Finite‐time optimal control for interconnected nonlinear systems

This work addresses the finite‐time optimal control problem for a class of interconnected nonlinear systems with powers of positive odd rational numbers. A series of homogeneous controllers, which are capable of guaranteeing the local finite‐time stability of the closed‐loop systems, are first developed using the adding one power integrator method and backstepping technique. Then, the nested saturation controllers are further proposed to achieve global finite‐time stability. Furthermore, the corresponding design parameters are optimized, and thus, an optimal controller is obtained. A numerical simulation example is finally given to illustrate the effectiveness of the proposed control strategy.     

Finite‐time formation control of multiple nonholonomic mobile robots

This paper considers finite‐time formation control problem for a group of nonholonomic mobile robots. The desired formation trajectory is represented by a virtual dynamic leader whose states are available to only a subset of the followers and the followers have only local interaction. First of all, a continuous distributed finite‐time observer is proposed for each follower to estimate the leader's states in a finite time. Then, a continuous distributed cooperative finite‐time tracking control law is designed for each mobile robot. Rigorous proof shows that the group of mobile robots converge to the desired geometric formation pattern in finite time. At the same time, all the robots can track the desired formation trajectory in finite time. Simulation example illustrates the effectiveness of our method. Copyright © 2012 John Wiley & Sons, Ltd.     

Finite‐time control for LPV systems with parameter‐varying time delays and exogenous disturbances

In this paper, we consider the stability analysis and control synthesis of finite‐time boundedness problems for linear parameter‐varying (LPV) systems subject to parameter‐varying time delays and external disturbances. First, the concepts of uniform finite‐time stability and uniform finite‐time boundedness are introduced to LPV systems. Then, sufficient conditions, which guarantee LPV systems with parameter‐varying time delays finite‐time bounded, are presented by using parameter‐dependent Lyapunov–Krasovskii functionals and free‐weight matrix technologies. Moreover, on the basis of the results on the uniform finite‐time boundedness, the parameter‐dependent state feedback controllers are designed to finite‐time stabilize LPV systems. Both analysis and synthesis conditions are delay‐dependent, and they are formulated in terms of linear matrix inequalities by using efficient interior‐point algorithms. Finally, results obtained in simulation demonstrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite‐time boundary stabilization of reaction‐diffusion systems

In this paper, the problem of boundary finite‐time stabilization is considered for reaction‐diffusion systems (RDSs). First, a full‐domain controller is designed, and sufficient conditions are given to ensure finite‐time stability of RDSs under the designed controller. Then, for practical applications, a boundary controller is designed to obtain finite‐time stability. By virtue of the finite‐time stability lemma, criteria are presented to guarantee the finite‐time stability of RDSs for the Neumann boundary conditions and the mixed boundary conditions. As an extension to uncertain RDSs, robust finite‐time stabilization is studied, and criterion is obtained under the boundary control. Numerical simulations verify the effectiveness of the proposed design techniques.     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.     

Finite‐time stability of switched nonlinear time‐delay systems

This article addresses the problem of finite‐time stability (FTS) and finite‐time contractive stability (FTCS) for switched nonlinear time‐delay systems (SNTDSs). By virtues of the Lyapunov‐Razumikhin method, Lyapunov functionals approach, and the comparison principle technique, we obtain some improved Razumikhin‐type theorems that verify FTS and FTCS property for SNTDSs. Moreover, our results allow the estimate of the upper bound of the derivatives for Lyapunov functions to be mode dependent functions which can be positive and negative. Meanwhile, the proposed results also improve the related existing results on the same topic by removing some restrictive conditions. Finally, two examples are presented to verify the effectiveness of our methods.     

Finite‐time formation control of multiagent systems via dynamic output feedback

Finite‐time formation control of multiple second‐order agents via dynamic output feedback is investigated in this paper. Under the assumption that the velocities of all agents cannot be measured, a continuous consensus algorithm is first proposed such that the states of all agents will reach an agreement in finite time. Then, the consensus algorithm is applied to the finite‐time formation control, including stationary formation and moving formation, respectively. Rigorous proof shows that all agents will converge to the desired formation pattern in finite time. Finally, an example is given to verify the efficiency of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Finite‐time stabilization for a class of stochastic low‐order nonlinear systems with unknown control coefficients

This paper addresses the problem of finite‐time stabilization for a class of low‐order stochastic upper‐triangular nonlinear systems corrupted by unknown control coefficients. Unlike the relevant schemes, the control strategy draws into a dominate gain to cope with the deteriorative effects of both uncertain nonlinearities and unknown control coefficients without using traditional adaptive compensation method. Then, a state feedback controller is constructed by the adding a power integrator method and modified homogeneous domination approach, to ensure the finite‐time stability of the closed‐loop system. Finally, the effectiveness of proposed control strategy has been demonstrated by a simulation example.     

Finite‐time consensus tracking for harmonic oscillators using both state feedback control and output feedback control

This paper investigates the distributed finite‐time consensus‐tracking problem for coupled harmonic oscillators. The objective is to guarantee a team of followers modeled by harmonic oscillators to track a dynamic virtual leader in finite time. Only a subset of followers can access the information of the virtual leader, and the interactions between followers are assumed to be local. We consider two cases: (i) The followers can obtain the relative states between their neighbors and their own; and (ii) Only relative outputs between neighboring agents are available. In the former case, a distributed consensus protocol is adopted to achieve the finite‐time consensus tracking. In the latter case, we propose a novel observer‐based dynamic protocol to guarantee the consensus tracking in finite time. Simulation examples are finally presented to verify the theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Finite‐time stability of linear fractional‐order time‐delay systems

In this paper, a finite‐time stability results of linear delay fractional‐order systems is investigated based on the generalized Gronwall inequality and the Caputo fractional derivative. Sufficient conditions are proposed to the finite‐time stability of the system with the fractional order. Numerical results are given and compared with other published data in the literature to demonstrate the validity of the proposed theoretical results.     

Leaderless and leader‐following fixed‐time consensus for multiagent systems via impulsive control

This article addresses the leaderless fixed‐time consensus (LLFTC) and leader‐following fixed‐time consensus (LFFTC) problems for multiagent systems (MASs) via impulsive control. First, a novel fixed‐time stability for impulsive dynamical system is developed. Then the novel fixed‐time impulsive control protocols are designed to achieve leaderless and leader‐following consensus for MASs. Based on the impulsive control theory, fixed‐time stability theory and algebraic graph theory, some sufficient conditions are derived for each agent to achieve LLFTC and LFFTC under the proposed control protocols. Finally, numerical simulations are put forward to validate the theoretical results.     

Finite‐time adaptive robust control of nonlinear time‐delay uncertain systems with disturbance

This paper investigates finite‐time adaptive robust control problem for a general class of nonlinear time‐delay systems with uncertain and external disturbance via the Lyapunov‐Krasovskii (L‐K) method and presents some delay‐independent and delay‐dependent results on the issue. First, by applying the orthogonal decomposition method, this paper presents an equivalent form. Based on which, we study the finite‐time adaptive robust control problem for the systems by constructing a specific L‐K functional and designing a suitable controller. Different from existing works, this paper studies finite‐time adaptive robust control problem for general nonlinear delay system and presents a delay‐dependent sufficient condition on the problem. Finally, an illustrative example is given to show the effectiveness of the result in this paper.     

Finite‐time tracking control for a class of nonlinear systems with multiple mismatched disturbances

This article investigates the finite‐time output tracking problem for a class of nonlinear systems with multiple mismatched disturbances. To efficiently estimate the disturbances and their derivatives, a continuous finite‐time disturbance observer (CFTDO) design method is developed. Based on the modified adding a power integrator method and CFTDO technique, a composite tracking controller is constructed such that the system output can track the desired reference signal in finite time. Simulation results demonstrate the effectiveness of the proposed control approach.     

Finite‐time boundedness of switched systems with time‐varying delays via sampled‐data control

In the framework of sampled‐data control, finite‐time boundedness (FTB) of switched systems with time‐varying delays is investigated. Sufficient conditions for FTB of switched systems with time‐varying delays via sampled‐data control are proposed. Moreover, considering the relationship between the sampling period and the mode‐dependent average dwell time, switching signals are designed. In addition, finite‐time weighted L₂‐gain (FTW‐L₂‐gain) of switched systems with time‐varying delays is proposed to measure their disturbance tolerance capacity within a finite‐time interval. Multiple Lyapunov‐Krasovskii functionals are applied to complete subsequent proofs in detail. Simulation results are exemplified to verify the proposed method.     

Finite‐time stabilization of stochastic nonlinear systems with SiISS inverse dynamics

This paper investigates the finite‐time control problem for a class of stochastic nonlinear systems with stochastic integral input‐to‐state stablility (SiISS) inverse dynamics. Motivated by finite‐time stochastic input‐to‐state stability and the concept of SiISS using Lyapunov functions, a novel finite‐time SiISS using Lyapunov functions is introduced firstly. Then, by adopting this novel finite‐time SiISS small‐gain arguments, using the backstepping technique and stochastic finite‐time stability theory, a systematic design and analysis algorithm is proposed. Given the control laws that guarantee global stability in probability or asymptotic stability in probability, our design algorithm presents a state‐feedback controller that can ensure the solution of the closed‐loop system to be finite‐time stable in probability. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite‐time stability of switched nonlinear time‐varying systems via indefinite Lyapunov functions

This note considers the problem of finite‐time stability (FTS) for switched nonlinear time‐varying systems. First, a relaxed condition is proposed to verify the FTS of nonlinear time‐varying systems by using an indefinite Lyapunov function. Then, the result obtained is extended to study the FTS of switched nonlinear time‐varying systems. Several relaxed conditions are given by using a common indefinite Lyapunov function and multiple indefinite Lyapunov functions. Moreover, the corresponding estimates on convergence regions and times of systems are also given. Comparing with the existing results, the conditions obtained allow the time derivative of Lyapunov functions of subsystems (or systems) to be indefinite and all subsystems to be not finite‐time stable or even unstable. Finally, a numerical example is given to illustrate the theoretical results.     

Finite‐time control of switching linear systems: The uncertain resetting times case

In recent years, a number of papers have treated the problem of the finite‐time stability and stabilization of impulsive (or, more in general, switching) dynamical linear systems. Generally, these works assume that the sequence of switching (in the following resetting) times is a priori known. In this paper, we remove such (strong) assumption, so making the technique more appealing from the practical control engineering point of view. A first result provided in this work is a sufficient condition for finite‐time stability when the resetting times are known with a certain degree of uncertainty. Such condition requires the solution of a suitable feasibility problem based on coupled difference/differential LMIs. We show that as the uncertainty intervals reduce in size, our condition becomes less conservative, becoming necessary and sufficient in the certain case (i.e., the resetting instants are perfectly known). Eventually, we consider the conceptually different situation in which the resetting times are totally unknown, namely, the arbitrary switching case. The analysis results are then used to derive sufficient conditions for the existence of state‐feedback controllers that finite time stabilizes the closed‐loop system in the three cases mentioned earlier. A nontrivial example, considering the finite‐time control of the liquid levels into three interconnected reservoirs, shows the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐time geometric control for underactuated aerial manipulators with unknown disturbances

In this article, the finite‐time geometric control for underactuated aerial manipulators is investigated. The dynamics of the aerial manipulator with unknown disturbances is analyzed first. The dynamics of the system is decomposed into the locked subsystem and shape subsystem. The finite‐time controller for the aerial manipulator is then designed based on the analyzed dynamics. In the controller, the attitude tracking error of the aircraft base is expressed from the rotation matrix, which makes the controller continuous and almost globally stable on SO(3). A continuous adaptive term is added in the controller to compensate for the unknown disturbances. Finite‐time filters are designed to ensure the smoothness of the commands on each loop. The convergence of the entire controlled system is strictly proved using Lyapunov theory and the definition of finite‐time stability. The results show that the tracking error and the disturbance bound estimation error of the entire system are finite‐time bounded near origin. Finally, comparative simulation results are presented to show the performance of the proposed controller.     

Distributed output‐feedback finite‐time tracking control of nonaffine nonlinear leader‐follower multiagent systems

The distributed output‐feedback tracking control for a class of networked multiagents in nonaffine pure‐feedback form is investigated in this article. By introducing a low‐pass filter and some auxiliary variables, we first transform the nonaffine system into the affine form. Then, the finite‐time observer is designed to estimate the states of the newly derived affine system. By applying the fraction dynamic surface control approach and the neural network‐based approximation technique, the distributed output‐feedback control laws are proposed and it is proved that the tracking errors converge to an arbitrarily small bound around zero in finite time. Finally, some simulation examples are provided to confirm the effectiveness of the developed method.     

Finite‐time stability of switched positive linear systems

This brief paper addresses the finite‐time stability problem of switched positive linear systems. First, the concept of finite‐time stability is extended to positive linear systems and switched positive linear systems. Then, by using the state transition matrix of the system and copositive Lyapunov function, we present a necessary and sufficient condition and a sufficient condition for finite‐time stability of positive linear systems. Furthermore, two sufficient conditions for finite‐time stability of switched positive linear systems are given by using the common copositive Lyapunov function and multiple copositive Lyapunov functions, a class of switching signals with average dwell time is designed to stabilize the system, and a computational method for vector functions used to construct the Lyapunov function of systems is proposed. Finally, a concrete application is provided to demonstrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.