, the resilient DOF controller is developed in terms of LMIs, which can be of full order or reduced order. Compared with the previous ones, the proposed design methods do not impose extra constraints on system matrices or slack variables, which show less conservatism. Finally, numerical examples are given to illustrate the superiority and applicability of the new obtained methods.

Resilient estimation for T-S fuzzy descriptor systems with semi-Markov jumps and time-varying delay

This paper concerns the resilient estimation problem for nonlinear descriptor semi-Markov jumps systems (S-MJSs) with time-varying delay via Takagi–Sugeno (T-S) fuzzy model, where descriptor S-MJSs, T-S fuzzy model and resilient estimator design are firstly considered in a unified framework. The estimator to be designed is assumed to have additive gain perturbations. First, by constructing a comprehensive stochastic Lyapunov–Krasovskii functional, a sufficient condition is given such that the estimation error systems are stochastically admissible and have a prescribed H∞ noise attenuation performance index. Then, based on the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition is presented, which guarantees the estimation error systems are stochastically admissible and achieve a prescribed H∞ noise attenuation performance index. Meanwhile, the resilient fuzzy estimator is developed, which can be of full-order or reduced-order. The proposed design method doesn’t impose any constraints on slack variables, which are less conservative. Last, numerical examples are given to illustrate the superiority and applicability of the new obtained methods.

Performance Resilience Analysis of Dynamic Feedback Controllers for both Multiplicative and Additive Gain Perturbations

In this work, a procedure is presented for performance resilience analysis of continuous-time systems controlled by full-order dynamic feedback compensators. The resilience property is defined in terms of defining maximum perturbations on both the controller and observer gains that will maintain controller and observer eigenvalues in disjoint regions in the complex plane so that the closed loop system will sustain certain performance characteristics. The desired performance is characterized by the response speed and magnitude bounds on the response. Therefore, the intersection of two regions are chosen, vertical strips and sector regions, to guarantee upper and lower bounds on the settling (or response) time and an upper bound on the percent overshoot simultaneously. Maximum allowable gain perturbations are obtained based on the designer’s choices of closed loop eigenvalues and the regions in which eigenvalues remain when the gains are perturbed. The linear matrix inequality technique is used throughout the analysis process. Illustrative examples are included to demonstrate the effectiveness of the proposed methodology.

Robust resilient [formula omitted] control for uncertain stochastic systems with multiple time delays via dynamic output feedback

This paper deals with the problem of robust resilient L2−L∞ control for stochastic systems with multiple time delays and norm-bounded parameter uncertainties via dynamic output feedback. Both additive and multiplicative controller gain perturbations are considered. New delay-dependent conditions of robust mean-square exponential stability are developed by applying the Lyapunov–Krasovskii functional method and introducing free-weighting matrices. Two lemmas are given for reducing high-order nonlinearities, with the aid of which sufficient conditions are presented for the solvability of the robust resilient L2−L∞ control problem. The desired controllers can be constructed through the numerical solutions of a set of linear matrix inequalities. The proposed design conditions can be employed to determine reduced-order dynamic output feedback controllers without the need to impose any extra constraints on the system parameters. Numerical examples are provided to illustrate the effectiveness of the obtained results.

Robust Nonfragile Controllers Design for Fractional Order Large-Scale Uncertain Systems with a Commensurate Order1<α<2

The paper concerns the problem of stabilization of large-scale fractional order uncertain systems with a commensurate order1<α<2under controller gain uncertainties. The uncertainties are of norm-bounded type. Based on the stability criterion of fractional order system, sufficient conditions on the decentralized stabilization of fractional order large-scale uncertain systems in both cases of additive and multiplicative gain perturbations are established by using the complex Lyapunov inequality. Moreover, the decentralized nonfragile controllers are designed. Finally, some numerical examples are given to validate the proposed method.

Nonfragile Guaranteed Cost Control of Discrete-Time Fuzzy Bilinear System With Time-Delay

This paper focuses on the problem of nonfragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems (DFBS) with time-delay in both states and inputs. Based on the parallel distributed compensation approach, the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations.

Robust resilient controllers synthesis for uncertain fractional-order large-scale interconnected system

The problem of the decentralized stabilization for fractional order large-scale interconnected uncertain system with norm-bounded parametric uncertainties and controller gain perturbations is studied. It is solved under two circumstances: one is under the additive controller gain perturbations; the other is under the multiplicative ones. Sufficient conditions on the decentralized stabilization of fractional order large-scale interconnected system with a commensurate order 0<α<1 are established by applying a complex Lyapunov inequality method. The state feedback non-fragile controller designs for fractional order large-scale interconnected uncertain system under the two classes of gain perturbations are obtained in terms of solutions to LMIs. Numerical examples are used to illustrate the effectiveness of the proposed method.

Static Output Non-Fragile Control of Fuzzy Bilinear System

This paper focuses on the problem of non-fragile static output feedback control for discrete-time fuzzy bilinear systems. Based on the parallel distributed compensation approach, the sufficient conditions are derived in the presence of the additive controller gain perturbations. The stabilization conditions are further formulated into linear matrix inequalities (LMI) so that the desired controller can be easily obtained by using the LMI toolbox.

NON-FRAGILE GUARANTEED COST CONTROL OF T-S FUZZY TIME-VARYING DELAY SYSTEMS WITH LOCAL BILINEAR MODELS

This paper focuses on the non-fragile guaranteed cost control problem for a class of T-S fuzzy time-varying delay systems with local bi- linear models. The objective is to design a non-fragile guaranteed cost state feedback controller via the parallel distributed compensation (PDC) approach such that the closed-loop system is delay-dependent asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations. A sufficient condition for the existence of such non-fragile guaranteed cost controllers is derived via the linear matrix inequality (LMI) approach and the design problem of the fuzzy controller is formulated in term of LMIs. The simulation examples show that the proposed approach is effective.

Stabilization for Uncertain Multi-channel Markov Jump Stochastic Systems with Additive Gain Perturbations

In this paper, stabilization problem for a class of multi-channel Markov jump stochastic systems with additive gain perturbations is addressed. In order to design the state feedback stabilization controller, a novel control strategy that guarantees the adequate cost bound is established. A sufficient condition for the existence of the controller is derived in term of matrix inequality. In the sequel, for practical plants since it is not always easy to access the transition modes, the mode-independent strategy set is considered. As a result, it is shown that such strategy set can be obtained by solving the linear matrix inequality (LMI). Furthermore, in order to reduce the cost performance, fuzzy control for each input is combined with the static gain as additive gain perturbations. As a result, even if dramatic random parameter changes occur in the system, it is shown that the robust stability and the reduction of the cost can be attained. Finally, a simple numerical example is given to demonstrate the availability of the proposed method.

Decentralized State-Estimation of Interconnected Systems with Unknown Nonlinearities

An efficient state-estimation scheme is developed within the LMI framework for robust decentralized state estimation of systems composed of linear dynamic subsystems coupled by static nonlinear interconnections satisfying quadratic constraints. The procedure utilizes a general linear estimator structure, and consists of two steps, the first giving a block-diagonal Lyapunov matrix together with the robustness degree, and the second determining the filter parameters. Extension to the case of additive filter gain perturbations is established and numerical examples are provided to illustrate the applicability of the method.

Non-Fragile Decentralized Control for the Uncertain Singular Large-Scale Systems with Time-Delay

This paper is concerned with the non-fragile decentralized controller design problem for uncertain singular large-scale system with time-delay. Sufficient condition for the controller is expressed in terms of linear matrix inequalities(LMIs). When this condition is feasible, the desired controller can be obtained with additive gain perturbations and multiplicative gain perturbations. Finally, a numerical example is also given to illustrate the effectiveness.

Robust Non-fragile PID Controller Design for the Stroke Regulation of Metering Pumps

This job focuses on the stroke regulation of a class of high-precision metering pumps. A parameter-tuning method of robust non-fragile PID (proportional-integral-derivative) controllers is proposed with the assumption that a PID controller has additive gain perturbations. An H-infinite robust PID controller can be obtained by solving a linear matrix inequality. This approach can guarantee that the closed-loop control systems is asymptotically stable and the H-infinite norm of the transfer function from the disturbance to the output of a controlled system is less than a given constant to attenuate disturbances. The simulation case shows that the control performance of the proposed strategy is significantly better than the traditional PID approach in the situation with perturbations of controller parameters.