Robust packet-based nonlinear fuzzy networked control systems

A class of networked nonlinear control systems with norm-bounded uncertainties is presented in this paper. The class is represented by Takagi–Sugeno (T-S) fuzzy models with packet processing. The network loop delay is considered either as known delay or random delay. For the former case, we develop conditions that guarantee the robust asymptotic stability and state-feedback stabilization with strict dissipativity and cast the results in linear matrix inequality (LMI) framework. Next employing a probabilistic-based delay partitioning method to deal with random delay, we establish novel LMI criteria for strict dissipative stability analysis and feedback synthesis. The efficacy of the ensuing techniques is demonstrated by numerical solution of typical examples and Mont Carlo simulation.     

Vibration suppression and output constraint of a variable length drilling riser system

In this paper, we mainly concentrate on the control issue of a variable length drilling riser under condition of unknown disturbances and output constraint. The studied flexible drilling riser system with variable length, variable tension, variable speed and restricted boundary output is essentially a nonlinear distributed parameter system. For achieving the vibration suppression and ensuring the boundary output within the constrained range, an appropriate control scheme with output signal barrier is put forward by integrating boundary control method, barrier Lyapunov function with finite-dimensional backstepping technique, where disturbance observer is employed for coping with the boundary disturbance. Moreover, the Lyapunov’s synthetic method is applied for the steadiness research of the studied flexible drilling riser system, and the simulations are presented to display the usefulness of proposed control scheme.     

Lag projective synchronization of fractional-order delayed chaotic systems

This paper considers the lag projective synchronization of fractional-order delayed chaotic systems. The lag projective synchronization is achieved through the use of comparison principle of linear fractional equation at the presence of time delay. Some sufficient conditions are obtained via a suitable controller. The results show that the slave system can synchronize the past state of the driver up to a scaling factor. Finally, two different structural fractional order delayed chaotic systems are considered in order to examine the effectiveness of the lag projective synchronization. Feasibility of the proposed method is validated through numerical simulations.     

The stability analysis of time-varying delayed systems based on new augmented vector method

This paper focuses on the stability analysis of systems with interval time-varying delay. A new augmented vector containing single and double integral terms is constructed and the corresponding Lyapunov functional with triple integral terms is introduced. In order to improve the estimating accuracy of the derivatives of the constructed Lyapunov functional, single integral inequalities and double integral inequalities via auxiliary functions are employed on the first step, then an extended relaxed integral inequality and reciprocally convex approach are further utilized to narrow the scaling room of the functional derivatives. As a result, some novel delay-dependent stability criteria with less conservatism are derived. Finally, numerical examples are provided to check the effectiveness of the theoretical results and the improvement of the proposed method over the existing works.     

The obstacle problem of integro-partial differential equations with applications to stochastic optimal control/stopping problem

This paper is devoted to existence and uniqueness of minimal mild super solutions to the obstacle problem governed by integro-partial differential equations. We first study the well-posedness and local Lipschitz regularity of L^p solutions (p?≥?2) to reflected forward-backward stochastic differential equations (FBSDEs) with jump and lower barrier. Then we show that the solutions to reflected FBSDEs provide a probabilistic representation for the mild super solution via a nonlinear Feynman–Kac formula. Finally, we apply the results to study stochastic optimal control/stopping problems.     

Decentralized event-triggered H∞ control for switched systems with network communication delay

This paper is concerned with the decentralized event-triggered H_∞ control for switched systems subject to network communication delay and exogenous disturbance. Depending on different physical properties, the system state is divided into multiple communication channels and decentralized sensors are employed to collect signals on these channels. Furthermore, decentralized event-triggering mechanisms (DETMs) with a switching structure are proposed to determine whether the sampled data needs to be transmitted. In particular, an improved data buffer is presented which can guarantee more timely utilization of the sampled data. Then, with the proposed DETMs and data buffer, a time-delay closed-loop switched system is developed. After that, sufficient conditions are presented to guarantee the H_∞ performance of the closed-loop switched system by utilizing the average dwell time and piecewise Lyapunov functional method. Since the event-triggered instants and the switching instants may stagger with each other, the influence of their coupling on the H_∞ performance analysis is systematically discussed. Subsequently, sufficient conditions for designing the event-triggered state feedback controller gains are provided. Finally, numerical simulations are given to verify the effectiveness of the proposed method.     

Robust self-triggered MPC with fast convergence for constrained linear systems

In this paper, a robust self-triggered model predictive control (MPC) scheme is proposed for linear discrete-time systems subject to additive disturbances, state and control constraints. To reduce the amount of computation on controller sides, MPC optimization problems are only solved at certain sampling instants which are determined by a novel self-triggering mechanism. The main idea of the self-triggering mechanism is to choose inter-sampling times by guaranteeing a fast decrease in optimal costs. It implies a fast convergence of system states to a compact set where it is ultimately bounded and a reduction of computation times to stabilize the system. Once the state enters a terminal region, the system can be stabilized to a robust invariant set by a state feedback controller. Robust constraint satisfaction is ensured by utilizing the worst-case set-valued predictions of future states in such a way that recursive feasibility is guaranteed for all possible realisations of disturbances. In the case where a priority is given to reducing communication costs rather than improvement in control performance in a neighborhood of the origin, a feedback control law based on nominal state predictions is designed in the terminal region to avoid frequent feedback. Performances of the closed-loop system are demonstrated by a simulation example.     

Necessary and sufficient criteria for asynchronous stabilization of Markovian jump systems

This paper is concerned with asynchronous stabilization for a class of discrete-time Markovian jump systems. The mode of designed controller is considered to be not perfectly synchronous with the activated mode of the Markovian jump system. In order to achieve the asymptotic stability with asynchronous controller, a conditional probability is introduced to describe the asynchronism of system and controller modes, which is dependent on the active system mode. Besides, due to the difficulty in acquiring all the mode transition probabilities in practice, the transition probabilities of the Markovian jump system and the controllers are supposed to be partially unknown. A necessary and sufficient condition is developed to guarantee the stochastic stability of the resultant closed-loop system and further extended to asynchronous stabilization with partially known transition probabilities. Finally, the effectiveness and advantages of the proposed methods are demonstrated by two illustrative examples.     

Finite-time control in probability for time-varying systems with measurement censoring

This paper considers a parameter-dependent controller design problem for a class of discrete-time uncertain systems subject to censored measurement. First, a set of mutually independent stochastic variables obeying uniform distribution is used to describe the system uncertainty. Then, an array of new bounded variables is introduced to characterize the boundedness of the censored measurement. In addition, a novel definition, named as finite-time boundedness in probability (FTBP), is presented to depict the dynamic behavior of addressed systems in the sense of probability. In this case, the norm of controlled system states cannot exceed a given boundary under a probability constraint. By means of the hyper-rectangle depending on the value range of stochastic variables, a sufficient condition is presented to ensure that the system is FTBP. Finally, the corresponding controller design problem is formulated as an algorithm based on the recursive linear matrix inequality. Two simulation examples are given to illustrate the effectiveness of the proposed methodology.     

Moment matching model reduction for negative imaginary systems

In this paper, moment matching model reduction problem for negative imaginary systems is considered. For a given negative imaginary system with poles at the origin, our goal is to find a reduced-order negative imaginary system such that a prescribed number of the moments and the poles at the origin are preserved. Firstly, the original negative imaginary system is split into an asymptotically stable subsystem, a lossless negative imaginary subsystem and an average subsystem. Then, moment matching model reduction is implemented on the asymptotically stable subsystem and the lossless negative imaginary subsystem. The resulting reduced-order system preserves the negative imaginary structure and the poles at the origin. Also, the proposed model reduction method is extended to the positive real systems. Numerical examples demonstrate the effectiveness of the proposed model reduction method.