Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems

This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness(FTB) based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities(LMIs), which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control(SMC) law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface s(t) = c(c is a constant) in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.

Stability analysis for a second-order continuous finite-time control system subject to a disturbance

In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.

Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems

This article addresses the finite-time boundedness(FTB)problem for nonlinear descriptor systems.Firstly,the nonlinear descriptor system is represented by the Takagi-Sugeno(T-S)model,where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix.By using a descriptor redundancy approach,the fuzzy representation in the derivative matrix is reformulated into a linear one.Then,we introduce a fuzzy sliding mode control(FSMC)law,which ensures the finite-time boundedness(FTB)of closed-loop fuzzy control systems over the reaching phase and sliding motion phase.Moreover,by further employing the descriptor redundancy representation,the sufficient condition for designing FSMC law,which ensures the FTB of the closed-loop control systems over the entire finite-time interval,is derived in terms of linear matrix inequalities(LMIs).Finally,a simulation study with control of a photovoltaic(PV)nonlinear system is given to show the effectiveness of the proposed method.

<i>H</i>_∞Finite-Time Control for Switched Linear Systems with Time-Varying Delay

Finite-time boundedness and H∞ finite-time boundedness of switched linear systems with time-varying delay and exogenous disturbances are addressed. Based on average dwell time (ADT) and free-weight matrix technologies, sufficient conditions which can ensure finite-time boundedness and H∞ finite-time boundedness are given. And then in virtue of the results on finite-time boundedness, the state memory feedback controller is designed to H∞ finite-time stabilize a time-delay switched system. These conditions are given in terms of LMIs and are delay-dependent. An example is given to illustrate the efficiency of the proposed method.

New Approach to Observer-Based Finite-Time H_(∞)Control of Discrete-Time One-Sided Lipschitz Systems with Uncertainties

This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditions,the authors derive less conservative criterion for the controller design and observer design.A new criterion is proposed to ensure the closed-loop system is finite-time bounded(FTB).The sufficient conditions are established to ensure the closed-loop system is H_(∞)finite-time bounded(H_(∞)FTB)in terms of matrix inequalities.The controller gains and observer gains are given.A numerical example is provided to demonstrate the effectiveness of the proposed results.

Global finite-time attitude regulation using bounded feedback for a rigid spacecraft

This paper investigates the problem of global attitude regulation control for a rigid spacecraft under input saturation. Based on the technique of finite-time control and the switching control method, a novel global bounded finite-time attitude regulation controller is proposed. Under the proposed controller, it is shown that the spacecraft attitude can reach the desired attitude in a finite time. In addition, the bound of a proposed attitude controller can be adjusted to any small level to accommodate the actuation bound in practical implementation.

Robust Finite-time H_∞ Control of Linear Time-varying Delay Systems with Bounded Control via Riccati Equations

In this paper, we will present new results on robust finite-time H∞ control for linear time-varying systems with both time-varying delay and bounded control. Delay-dependent sufficient conditions for robust finite-time stabilization and H∞ control are first established to guarantee finite-time stability of the closed-loop system via solving Riccati differential equations. Applications to finite-time H∞ control to a class of linear autonomous time-delay systems with bounded control are also discussed in this paper.Numerical examples are given to illustrate the effectiveness of the proposed method.

Prescribed Performance Finite-Time Tracking Control for Uncertain Nonlinear Systems

This work investigates the finite-time tracking control problem for a class of uncertain strict-feedback nonlinear systems from a new perspective. First, a novel concept called finite-time performance function (FTPF) is defined. Further, a new sufficien t condition of finite-time st ability is derived and the tracking error can converge to a predefined region within a finite-time interval. The design process of the proposed technique is simpler. Finally, four simulation examples are carried out to illustrate the effectiveness of presented method.

Robust Finite-Time Stability and Stabilization of a Class of Fractional-Order Switched Nonlinear Systems

This paper deals with the problem of finite-time boundedness and fin计e-time stabilization boundedness of frax?tional-order switched nonlinear systems with exogenous inputs.By constructing a simple Lyapunov-like function and using some properties of Caputo derivative,the authors obtain some new sufficient conditions for the problem via linear matrix inequalities,which can be efficiently solved by using existing convex algorithms.A constructive geometric is used to design switching laws amongst the subsystems.The obtained results are more general and useful than some existing works,and cover them as special cases,in which only linear fractional-order systems were presented.Numerical examples are provided to demonstrate the effectiveness of the proposed results.

Finite-Time Stability for Interval Type-2 Fuzzy Nonlinear Systems via an Observer-Based Sliding Mode Control

This work focuses on the design of a sliding mode controller for a class of continuoustime interval type-2 fuzzy-model-based nonlinear systems with unmeasurable state information over a finite-time interval.Aiming at describing the nonlinearities containing parameter uncertainties that inevitably appear in practice,the interval type-2 fuzzy sets are employed to model the studied system.To improve the designing flexibility,a fuzzy observer model non-parallel distribution compensation scheme is designed to estimate the state information of the plant,i.e.,the observer is allowed to have a mismatching premise structure from the system.On this basis,the appropriate fuzzy sliding surface and fuzzy controller are constructed by following the same premise variables as the designed fuzzy observer.Then,by means of the sliding mode control theory and the Lyapunov function method,some novel sufficient criteria are established to ensure the finite-time boundedness for the studied systems via a partitioning strategy including the reaching phase,the sliding motion phase and the whole time interval.Furthermore,the designed gains are acquired by solving the matrix convex optimization problem.Finally,the effectiveness of the developed method is demonstrated by two simulation examples.

Finite-Time H_(∞)Sampled-Data Reliable Control for a Class of Markovian Jump Systems with Randomly Occurring Uncertainty via T-S Fuzzy Model

The paper analyzes finite-time H_(∞)sampled-data reliability control for nonlinear continuous time Markovian jump systems with randomly occurring uncertainty on account of T-S fuzzy model.In particular,the transition rates of the Markovian jump systems have both the upper bound and lower bound.Meanwhile,a new Lyapunov-Krasovskii functional(LKF)is considered,which fully captures the available characteristics of real sampling period,and a sampled-data controller with nonlinear actuator failures is designed.Based on the integral inequality technique,some less conservative conditions are proposed such that the stochastic fuzzy system is reliable in the sense,which satisfies finite-time bounded and certain H_(∞)performance levelγ.Additionally,some numerical examples can illustrate the effectiveness of the results.