Finite-Time Stabilization for Constrained Discrete-time Systems by Using Model Predictive Control

In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guarantees the finite-time convergence property by assigning the control horizon equal to the dimension of the overall system, and only penalizing the terminal cost in the optimization, where the stage costs are not penalized explicitly. A terminal inequality constraint is added to guarantee the feasibility and stability of the closed-loop system.Initial feasibility can be improved via augmentation. The finite-time convergence of the proposed MPC is proved theoretically,and is supported by simulation examples.

Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.

Controlling chaos in power system based on finite-time stability theory

Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.

Finite-time stability with respect to a closed invariant set for a class of discontinuous systems

This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.

Analysis of finite-time practical stability for time-varying polytopic systems

The problem of finite-time practical stability （FTPS） for time-varying polytopic systems is discussed. Three equivalent conditions for FTPS are first proposed. To facilitate the system analysis, a sufficient linear matrix inequality （LMI） criterion on the FTPS is further provided. The definition of finite-time practical boundedness and a sufficient LMI criterion are also provided to overcome the exogenous disturbance. A numerical example is used to illustrate the effect of the proposed approach.

Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects

Many practical systems in physics, biology, engineer- ing and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynami- cal processes. The problems of finite-time stab!lity analysis are investigated for a class of Markovian switching stochastic sys- tems, in which exist impulses at the switching instants. Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system. Furthermore, a state feedback controller, which stabilizes the closed loop sys- tems in the finite-time sense, is then addressed. Moreover, the controller appears not only in the shift part but also in the diffu- sion part of the underlying stochastic subsystem. The results are reduced to feasibility problems involving linear matrix inequalities （LMIs）. A numerical example is presented to illustrate the proposed methodology.

Finite-Time Stability for Nonlinear Fractional Differential Equations with Time Delay

The finite-time stability and the finite-time contractive stability of solutions for nonlinear fractional differential equations with bounded delay are investigated. The derivative of Lyapunov function along solutions of the considered system is defined in terms of the Caputo fractional Dini derivative. Based on the Lyapunov-Razumikhin method, several sufficient criteria are established to guarantee the finite-time stability and the finite-time contractive stability of solutions for the related systems. An example is provided to illustrate the effectiveness of the obtained results.

Finite-time Stability of Heating Furnace Temperature Control System

A finite-time stabilization controller for the heating furnace temperature control system is proposed.Based on the extended Lyapunov finite-time stability theory and power integral method,a finite-time stable condition of the heating furnace temperature control system is given.The temperature of the heating furnace is directed by the finite-time stabilization controller to make it stable in finite time.And the quality and quantity of slabs is improved.The simulation example is presented to illustrate the applicability of the developed results.

Finite-Time Stability of Nonautonomous Delayed Systems

The finite-time stability to linear discontinuous time-varying delayed system was investigated. By applying the method of upper and lower solutions, some sufficient conditions of this kind of stability were obtained. Furthermore, it also developed a monotone iterative technique for obtaining solutions which are obtained as limits of monotone sequences

Study on the Price Design and Contract Stability of "Company + Farmer" Model with Time Preference under Double Moral Hazards

The double moral hazard of ＂company ＋ farmer＂ and the time preference cost of company and farmer was analyzed. According to static game model, it re-vealed that the reason for low compliance rate of ＂company ＋ farmer＂ model was the existence of market risk, namely, the fluctuation of market price, and the stable market price in contracts was actualy a kind of interval, instead of a specific value. Furthermore, the effect of default penalty, market transaction cost and time prefer-ence cost on the stability of contract was studied. The results showed that default penalty, market transaction cost and time preference cost had positive influence on the price interval range of a contract.

Finite-time fault-tolerant control of teleoperating cyber physical system against faults

This paper studies a finite-time adaptive fractionalorder fault-tolerant control(FTC)scheme for the slave position tracking of the teleoperating cyber physical system(TCPS)with external disturbances and actuator faults.Based on the fractional Lyapunov stability theory and the finite-time stability theory,a fractional-order nonsingular fast terminal sliding mode(FONFTSM)control law is proposed to promote the tracking and fault tolerance performance of the considered system.Meanwhile,the adaptive fractional-order update laws are designed to cope with the unknown upper bounds of the unknown actuator faults and external disturbances.Furthermore,the finite-time stability of the closed-loop system is proved.Finally,comparison simulation results are also provided to show the validity and the advantages of the proposed techniques.

Finite-time Stabilization of the Double Integrator Subject to Input Saturation and Input Delay

Abstract--The time-optimal control design of the double integrator is extended to the finite-time stabilization design that compensates both input saturation and input delay. With the aid of the Artstein＇s transformation, the problem is reduced to assigning a saturated finite-time stabilizer. Index Terms--Finite-time stabilization, input delay, saturated design.

Finite-time Feedback Stabilization of a Class of Input-delay Systems With Saturating Actuators via Digital Control

In this paper, the problem of making an input-delay system with saturating actuators finite-time stable by virtue of digital control is investigated. A digital state feedback controller and digital observer-controller compensator are designed for two cases: when the state of the input-delay system are available or when it is unavailable. Sufficient conditions which guarantee finite-time stability of a closed-loop input-delay system are given and the proof procedure is presented in a heuristic way by constructing appropriate comparison functions. The condition can be transformed into the intersection of two curves satisfying some constraints, which reveals the relationship between designed parameters clearly. Finally, simulation results are presented to validate the method proposed in this paper.

Finite-time economic model predictive control for optimal load dispatch and frequency regulation in interconnected power systems

This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.

Contract stability and default risk control of pig farming in the company and farmer mode

To investigate contract stability in the company and farmer mode and to explore control measures of market price risk and production risk,a multiperiod game model was established in this study.Considering multiple periods and losses caused by deaths simultaneously,a stable contract price interval depending on the breaching penalty,transaction cost,spot market price,and quantity of pigs was observed.Results indicate that the higher the penalty and transaction cost savings,the better the stability of the contract;the contract price should be negotiated around the weighted average of the spot market price.When the production risk is higher,hog insurance can significantly improve the contract stability;when the market price is lower,hog price index insurance improves the contract stability by guaranteeing the company income;when the market price is higher,the profit-returning mechanism improves the stability by protecting farmers incomes.Applying three measures simultaneously results in the best stability.Examples based on data from 2014 to 2018 in Henan Province,China,were given.

Global finite-time stabilization design for a class of high-order uncertain nonlinear systems

The problem of finite-time stabilization for uncertain nonlinear systems is investigated.It is proved that a class of high-order nonlinear systems in the lower-triangular form is globally stabilized via non-Lipschitz continuous state feedback.By using the finite-time Lyapunov stability theorem and the method of non-smooth feedback design,a recursive design procedure is provided,which guarantees the finite-time stability of the closed-loop system.The simulation results show the effectiveness of the theoretical results.

Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters

This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lu¨ and Chen systems are presented to validate the design and analysis.

Finite-time State Feedback Stabilization Method for a Class of Flexible Manipulators

Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.

Finite-Time Stabilization of Dynamical System with Adaptive Feedback Control

In this paper, an adaptive feedback controller is proposed to achieve the finite-time stability of dynamical system. In the proposed scheme, the feedback gain of the adaptive feedback controller is automatically tuned according to the adaptation law in order to stabilize unstable fixed points of the system. Based on the Lyapunov function method and the finite-time stability theory, we get a sufficient condition for the finite-time stability. Finally, simulation results show the effectiveness and feasibility of the proposed finite-time controller.

Nonsmooth finite-time control of uncertain second-order nonlinear systems

Nonsmooth finite-time stabilizing control laws have been developed for the double integrator system. The objective of this paper is to further explore the finite-time tracking control problem of a general form of uncertain secondorder affine nonlinear system with the new forms of terminal sliding mode （TSM）. Discontinuous and continuous finite-time controllers are also developed respectively without the singularity problem. Complete robustness can be acquired with the former, and enhanced robustness compared with the conventional boundary layer method can be expressed as explicit bounded function with the latter. Simulation results on the stabilizing and tracking problems are presented to demonstrate the effectiveness of the control algorithms.