Mode-independent Controller Research Articles

Stabilizing Large-Scale Probabilistic Boolean Networks by Pinning Control.

This article aims to stabilize probabilistic Boolean networks (PBNs) via a novel pinning control strategy. In a PBN, the state evolution of each gene switches among a collection of candidate Boolean functions with preassigned probability distributions, which govern the activation frequency of each Boolean function. Due to the existence of stochasticity, the mode-independent pinning controller might be disabled. Thus, both mode-independent and mode-dependent pinning controller are required here. Moreover, a criterion is derived to determine whether mode-independent controllers are applicable while the pinned nodes are given. It is worth pointing out that this pinning control is based on the n×n network structure rather than 2n ×2n state transition matrix. Therefore, compared with the existing results, this pinning control strategy is more practicable and has the ability to handle large-scale networks, especially sparsely connected networks. To demonstrate the effectiveness of the designed control scheme, a PBN that describes the mammalian cell-cycle encountering a mutated phenotype is discussed as a simulation.

Modeling and SPM-dependent control of multi-rate networked control system with long time delay

In this paper, an efficient approach of modeling and control is presented for Multi-Rate Networked Control System (MRNCS) with considering long time delay. Firstly, the system is modeled as a switched system with a random switching signal which is subject to random networked-induced delay. For this, time delay is defined as a Markov chain and the model of MRNCS is obtained as a Markovian jump linear system. Afterward, a dynamic output feedback controller is designed for output tracking as well as stabilization of closed-loop system. The modeling and control of MRNCS are presented for two structures. At first, a new model of single-side MRNCS is proposed and a mode-independent controller is designed for stabilizing the system. Then the proposed modeling method is generalized to double-side MRNCS and by introducing the Set of Possible Modes (SPM) concept, an SPM-dependent controller is proposed for double-side MRNCS. To show the effectiveness of the proposed methods, some numerical results are provided on the quadruple-tank process.

Exponential synchronization of semi-Markovian coupled neural networks with mixed delays via tracker information and quantized output controller

In this paper, exponential synchronization of semi-Markovian coupled neural networks (NNs) with bounded time-varying delay and infinite-time distributed delay (mixed delays) is investigated. Since semi-Markov switching occurs by time-varying probability, it is difficult to capture its precise switching signal. To overcome this difficulty, a tracker is used to track the switching information with some accuracy. Then a quantized output controller (QOC) is designed by using the tracked information. Novel Lyapunov–Krasovskii functionals (LKFs) with negative terms and delay-partitioning approach, which reduce the conservativeness of the obtained results, are utilized to obtain LMI conditions ensuring the exponential synchronization. Moreover, an algorithm is proposed to design the control gains. Our results include both those derived by mode-dependent and mode-independent control schemes as special cases. Finally, numerical simulations validate the effectiveness of the methodology.

Robust Non-fragile Asynchronous Controller Design for Continuous-Time Markov Jump Linear Systems: Non-homogeneous Markov Process Approach

This paper proposes a robust asynchronous controller for continuous-time Markov jump linear systems (MJLSs). The asynchronous structure considers a case in which the Markov chain governing candidate controllers does not match the chain which manages the switching between system modes. This type of asynchronousy arises because the real-time, exact and precise detection of the system modes is not practical; therefore, the observed modes slightly differ with the actual modes. This paper models the asynchronousy through an additional, observed Markov chain which depends on the original Markov chain of the system according to uncertain transition probabilities. By this representation, the whole system is viewed as a non-homogeneous MJLS, and the sufficient stabilizability conditions as well as the controller gains are obtained through multiple mode-dependent Lyapunov functions. This approach leads to less conservative design results than the previous mode-independent schemes and proposes a much simple methodology to obtain the controller than the previous mode-dependent studies. For more generality, the proposed controller also takes the possible gain variations occurring in the implementation procedures into account and reports all the results in terms of linear matrix inequalities. Simulation results on a vertical takeoff and landing helicopter are presented and compared with the common mode-independent controller to illustrate the effectiveness of the developed method.

General synchronization criteria for nonlinear Markovian systems with random delays

It is well known that control of Markovian systems is a difficult problem. This paper considers synchronization control of Markovian coupled nonlinear systems with random delays. A new control scheme is proposed. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained such that the coupled system can be asymptotically synchronized onto an isolated system. The synchronization criteria include classical mode-dependent and mode-independent results as special cases. The design method of the control gains is also given. Compared with mode-dependent and mode-independent control methods, our results are more practical and have lower conservatism, respectively. Numerical simulations are given to verify the effectiveness of the theoretical results.

Optimal state feedback sampled-data control design for Markov jump linear systems

ABSTRACTThis paper is entirely devoted to analyse and solve the optimal state feedback sampled-data control design problem for continuous-time Markov jump linear systems. This is an important unsolved problem in the context of optimal control theory. To this end, necessary and sufficient optimality conditions are characterised in terms of a specific nonlinear two-point boundary value problem. A global convergent algorithm able to solve iteratively the optimality conditions is provided. Moreover, some mathematical properties of the solution of a differential Riccati equation are raised in order to translate the previous conditions into linear matrix inequalities. This result allows a mode independent feedback control structure for the Markovian system under analysis. A practical application borrowed from the literature is included for illustration.

Passivity-Based Asynchronous Control for Markov Jump Systems

The issue of asynchronous passive control is addressed for Markov jump systems in this technical note. The asynchronization phenomenon appears between the system modes and controller modes, which is described by a hidden Markov model. Accordingly, a hidden Markov jump model is used to name the resultant closed-loop system. By utilizing the matrix inequality technique, three equivalent sufficient conditions are obtained, which can guarantee the hidden Markov jump systems to be stochastically passive. Based on the established conditions, the design of asynchronous controller, which covers the well-known mode-independent controller and synchronous controller as special cases, is addressed. The DC motor device is applied to demonstrate the practicability of the derived asynchronous synthesis scheme.

Stabilization of Continuous-Time Random Switching Systems via a Fault-Tolerant Controller

This paper focuses on the stabilization problem of continuous-time random switching systems via exploiting a fault-tolerant controller, where the dwell time of each subsystem consists of a fixed part and random part. It is known from the traditional design methods that the computational complexity of LMIs related to the quantity of fault combination is very large; particularly system dimension or amount of subsystems is large. In order to reduce the number of the used fault combinations, new sufficient LMI conditions for designing such a controller are established by a robust approach, which are fault-free and could be solved directly. Moreover, the fault-tolerant stabilization realized by a mode-independent controller is considered and suitably applied to a practical case without mode information. Finally, a numerical example is used to demonstrate the effectiveness and superiority of the proposed methods.

Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information

In this paper, synchronization in an array of discrete-time neural networks (DTNNs) with time-varying delays coupled by Markov jump topologies is considered. It is assumed that the switching information can be collected by a tracker with a certain probability and transmitted from the tracker to controller precisely. Then the controller selects suitable control gains based on the received switching information to synchronize the network. This new control scheme makes full use of received information and overcomes the shortcomings of mode-dependent and mode-independent control schemes. Moreover, the proposed control method includes both the mode-dependent and mode-independent control techniques as special cases. By using linear matrix inequality (LMI) method and designing new Lyapunov functionals, delay-dependent conditions are derived to guarantee that the DTNNs with Markov jump topologies to be asymptotically synchronized. Compared with existing results on Markov systems which are obtained by separately using mode-dependent and mode-independent methods, our result has great flexibility in practical applications. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.

From adaptive control to variable structure systems – seeking harmony

From adaptive control to variable structure systems – seeking harmony

Mode-independent control of singular Markovian jump systems: A stochastic optimization viewpoint

In this paper, the mode-independent control problem of singular Markovian jump systems is firstly studied by exploiting a stochastic optimization viewpoint. A new kind of mode-independent H∞ controller satisfying a minimum variance approximation is constructed, whose gain is composed of some mode-dependent control gains. The available probability of system mode is described by the Bernoulli variable and taken into account. It shows that such a probability plays an important role in system analysis and associates mode-independent controller with mode-dependent controllers. When the probability is unknown, a kind of adaptive controller is proposed such that the resulting closed-loop system is robust stochastically admissible with an H∞ performance. All the proposed conditions are given in terms of linear matrix inequalities. Two numerical examples are used to demonstrate the effectiveness of the proposed methods.

Stabilization of discrete-time singular Markovian jump repeated vector nonlinear systems

This paper studies the control problem for discrete-time singular Markovian jump systems with repeated vector nonlinearities. Sufficient conditions for stochastic stability are established, where the uniqueness of solution to the underlying system is also guaranteed. Then, a series of formulations of stabilizing conditions is further developed to design mode-dependent and mode-independent controllers by using the linear matrix inequality approach. Based on the proposed results, more special cases for stabilizing controller are considered. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.

H∞ control of singular Markovian jump systems with operation modes disordering in controllers

This paper considers the H∞ control problem for a class of singular Markovian jump systems, where the operation mode of a controller has a disordering phenomenon. Because of the operation modes in system matrices and control gains having a disagreement, an augmented Markov chain is introduced, and the corresponding controller is related to the new operation mode. Instead of designing a controller of new operation mode directly, a kind of H∞ controller referring to the original operation mode is developed, which is composed of controllers depending on the new operation modes and satisfies a minimum variance approximation. Based on the developed methods, a special case of mode-independent control is studied. All the proposed conditions are given in terms of linear matrix inequalities. A numerical example is used to demonstrate the effectiveness of the proposed methods.

Exponential synchronization criteria for Markovian jumping neural networks with time-varying delays and sampled-data control

This paper deals with the problem of exponential synchronization of Markovian jumping neural networks with time-varying delays and variable sampling control. Several delay-dependent synchronization criteria are derived to ensure the convergence of the error systems, that is, the master systems stochastically synchronized with the slave systems. By employing an improved Lyapunov–Krasovskii functional (LKF) with the triple integral terms and combining the convex technique, two new sufficient conditions are derived to guarantee that a class of delayed neural networks (DNNs) to be globally exponentially stable. The information about the lower bound of the discrete time-varying delay is fully used in the LKF. Moreover, the conditions obtained in this paper are formulated in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. The maximum sampling intervals are obtained based on the design of mode-independent controller. Finally, three numerical examples are given to demonstrate the efficiency of the proposed theoretical results.

Finite-time synchronization control for uncertain Markov jump neural networks with input constraints

This paper is concerned with the problem of finite-time synchronization control for uncertain Markov jump neural networks in the presence of constraints on the control input amplitude. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. By using a parameter-dependent Lyapunov functional and a simple matrix decoupling method, a sufficient condition is proposed to ensure that the considered networks are stochastically synchronized over a finite-time interval. The desired mode-independent controller parameters can be computed via solving a convex optimization problem. Finally, two chaos neural networks are employed to demonstrate the effectiveness of our proposed approach.

Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data

In this paper, the problem of sampled-data synchronization for Markovian jump neural networks with time-varying delay and variable samplings is considered. In the framework of the input delay approach and the linear matrix inequality technique, two delay-dependent criteria are derived to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems. The desired mode-independent controller is designed, which depends upon the maximum sampling interval. The effectiveness and potential of the obtained results is verified by two simulation examples.

A Unified Approach to H∞ Control of Singular Markovian Jump Systems

This paper considers the H∞ control problem for a class of singular Markovian jump systems (SMJSs), where the jumping signal is not always available. The main contribution of this paper introduces a new approach to a mode-independent (MI) H∞ controller by exploiting the nonfragile method. Based on the given method, a unified control approach establishing a direct connection between mode-dependent (MD) and mode-independent controllers is presented, where both existence conditions are given in terms of linear matrix inequalities. Moreover, another three cases of transition probability rate matrix (TRPM) with elementwise bounded uncertainties, being partially unknown and to be designed are analyzed, respectively. Numerical examples are used to demonstrate the effectiveness of the proposed methods.

Robust stabilization of singular markovian jump systems with uncertain switching

This paper focuses on the robust stabilization problem for a class of singular Markovian jump systems with uncertain switching probabilities. Based on a slack matrix method on transition probabilities, a new criterion for quadratically stochastic admissibility of such an uncertain system is established. Then, two new sufficient conditions for the existence of mode-dependent controller are given as linear matrix inequalities. Especially, a more practical controller named as mode-independent controller is derived by a mode-dependent Lyapunov function. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.

H∞ control for networked control systems with limited information

In this paper, H∞ control problems are investigated for a class of networked control systems. An improved networked control system model is proposed and the effects of random packet dropout, delay and sensor fault are considered simultaneously. The packet dropout process is modeled as a Markov chain, and the delays are bounded and occurred in a random way in this paper. The fault for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution. The resulting closed-loop system is transformed to a Markovian switching system. Sufficient conditions for stochastic stability of the closed-loop system are given in terms of linear matrix inequality. A mode-independent controller is designed such that the closed-loop system is stochastically stable and achieves the given H∞ disturbance attenuation level. Finally, the simulation of the inverted pendulum control is given to illustrate the effectiveness of the proposed method.

Dissipative control for singular Markovian jump systems with time delay

SUMMARY This paper focuses on the problem of dissipative control for continuous-time singular time-delayed systems with Markovian jump parameters. Different from usually mode-dependent or mode-independent controller design methods, a partially mode-dependent dissipative controller is firstly proposed via using a mode-dependent Lyapunov function. The stochastic property of the mode available to a controller operation is taken into consideration in the corresponding controller design. Moreover, the existence of the established controller is given in terms of strict linear matrix inequalities. Finally, numerical examples are used to demonstrate the effectiveness of the given theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.