Wireless sensor networks (WSN) are becoming increasingly promising in practice. As the predeployment design and optimization are usually unpractical in random deployment scenarios, the global optimum of the WSN’s performance is achievable only if the topology dependent self-organizing process acquires the overview of the WSN, in which the boundary is the most important. The idea of this paper comes from the fact that contours only break on the geometrical boundary and the WSN are discrete sampling systems of real environments. By simulating a diffusion process in discrete form, the end point of semi-contours suggests the boundary nodes of a WSN. The simulation cases show the algorithm is well worked in WSN with average degree higher than 10. The boundary recognition could be very valuable for other algorithms dedicated to optimize the overall performance of WSN.

Integration-by-parts formulas for functions of fundamental jump processes relating to a continuous-time, finite-state Markov chain are derived using Bismut's change of measures approach to Malliavin calculus. New expressions for the integrands in stochastic integrals corresponding to representations of martingales for the fundamental jump processes are derived using the integration-by-parts formulas. These results are then applied to hedge contingent claims in a Markov chain financial market, which provides a practical motivation for the developments of the integration-by-parts formulas and the martingale representations.

For the technology of mechanical elastic energy storage utilizing spiral torsion springs as the energy storage media presented previously, a global multivariable control algorithm based on nonlinear internal model principle under multiclass external disturbances is proposed. The nonlinear external disturbances with nonharmonic periodic characteristics are generated by multiclass nonlinear external systems. New equations of nonlinear internal model are designed to estimate the multiclass external disturbances. On the basis of constructing the control law of nominal system, a state feedback controller is designed to guarantee the closed-loop system globally uniformly bounded, and a Lyapunov function is constructed to theoretically prove the global uniform boundedness of the multivariable closed-loop system signals. The simulation results verify the correctness and effectiveness of the presented algorithm.

For the response acquisition of the structure section measuring points, the method of identifying the structural stiffness parameters is developed by using the extended Kalman filter. The state equation of structural system parameter is a nonlinear equation. Dispersing the structural dynamic equation by using Newmark-$\beta$ method, the state transition matrix of discrete state equation is deduced and the solution of discrete state equation is simplified. The numerical simulation shows that the error of structural recognition doesnot exceed 5% when the noise level is 3%. It meets the requirements of the error limit of the engineering structure, which indicates that the derivation described in this paper has the robustness for the structural stiffness recognition. Shear structure parameter identification examples illustrate its applicability, and the method can also be used to identify physical parameters of large structure.

The problem of finite-time $L_2\text{-}{L}_{\infty }$ control for Markovian jump systems (MJS) is investigated. The systems considered time-varying delays, actuator saturation, and polytopic uncertain transition description. The purpose of this paper is to design a state feedback controller such that the system is finite-time bounded (FTB) and a prescribed $L_2\text{-}{L}_{\infty }$ disturbance attenuation level during a specified time interval is guaranteed. Based on the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design the delayed feedback controller which satisfies the given attenuation level. Finally, illustrative examples show that the proposed conditions are effective for the design of robust state feedback controller.

The delay-dependent resilient robust finite-time $L_2\text{-}{L}_{\infty }$ control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a given $L_2\text{-}{L}_{\infty }$ constraint condition. Simulation results illustrate the validity of the proposed approach.

This paper investigates the problem of output feedback adaptive stabilization control design for a class of nonholonomic chained systems with uncertainties, involving virtual control coefficients, unknown nonlinear parameters, and unknown time delays. The objective is to design a robust nonlinear output-feedback switching controller, which can guarantee the stabilization of the closed loop systems. An observer and an estimator are employed for states and parameters estimates, respectively. A constructive controller design procedure is proposed by applying input-state scaling transformation, parameter separation technique, and backstepping recursive approach. Simulation results are provided to show the effectiveness of the proposed method.

The exponential stability is investigated for neutral stochastic differential equations with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequalities (LMIs) technique, some delay-dependent criteria are established to guarantee the exponential stability in almost sure sense. Finally a numerical example is provided to illustrate the feasibility of the result.

State estimation problem is considered for a kind of wireless network control system with stochastic uncertainty and time delay. A sliding mode observer is designed for the system under the situation that no missing measurement occurs and system uncertainty happens in a stochastic way. The observer designed for the system can guarantee the system states will be driven onto the sliding surface under control law, and the sliding motion of system states on sliding surface will be stable. By constructing proper Lyapunov-Krasovskii functional, sufficient conditions are acquired via linear matrix inequality. Finally, simulation result is employed to show the effectiveness of the proposed method.

The fault detection problem for a class of wireless networked control systems is investigated. A Bernoulli distributed parameter is introduced in modeling the system dynamics; moreover, multiple time delays arising in the communication are taken into account. The detection observer for tracking the system states is designed, which generates both the state errors and the output errors. By adopting the linear matrix inequality method, a sufficient condition for the stability of wireless networked control systems with stochastic uncertainties and multiple time delays is proposed, and the gain of the fault detection observer is obtained. Finally, an illustrated example is provided to show that the observer designed in this paper tracks the system states well when there is no fault in the systems; however, when fault happens, the observer residual signal rises rapidly and the fault can be quickly detected, which demonstrate the effectiveness of the theoretical results.

Explicit formulae of constants within the a posteriori error estimate for optimal control problems are investigated with Legendre-Galerkin spectral methods. The constrained set is put on the control variable. For simpleness, one-dimensional bounded domain is taken. Meanwhile, the corresponding a posteriori error indicator is established with explicit constants.

We consider a class of stochastic delay recurrent neural networks with distributed parameters and Markovian jumping. It is assumed that the coefficients in these neural networks belong to the interval matrices. Several sufficient conditions ensuring robust exponential stabilization are derived by using periodically intermittent control and Lyapunov functional. The obtained results are very easy to verify and implement, and improve the existing results. Finally, an example with numerical simulations is given to illustrate the presented criteria.

An improved design approach of robust H _∞ filter for a class of nonlinear systems described by the Takagi-Sugeno (T-S) fuzzy model is considered. By introducing a free matrix variable, a new sufficient condition for the existence of robust H _∞ filter is derived. This condition guarantees that the filtering error system is robustly asymptotically stable and a prescribed H _∞ performance is satisfied for all admissible uncertainties. Particularly, the solution of filter parameters which are independent of the Lyapunov matrix can be transformed into a feasibility problem in terms of linear matrix inequalities (LMIs). Finally, a numerical example illustrates that the proposed filter design procedure is effective.

This paper deals with the couple-group consensus problem for multiagent systems via output feedback control. Both continuous- and discrete-time cases are considered. The consensus problems are converted into the stability problem of the error systems by the system transformation. We obtain two necessary and sufficient conditions of couple-group consensus in different forms for each case. Two different algorithms are used to design the control gains for continuous- and discrete-time case, respectively. Finally, simulation examples are given to show the effectiveness of the proposed results.

A performance assessment method for nonlinear feedforward and feedback control systems is proposed in this paper. First, the existence of minimum variance performance bound for two nonlinear systems with different structures is analyzed, and the closed-loop model of nonlinear system is obtained with the help of iterative orthogonal least squares identification method. Then, the technology of variance analysis is introduced to establish the variance contributions due to both disturbances and controller. A nonlinear performance index for the feedforward and feedback control systems is estimated using an ANOVA-like variance decomposition method. Finally, a meaningful example is simulated to show the effectiveness of our method.

This paper is concerned with the problem of predictive function control (PFC) for a class of hydraulic vibration servo control systems. Our aim is to design a new advanced control strategy such that the control system can track trajectory in a fast and accurate way. For this end, the mathematical model of the hydraulic vibration servo control system is firstly studied. By analyzing the nonlinear, time-varying, and model structure uncertainty features of the objects, the desired control strategy is presented based on PFC. Finally, the simulation results show that our proposed method is effective and can be used to improve the tracking speed, accuracy, and robustness.

This paper is concerned with the $L_2-L_{\infty }$ filtering problem for a kind of Takagi-Sugeno (T-S) fuzzy stochastic system with time-varying delay and parameter uncertainties. Parameter uncertainties in the system are assumed to satisfy global Lipschitz conditions. And the attention of this paper is focused on the stochastically mean-square stability of the filtering error system, and the $L_2-L_{\infty }$ performance level of the output error with the disturbance input. The method designed for the delay-dependent filter is developed based on linear matrix inequalities. Finally, the effectiveness of the proposed method is substantiated with an illustrative example.

This paper focuses on the stability issue of discrete-time networked control systems with random Markovian delays and uncertain transition probabilities, wherein the random time delays exist in the sensor-to-controller and controller-to-actuator. The resulting closed-loop system is modeled as a discrete-time Markovian delays system governed by two Markov chains. Using Lyapunov stability theory, a result is established on the Markovian structure and ensured that the closed-loop system is stochastically stable. A simulation example illustrates the validity and feasibility of the results.

This paper investigates the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. The finite-time $H_{\infty }$ controller via state feedback is designed to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic control performance of discrete-time Markov jump systems are derived in the form of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

A stochastic pinning approach for multiagent systems is developed, which guarantees such systems being almost surely stable. It is seen that the pinning is closely related to being a Bernoulli variable. It has been proved for the first time that a series of systems can be stabilized by a Brownian noise perturbation in terms of a pinning scheme. A new terminology named “stochastic pinning control” is introduced to describe the given pinning algorithm. Additionally, two general cases that the expectation of the Bernoulli variable with bounded uncertainty or being unknown are studied. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed methods.

This paper is concerned with the optimal linear estimation for a class of direct-time Markov jump systems with missing observations. An observer-based approach of fault detection and isolation (FDI) is investigated as a detection mechanic of fault case. For systems with known information, a conditional prediction of observations is applied and fault observations are replaced and isolated; then, an FDI linear minimum mean square error estimation (LMMSE) can be developed by comprehensive utilizing of the correct information offered by systems. A recursive equation of filtering based on the geometric arguments can be obtained. Meanwhile, a stability of the state estimator will be guaranteed under appropriate assumption.

This paper is concerned with the state estimation problem for a class of time-delay systems with Markovian jump parameters and missing measurements, considering the fact that data missing may occur in the process of transmission and its failure rates are governed by random variables satisfying certain probabilistic distribution. By employing a new Lyapunov function and using the convexity property of the matrix inequality, a sufficient condition for the existence of the desired state estimator for Markovian jump systems with missing measurements can be achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Furthermore, the gain of state estimator can also be derived based on the known conditions. Finally, a numerical example is exploited to demonstrate the effectiveness of the proposed method.

This paper is concerned with pth moment input-to-state stability (p-ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic systems with time delays. Razumikhin-type theorems ensuring p-ISS/SISS are established for the mentioned systems with external input affecting both the continuous and the discrete dynamics. It is shown that when the impulse-free delayed stochastic dynamics are p-ISS/SISS but the impulses are destabilizing, the p-ISS/SISS property of the impulsive stochastic systems can be preserved if the length of the impulsive interval is large enough. In particular, if the impulse-free delayed stochastic dynamics are p-ISS/SISS and the discrete dynamics are marginally stable for the zero input, the impulsive stochastic system is p-ISS/SISS regardless of how often or how seldom the impulses occur. To overcome the difficulties caused by the coexistence of time delays, impulses, and stochastic effects, Razumikhin techniques and piecewise continuous Lyapunov functions as well as stochastic analysis techniques are involved together. An example is provided to illustrate the effectiveness and advantages of our results.

This paper deals with the absolute stability for a class of nonlinear singular systems with time delay. By employing a new Lyapunov-Krasovskii functional with the idea of partitioning delay length, improved delay-dependent stability criteria are established. The resulting condition is formulated in terms of linear matrix inequalities (LMIs), which is easy to be verified by exiting LMI optimization algorithms. A numerical example is given to show the effectiveness of the proposed technique and its improvements over the existing results.

This paper considers the constrained multiagent optimization problem. The objective function of the problem is a sum of convex functions, each of which is known by a specific agent only. For solving this problem, we propose an asynchronous distributed method that is based on gradient-free oracles and gossip algorithm. In contrast to the existing work, we do not require that agents be capable of computing the subgradients of their objective functions and coordinating their step size values as well. We prove that with probability 1 the iterates of all agents converge to the same optimal point of the problem, for a diminishing step size.

Multigranulation rough set is an extension of classical rough set, and optimistic multigranulation and pessimistic multigranulation are two special cases of it. β multigranulation rough set is a more generalized multigranulation rough set. In this paper, we first introduce fuzzy rough theory into β multigranulation rough set to construct a β multigranulation fuzzy rough set, which can be used to deal with continuous data; then some properties are discussed. Reduction is an important issue of multigranulation rough set, and an algorithm of granular space reduction to β multigranulation fuzzy rough set for preserving positive region is proposed. To test the algorithm, experiments are taken on five UCI data sets with different values of β. The results show the effectiveness of the proposed algorithm.

A simplified model predictive control algorithm is designed for discrete-time Markov jump systems with mixed uncertainties. The mixed uncertainties include model polytope uncertainty and partly unknown transition probability. The simplified algorithm involves finite steps. Firstly, in the previous steps, a simplified mode-dependent predictive controller is presented to drive the state to the neighbor area around the origin. Then the trajectory of states is driven as expected to the origin by the final-step mode-independent predictive controller. The computational burden is dramatically cut down and thus it costs less time but has the acceptable dynamic performance. Furthermore, the polyhedron invariant set is utilized to enlarge the initial feasible area. The numerical example is provided to illustrate the efficiency of the developed results.

The problem of a portfolio strategy for financial market with regime switching driven by geometric Lévy process is investigated in this paper. The considered financial market includes one bond and multiple stocks which has few researches up to now. A new and general Black-Scholes (B-S) model is set up, in which the interest rate of the bond, the rate of return, and the volatility of the stocks vary as the market states switching and the stock prices are driven by geometric Lévy process. For the general B-S model of the financial market, a portfolio strategy which is determined by a partial differential equation (PDE) of parabolic type is given by using Itô formula. The PDE is an extension of existing result. The solvability of the PDE is researched by making use of variables transformation. An application of the solvability of the PDE on the European options with the final data is given finally.

We deal with the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. A controller designed for unconstrained systems combined with a dynamic antiwindup compensator is given to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. The proposed conditions allow us to find dynamic anti-windup compensator which stabilize the closed-loop systems in the finite-time sense. All these conditions can be expressed in the form of linear matrix inequalities and therefore are numerically tractable, as shown in the example included in the paper.

This paper deals with the problem of robust exponential stability and $H_{\infty }$ performance analysis for a class of uncertain Markovian jumping system with multiple delays. Based on the reciprocally convex approach, some novel delay-dependent stability criteria for the addressed system are derived. At last, numerical examples is given presented to show the effectiveness of the proposed results.

This paper mainly focuses on the generalized mutual synchronization between two controlled interdependent networks. First, we propose the general model of controlled interdependent networks $A$ and $B$ with time-varying internetwork delays coupling. Then, by constructing Lyapunov functions and utilizing adaptive control technique, some sufficient conditions are established to ensure that the mutual synchronization errors between the state variables of networks $A$ and $B$ can asymptotically converge to zero. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results and to explore potential application in future smart grid. The simulation results also show how interdependent topologies and internetwork coupling delays influence the mutual synchronizability, which help to design interdependent networks with optimal mutual synchronizability.

The problem of $H_{\infty }$ control performance analysis of continuous-time systems with random abrupt changes is concerned in this paper. By employing an augmented multiple mode-dependent Lyapunov-Krasovskii functional and using some integral inequalities, new sufficient conditions are obtained relating to finite-time bounded and an $H_{\infty }$ performance index. The finite-time $H_{\infty }$ control performance problem is solved and desired controller is given to ensure the system trajectory stays within a prescribed bound during a given time interval. At last, two numerical examples are provided to show that our results are less conservative than the existing ones.

This paper is concerned with the problem of robust finite-time $H_{\infty }$ control for a class of nonlinear Markovian jump systems with time delay under partially known transition probabilities. Firstly, for the nominal nonlinear Markovian jump systems, sufficient conditions are proposed to ensure finite-time boundedness, $H_{\infty }$ finite-time boundedness, and finite-time $H_{\infty }$ state feedback stabilization, respectively. Then, a robust finite-time $H_{\infty }$ state feedback controller is designed, which, for all admissible uncertainties, guarantees the $H_{\infty }$ finite-time boundedness of the corresponding closed-loop system. All the conditions are presented in terms of strict linear matrix inequalities. Finally a numerical example is provided to demonstrate the effectiveness of all the results.

This paper is concerned with the nonfragile $H_{\infty }$ control problem for stochastic systems with Markovian jumping parameters and random packet losses. The communication between the physical plant and controller is assumed to be imperfect, where random packet losses phenomenon occurs in a random way. Such a phenomenon is represented by a stochastic variable satisfying the Bernoulli distribution. The purpose is to design a nonfragile controller such that the resulting closed-loop system is stochastically mean square stable with a guaranteed $H_{\infty }$ performance level γ. By using the Lyapunov function approach, some sufficient conditions for the solvability of the previous problem are proposed in terms of linear matrix inequalities (LMIs), and a corresponding explicit parametrization of the desired controller is given. Finally, an example illustrating the effectiveness of the proposed approach is presented.

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results.