Hybrid Impulsive Control Research Articles

Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

SummaryThis paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional‐derivative control strategy is presented, where the derivative gain is to make the closed‐loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.

Hybrid Impulsive Control of Stochastic Systems with Multiplicative Noise Under Markovian Switching

A problem of state output feedback stabilization of discrete-time stochastic systems with multiplicative noise under Markovian switching is considered. Under some appropriate assumptions, the stability of this system under pure impulsive control is given. Further under hybrid impulsive control, the output feedback stabilization problem is investigated. The hybrid control action is formulated as a combination of the regular control along with an impulsive control action. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the stochastic and the deterministic terms. Sufficient conditions based on stochastic semi-definite programming and linear matrix inequalities (LMIs) for both stochastic stability and stabilization are obtained. Such a nonconvex problem is solved using the existing optimization algorithms and the nonconvex CVX package. The robustness of the stability and stabilization concepts against all admissible uncertainties are also investigated. The parameter uncertainties we consider here are norm bounded. Two examples are given to demonstrate the obtained results.

Hybrid Impulsive Control for Closed Quantum Systems

The state transfer problem of a class of nonideal quantum systems is investigated. It is known that traditional Lyapunov methods may fail to guarantee convergence for the nonideal case. Hence, a hybrid impulsive control is proposed to accomplish a more accurate convergence. In particular, the largest invariant sets are explicitly characterized, and the convergence of quantum impulsive control systems is analyzed accordingly. Numerical simulation is also presented to demonstrate the improvement of the control performance.

Quantum Control and Quantum Information Technology

Quantum information technology has been recognized as one of the most promising future technologies (e.g., see [1]). The development of quantum control theory is a key task for practical quantum information technology (e.g., see [2–4]. Recent advances in quantum information technologies and robust quantum information processing require the dynamics of realistic quantum systems to be characterized and controlled with unprecedented accuracy and efficiency. The interactive promotion between the two fields is a rapidly developing research area. The purpose of this special issue is to provide an account of the state of the art in this fast moving and cross-disciplinary field. 18 papers have been received for this special issue and 9 among them have been accepted for publication. The paper by C. Chen et al. presents a survey on the recent development of closed-loop control strategies in quantum control including closed-loop learning control and quantum feedback control as well as an introduction to quantum robust control. The paper by S. Cong and F. Meng presents a survey on Lyapunov control of quantum systems which is a “feedback design” and “open-loop control” strategy. The paper by S. N. Khonina et al. develops an algorithm for solving the steady-state Schodinger equation for a class of potentials. The paper by S. Zhao et al. proposes a hybrid impulsive control method combined with Lyapunov control to achieve a more accurate convergence for a class of nonideal quantum systems. The paper by V. Tiporlini and K. Alameh investigates the principles of operation and the optimal design of an optically pumped quantum magnetometer. The paper by W. Yang and J. Sun investigates the Lyapunov control of finite-dimensional quantum systems with impulsive control fields. The paper by M. Li et al. proposes a feedback control scheme through Rabi oscillation stabilization to preserve the coherence in cavity QED. The paper by Y. Xing and J. Wu presents a quantum control method to control the Shannon entropy of quantum systems. The paper by M. Li proposes a numerical simulation algorithm for stochastic process of direct photodetection of a driven two-level system.

Hybrid impulsive control for switched singular systems

In this study, the authors investigate the control problem of switched singular systems aiming to compress their inconsistent state jumps when switch occurs between two different singular subsystems. The proposed hybrid impulsive controller consists of a feedback controller and an impulsive controller. With introduction of the impulsive controller, the state at each switching instant for the closed-loop system can be changed. Based on the given controller structure, some sufficient conditions are derived under which the closed-loop system is admissible (regular, impulse free and stable) and such a controller has the capability of eliminating or minimising the instantaneous state jumps at switching instants. The validity and advantage of the proposed hybrid impulsive controller are illustrated using two examples.

Modelling and Analysis of a Pest‐Control Pollution Model with Integrated Control Tactics

A hybrid impulsive pest control model with stage structure for pest and Holling II functional response is proposed and investigated, in which the effects of impulsive pesticide input in the environment and in the organism are considered. Sufficient conditions for global attractiveness of the pest‐extinction periodic solution and permanence of the system are obtained, which show that there exists a globally asymptotically stable pest‐extinction periodic solution when the number of natural enemies released is more than some critical value, whereas the system can be permanent when the number of natural enemies released is less than another critical value. Furthermore, numerical simulations are carried out to illustrate our theoretical results and facilitate their interpretation.

Stabilization of complex network with hybrid impulsive and switching control

This paper studies the asymptotic stability properties of a class of complex dynamical networks under a hybrid impulsive and switching control. By utilizing the concept of impulsive control and the stability results for impulsive systems, some new criteria for global and local stability are established for this model. Some numerical examples and simulations are included to illustrate the effectiveness of the theoretical results.

A HYBRID IMPULSIVE AND SWITCHING CONTROL STRATEGY FOR SYNCHRONIZATION OF NONLINEAR SYSTEMS AND APPLICATION TO CHUA'S CHAOTIC CIRCUIT

In this paper, a new hybrid impulsive and switching control strategy for synchronization of nonlinear systems is developed. Using switched Lyapunov functions, several new criteria for global exponential stability of hybrid impulsive and switching nonlinear systems are established and, particularly, some simple sufficient conditions for driving the synchronization error to zero exponentially are proposed. As an application, Chua's chaotic circuit is investigated.

On hybrid impulsive and switching systems and application to nonlinear control

In this note, a new class of hybrid impulsive and switching models is introduced and their asymptotic stability properties are investigated. Using switched Lyapunov functions, some new general criteria for exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching are established. In addition, a new hybrid impulsive and switching control strategy for nonlinear systems is developed. A typical example, the unified chaotic system, is given to illustrate the theoretical results.

STABILITY OF A CLASS OF HYBRID IMPULSIVE AND SWITCHING SYSTEMS

In this paper, a new class of hybrid impulsive and switching models are introduced. Using switched Lyapunov functions, some new general criteria for exponential stability and asymptotic stability of hybrid impulsive and switched nonlinear systems are established. Further more, a new hybrid impulsive and switching control strategy for the nonlinear systems is developed to improve the system performance. A typical example, the Chua's chaotic circuit, is provided for illustrating and visualizing the analytical results.