Finite-time Problem Research Articles

Synchronization of Multi-links Memristor-Based Switching Networks Under Uniform Random Attacks

A variety of influence factors are common to the support networks which are used as cyber-physical systems. In this paper, we consider the problem of finite-time and exponential synchronization for the memristor-based switching networks (MSNs) with multi-links and multiple time-varying delays under uniform random attacks via asymptotic controller and adaptive controller. We propose a more general system model and utilize an analytical method which is different from the classical analytical techniques like set-valued mappings technique and differential inclusions to preprocess the MSNs to a class of switching networks with some uncertain parameters. Then, based on appropriate Lyaponov functionals and linear matrix inequality, several useful criteria ensuring the finite-time synchronization or asymptotic synchronization of MSNs with multi-links and time-varying delays under uniform random attacks via designed control law are obtained. Finally, two numerical examples are designed to show the feasibility and the correctness of our proposed results.

Robust Finite-Time <i>H</i><sub>∞</sub> Filtering for Discrete-Time Markov Jump Stochastic Systems

This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the finite-time stability of the filtering error system and preserve a prescribed H∞ performance level for all admissible uncertainties. Sufficient conditions of filtering design for the system under consideration are developed and the corresponding filter parameters can be achieved in terms of linear matrix inequalities (LMI). Finally, a numerical example is provided to illustrate the validity of the proposed method.

Finite-time H∞ boundedness of discrete-time neural networks normbounded disturbances with time-varying delay

The problem of finite-time H∞ performance of discrete time neural network with norm-bounded disturbances and time varying delays is studied in this paper. By constructing a delay-dependent Lyapunov-Krasovskii functional and using a two-term approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Comparision with the existing results given to show that, the derived stability conditions are less conservative. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

Finite-time and fixed-time observer design: Implicit Lyapunov function approach

This work deals with the problem of finite-time and fixed-time observation of linear multiple input multiple output (MIMO) control systems. The proposed nonlinear dynamic observers guarantee convergence of the observer states to the original system state in a finite and in a fixed (defined a priori) time. Algorithms for the observers parameters tuning are also provided and a robustness analysis against input disturbances and measurement noises is carried out. The theoretical results are illustrated by numerical examples that consider both noisy and noise-free measurements and a comparison with a high-gain observer is included.

Design the finite-time H∞ resilient filter of a class of switched systems with uncertain parameters

This paper is concerned with the problem of finite-time H∞ resilient filtering for a class of switch systems. The filtering error dynamics is constructed based on the H∞ resilient filter. The objective is to design a filter such that the finite-time H∞ gain from the unknown input to an estimation error is minimized or guaranteed to be less than or equal to a prescribed value. By selecting the proper multiple Lyapunov function and using the average dwell-time approach, sufficient conditions are obtained for the existence of the desired H∞ resilient filter, which also guarantee the finite-time boundedness of the filtering error dynamic systems. The design criteria are proposed in the form of linear matrix inequalities and then described as an optimization algorithm. Finally, a numerical example is employed to illustrate the effectiveness of the developed techniques.

Investment and consumption problem in finite time with consumption constraint

In this paper, we consider an investment-consumption problem where the consumption is subject to an upper limit. This upper limit on consumption may reflect the following fact. Investors may have to finance their consumption first by using credits then pay the balance by cashing out part of their portfolio in the stock market. Credit companies set up an upper limit for the credit, thus imposing an upper bound for consumption. We also set up our model in finite horizon, which makes the problem much harder due to the loss of stationary when T < ∞. We prove that the above described problem is equivalent to a free boundary problem of nonlinear parabolic equations. We aim to characterize explicitly the free boundary by applying a dual transformation technique to convert the original nonlinear parabolic equation to a linear differential equation. This trick allows us to characterize explicitly the free boundary and the optimal consumption strategy. We also prove that the regularity of the value function, which is critical for the application of Ito formula.

Robust finite-time control for neutral systems with time-varying delays via sliding mode observer

This paper is concerned with the problem of robust finite-time sliding mode control (SMC) for a class of continuous-time uncertain neutral systems with time-varying delays. Firstly, based on the constructed sliding mode observer, an integral sliding surface is put forward on the estimation space. Secondly, the synthesized SMC law guarantees the finite-time reachability of the predefined sliding surface. Thirdly, through finite-time stability analysis, sufficient conditions are established to guarantee the required performance of the system during both reaching phase and sliding motion phase. Finally, a practical example is provided to verify the effectiveness of the proposed method.

The Feedback Control Problem for Switched System with Uncertainties

This paper deals with feedback control problem for a piecewise affine system with autonomous, state-dependent switchings, subject to unknown but bounded disturbances, with hard bounds on controls and uncertain parameters. A target control problem in finite time is considered. In order to obtain the control strategy auxiliary solvability tubes with branching structure are introduced. They can be specified by means of some value functions. The paper presents a scheme for approximating these functions and corresponding solvability tubes using the comparison principle for the first-order ODEs of the Hamilton–Jacobi–Bellman type and also a special class of piecewise quadratic approximating functions. The parameters of these functions are obtained from a set of Riccati type matrix differential equations. This enables to produce an effective computational scheme.

Finite-time H∞ control of uncertain networked control systems with randomly varying communication delays

This paper is concerned with the problem of finite-time H∞ stability analysis of uncertain discrete-time Networked Control Systems (NCSs) with varying communication delays in a random fashion. Both measurement and actuation delays are modeled by two independent Bernoulli distributed white sequences. A dynamic output feedback controller is designed to realize finite time control for this class of NCSs with prescribed H∞ performance level. An iterative algorithm is developed to compute the controller's parameters by means of the Cone Complementarity Linearization Method (CCLM). The validity and feasibility of the proposed stability criterion are confirmed via numerical simulation examples.

Reliable finite-time H∞ control of uncertain singular nonlinear Markovian jump systems with bounded transition probabilities and time-varying delay

ABSTRACTThis paper investigates the problem of reliable finite-time H∞ control for one class of uncertainsingular nonlinear Markovian jump systems with time-varying delay subject to partial information on the transition probabilities. Continuous fault model is more general and practical to serve as the actuator fault. Time delay is a kind of positive time-varying differentiable bounded delays. First, based on a state estimator the resulting closed-loop error system is constructed and sufficient criteria are provided to guarantee that the augmented system is singular stochastic finite-time boundedness and singular stochastic H∞ finite-time boundedness in both normal and fault cases via constructing a delay-dependent Lyapunov–Krasonskii function. Then, the gain matrices of state-feedback controller and state estimator are fixed by solving a feasibility problem in terms of linear matrix inequalities through decoupling technique, respectively. Finally, numerical examples are given to show the validity of the proposed design approach.

A recurrent neural network with finite-time convergence for convex quadratic bilevel programming problems

In this paper, a recurrent neural network with a new tunable activation is proposed to solve a kind of convex quadratic bilevel programming problem. It is proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov, and the state of the proposed neural network converges to an equilibrium point in finite time. In contrast to the existing related neurodynamic approaches, the proposed neural network in this paper is capable of solving the convex quadratic bilevel programming problem in finite time. Moreover, the finite convergence time can be quantitatively estimated. Finally, two numerical examples are presented to show the effectiveness of the proposed recurrent neural network.

Robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay

This paper is concerned with the problem of robust finite-time guaranteed cost control for a class of impulsive switched systems with time-varying delay. Firstly, the definitions of finite-time boundedness, finite-time stabilization, and robust finite-time guaranteed cost control are presented. Next, based on the average dwell-time approach, sufficient conditions on robust finite-time guaranteed cost control are obtained for the uncertain impulsive switched systems. Then, by using multiple Lyapunov-like functional method and linear matrix equality (LMI) technique, the state feedback controller is designed to guarantee that the uncertain impulsive switched system is finite-time stabilized. Furthermore, a finite-time guaranteed cost bound is given. Finally, a numerical example is shown to illustrate the effectiveness of the proposed results.

OPTIMAL CONTROL OF AN ENERGY STORAGE FACILITY UNDER A CHANGING ECONOMIC ENVIRONMENT AND PARTIAL INFORMATION

In this paper, we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage manager and the energy price process, which is a diffusion process the drift of which is assumed to be unobservable. We apply filtering theory to find an alternative state process which is adapted to our observation filtration. For this alternative state process, we derive the associated Hamilton–Jacobi–Bellman equation and solve the optimization problem numerically. This results in a candidate for the optimal policy for which it is a priori not clear whether the controlled state process exists. Hence, we prove an existence and uniqueness result for a class of time-inhomogeneous stochastic differential equations with discontinuous drift and singular diffusion coefficient. Finally, we apply our result to prove admissibility of the candidate optimal control.

Finite-time H∞ state estimation for switched neural networks with time-varying delays

This study considers the problem of finite-time H∞ state estimation for the switched neural networks with time varying delay, based on the theories of the switched systems. Sufficient conditions for the switched neural networks to be finite time stable and finite time bounded are derived. These conditions are delay dependent and are given in terms of linear matrix inequalities (LMIs). Average dwell time of switching signals is also given such that switched neural networks are finite-time stable or finite-time bounded. By resorting to the average dwell time approach and Lyapunov–Krasovskii functional technology, the H∞ estimator design are developed in terms of solvability of a set of linear matrix inequalities. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.

Robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation

In this paper, the problem of robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation is studied. First, sufficient conditions that guarantee the systems singular stochastic finite-time boundedness are derived via constructing a delay-dependent Lyapunov–Krasonskii functional and linear matrix inequalities (LMI) approaches. Then the results are extended to singular stochastic finite-time H∞ boundedness. Furthermore, with these conditions and convex optimization arithmetic, the design method of H∞ controller and conditions that ensure the H∞ disturbance attenuation level are obtained. Finally, some numerical examples are presented to illustrate the validity and efficiency of the proposed methods.

Robust Finite-Time &amp;lt;em&amp;gt;H&amp;lt;/em&amp;gt;&amp;lt;sub&amp;gt;&amp;lt;em&amp;gt;∞&amp;lt;/em&amp;gt;&amp;lt;/sub&amp;gt; Filtering for It&amp;#244; Stochastic Systems

This paper investigates the problem of robust finite-time H∞ filter design for Ito stochastic systems. Based on linear matrix inequalities (LMIS) techniques and stability theory of stochastic differential equations, stochastic Lyapunov function method is adopted to design a finite-time H∞ filter such that, for all admissible uncertainties, the filtering error system is stochastic finite-time stable (SFTS). A sufficient condition for the existence of a finite-time H∞ filter for the stochastic system under consideration is achieved in terms of LMIS. Moreover, the explicit expression of the desired filter parameters is given. A numerical example is provided to illustrate the effectiveness of the proposed method.

Finite-time asynchronous [formula omitted] control for Markov jump repeated scalar non-linear systems with input constraints

This paper is concerned with the problem of finite-time H∞ control for Markov jump repeated scalar nonlinear systems (MJRSNSs) with input constraints. The jumps between MJRSNSs and desired mode-dependent controllers are considered to be nonsynchronous. The mode transition of the controllers is governed by a nonstationary Markov chain, which can model the different degrees of asynchronous jumps between MJRSNSs and controllers. With the aid of Lyapunov–Krasovskii methodology, some H∞ performance criteria for the MJRSNSs are proposed. Based on these criteria, sufficient conditions on the existence of the desired controllers are established, and then the gains of the controllers can be obtained by solving a convex optimization problem. Finally, an example is presented to illustrate the effectiveness of our method.

An optimal consumption problem in finite time with a constraint on the ruin probability

In this paper, we investigate the following problem: For a given upper bound for the ruin probability, maximize the expected discounted consumption of an investor in finite time. The endowment of the agent is modeled by a Brownian motion with positive drift. We give an iterative algorithm for the solution of the problem, where in each step an unconstrained, but penalized problem is solved. For the discontinuous value function $V(t,x)$ of the penalized problem, we show that it is the unique viscosity solution of the corresponding Hamilton–Jacobi–Bellman equation. Moreover, we characterize the optimal strategy as a barrier strategy with continuous barrier function.

Reliable finite-time H∞ filtering for discrete time-delay systems with Markovian jump and randomly occurring nonlinearities

This paper is concerned with the problem of reliable finite-time H∞ filtering for discrete time-varying delay systems with Markovian jump and randomly occurring nonlinearities (RONs). RONs are introduced to model a class of sector-like nonlinearities that occur in a probabilistic way according to a two-dimensional discrete random variables joint distribution. The failures of sensors are quantified by a variable varying in a given interval. The time-varying delay is unknown with given lower and upper bounds. Firstly, the filtering errr dynamic system is constructed based on an H∞ filter, sufficient criteria are provided to guarantee that the resulting filtering error system is stochastic finite-time boundedness and stochastic finite-time H∞ filtering in both normal and fault cases. The gain matrices of the controller and filter are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to demonstrate the effectiveness of the proposed design approach.

Finite-time [formula omitted] control for singular Markovian jump systems with partly unknown transition rates

This paper investigates the problem of finite-time H∞ control for a class of singular Markovian jump systems with partly unknown transition rates. Firstly, sufficient conditions on singular stochastic finite-time boundedness of singular Markovian jump systems with partly unknown transition rates are obtained. Secondly, the results are extended to singular stochastic H∞ finite-time boundedness of singular Markovian jump systems with partly unknown transition rates. Then state feedback controllers are designed to ensure the singular stochastic finite-time boundedness and the singular stochastic H∞ finite-time boundedness of the underlying closed singular Markovian jump systems in the forms of strict LMIs. Finally, numerical examples are given to illustrate the validity of the proposed methods.