Robust stabilization of stochastic systems based on the LQ controller

The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we have designed an optimal controller which guarantees the exponential stability of the system. Actually, we employed Lyapunov fimction approach and the stochastic algebraic Riccati equation (SARE) to have shown the robusmess of the linear quadratic(LQ) optimal control law.And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed-loop systems are given.     

The stochastic semantics and verification for periodic control systems

Periodic control systems(PCS) are widely used in the embedded industry like aerospace and automotive.Such systems usually run periodic tasks and respond to the external signals.Based on our previous work on Mode diagram modeling(MDM) notations for specifying the periodic control system,we present the stochastic semantics for MDM in this paper.The stochastic semantics of MDM is based on the Markov chain.The semantics proposed here provides the basis for the satisfaction of formulae of the interval temporal logic(ITL) based specification language that is aimed to specify the properties of PCS.To verify whether the system satisfies the ITL-based properties,we apply the statistical model checking technique to efficiently estimate the probability of the system satisfying the given property with a desired level of confidence.The empirical experiments show that our approach is both effective and efficient.     

Robust stabilitv of neutral stochastic interval svstems

Although interval systems have received a great deal of attention, so far there is few work on neutral stochastic interval systems (NSIS). The purpose of this paper is to initiate the study of NSIS. Using Raumikhin-type technique, a sufficient condition of exponential stability on NSIS is given. It is interesting that the NSIS changes into general stochastic interval system when the neutral item disappeared. So the results in this paper generalize some conclusions existed.     

Stabilization of stochastic Hopfield neural network with distributed parameters

In this paper, the stability of stochastic Hopfield neural network with distributed parameters is studied. To discuss the stability of systems, the main idea is to integrate the solution to systems in the space variable. Then, the integration is considered as the solution process of corresponding neural networks described by stochastic ordinary differential equations. A Lyapunov function is constructed and Ito formula is employed to compute the derivative of the mean Lyapunov function along the systems, with respect to the space variable. It is difficult to treat stochastic systems with distributed parameters since there is no corresponding Ito formula for this kind of system. Our method can overcome this difficulty. Till now, the research of stability and stabilization of stochastic neural networks with distributed parameters has not been considered.     

Consensus control of second-order stochastic discrete-time multi-agent systems without velocity transmission

This article studies the almost-sure and the mean-square consensus control problems of second-order stochastic discretetime multi-agent systems with multiplicative noises. First, a control law based on the absolute velocity and relative position information is designed. Second, considering the existence of multiplicative noises and nonlinear terms with Lipschitz constants, the consensus control problem is solved through the use of a degenerated Lyapunov function. Then, for the linear second-order multi-agent systems, some explicit consensus conditions are provided. Finally, two sets of numerical simulations are performed.     

Approximate controllability of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces

Many practical systems in physical and technical sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, we prove the approximate controllability of control systems governed by a class of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established under the natural assumption that the corresponding linear system is approximately controllable. The results are obtained by using semigroup theory, stochastic analysis techniques, fixed point approach and abstract phase space axioms. An example is provided to illustrate the application of the obtained results.     

A phase-space formulation and Gaussian approximation of the filtering equations for nonlinear quantum stochastic systems

This paper is concerned with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel nondemolition measurements. The system-observation dynamics are governed by a Markovian Hudson-Parthasarathy quantum stochastic differential equation driven by quantum Wiener processes of bosonic fields in vacuum state. The Hamiltonian and system-field coupling operators, as functions of the system variables, are assumed to be represented in a Weyl quantization form. Using the Wigner-Moyal phase-space framework, we obtain a stochastic integro-differential equation for the posterior quasi-characteristic function (QCF) of the system conditioned on the measurements. This equation is a spatial Fourier domain representation of the Belavkin-Kushner-Stratonovich stochastic master equation driven by the innovation process associated with the measurements. We discuss a specific form of the posterior QCF dynamics in the case of linear system-field coupling and outline a Gaussian approximation of the posterior quantum state.     

Observability conditions of switched linear singular systems

The observability problem of switched linear singular(SLS) systems is studied in this paper. Based on the observability definition, the unobservable subspaces of given switching laws are investigated under the condition that all subsystems are regular. A necessary condition and a sufficient condition for observability of SLS systems are given. It is shown that the observability and controllability are dual for some special SLS systems with circulatory switching laws. The method developed here is applicable to the observability analysis of normal switched linear systems.     

Discretization of nonlinear non-affine time delay systems based on second-order hold

When calculating the sampled-date representation of nonlinear systems second-order hold(SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on Taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the Taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine input.Different input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed method.The simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine systems.The comparison between SOH assumption with first-order hold(FOH) and zero-order hold(ZOH) assumptions is given to show the advantages of the proposed method.     

Time-scheduled observer design for switched linear systems with unknown inputs

<正>Dear editor, Since uncertain disturbance, actuator faults and unmodeled dynamics can all be viewed as unknown inputs in various practical systems, the issue of unknown input observer design is of great significance. Meanwhile, switched systems have attracted extensive attention, which are prevailingly motivated by superior capabilities in modeling numerous practical systems possessing switching characteristics. Recently, the state observation for switched systems with unknown inputs has...     

Detecting and diagnosing faults in dynamic stochastic distributions using a rational B-splines approximation to output PDFs

This paper presents a novel approach to detect and diagnose faults in the dynamic part of a class of stochastic systems . the Such a group of systems are subjected to a set of crisp inputs but the outputs considered are the measurable probability density functions (PDFs) of the system output, rather than the system output alone. A new approximation model is developed for the output probability density functions so that the dynamic part of the system is decoupled from the output probability density functions. A nonlinear adaptive observer is constructed to detect and diagnose the fault in the dynamic part of the system. Conver-gency analysis is performed for the error dynamics raised from the fault detection and diagnosis phase and an applicability study on the detection and diagnosis of the unexpected changes in the 2D grammage distributions in a paper forming process is included.     

State-feedback H2/H-infinity controller design with D-stability constraints for stochastic systems

This paper addresses the state-feedback H2/H-infinity controller design that satisfies D-stability constraints for stochastic systems. Firstly, the concept of regional stability for stochastic systems is defined in linear matrix inequality（LMI） regions; Secondly, the characterization about stochastic D-stability is presented. This paper introduces a new technique to solve the regional stability problem for stochastic systems, which is different from the pole placement technique ever used in deterministic systems. Based on this, in the state-feedback case, mixed H2/H-infinity synthesis with D-stability constraints is discussed via LMI optimization.     

Output feedback stabilization of switched stochastic nonlinear systems under arbitrary switchings

This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in output feedback form and driven by white noise. By introducing a common Lyapunov function, the common output feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment exponentially stable. An example is given to show the effectiveness of the proposed method.     

Study on the stability of switched dissipative Hamiltonian systems

The hybrid Hamiltonian system is a kind of important nonlinear hybrid systems. Such a system not only plays an important role in the development of hybrid control theory, but also finds many applications in practical control designs for obtaining better control performances. This paper investigates the stability of switched dissipative Hamiltonian systems under arbitrary switching paths. Under a realistic assumption, it is shown that the Hamiltonian functions of all the subsystems can be used as the multiple-Lyapunov functions for the switched dissipative Hamiltonian system. Based on this and using the dissipative Hamiltonian structural properties, this paper then proves that the P-norm of the state of switched dissipative Hamiltonian system converges to zero with the time increasing, and presents two sufficient conditions for the asymptotical stability under arbitrary switching paths. Utilizing these new results, this paper also obtains two useful corollaries for the asymptotical stability of switched nonlinear time-invariant systems. Finally, two examples are studied by using the new results proposed in this paper, and some numerical simulations are carried out to support our new results.     

A Traffic Partition Algorithm for Switched LANs and Its Performance Analysis

An algorithm is proposed which can be used for the topology design of switched LAN with heavy traffic and multi-segments.The main principle of the algorithm is to split the whole traffic to segments as even as possible.The algorithm consists of binary division and ordinary division.When the number of segments equals to powers of 2,binary division is used;ordinary division is based on binary division but suitable to more common cases.Both correctness and time complexity of the algorithm are discussed in detail,and a comparison of the algorithm with the best result is given at the same time.     

Explicit solution to forward and backward stochastic differential equations with state delay and its application to optimal control

This paper is concerned with linear forward–backward stochastic differential equations (FBSDEs) with state delay, the solvability which is much more complex than the case of no delay or input delay caused by the prediction of the backward processes of the future time. To overcome this difficulty, we innovatively establish the non-homogeneous relationship between the backward and forward processes with the help of the corresponding discrete-time system. The main contribution is to give the explicit solution to the FBSDEs with state delay in terms of partial Riccati equations for the first time. The presented results form the basis to solve the challenging problem of linear quadratic optimal control for multiplicative-noise stochastic systems with state delay.     

Stability and boundedness in terms of two measures for nonlinear impulsive control systems

In this paper we study stability and boundedness in terms of two measures for impulsive control systems. By using variational Lyapunov method, a new variational comparison principle and some criteria on stability and boundedness are obtained. An example is presented to illustrate the efficiency of proposed result.     

Asymptotic stability and disturbance attenuation properties for a class of networked control systems

In this paper, stability and disturbance attenuation issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H∞ disturbance attenuation properties are preserved to a desired level. The basic idea in this paper is to formulate such Networked Control System as a discrete-time switched system. Then the NCSs’ stability and performance problems can be reduced to the corresponding problems for switched systems, which have been studied for decades and for which a number of results are available in the literature. The techniques in this paper are based on recent progress in the discrete-time switched systems and piecewise Lyapunov functions.     

Asymptotic stability and disturbance attenuation properties for a class of networked control systems

In this paper, stability and disturbance attenuation issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H∞ disturbance attenuation properties are preserved to a desired level. The basic idea in this paper is to formulate such Networked Control System as a discrete-time switched system. Then the NCSs’ stability and performance problems can be reduced to the corresponding problems for switched systems, which have been studied for decades and for which a number of results are available in the literature. The techniques in this paper are based on recent progress in the discrete-time switched systems and piecewise Lyapunov functions.     

Sampled-data-based LQ control of stochastic linear continuous-time systems

Sampled-data (SD) based linear quadratic (LQ) control problem of stochastic linear continuous-time (LCT) systems is discussed. Two types of systems are involved. One is time-invariant and the other is time-varying. In addition to stability analysis of the closed-loop systems, the index difference between SD-based LQ control and conventional LQ control is investigated. It is shown that when sample time ?T is small, so is the index difference. In addition, the upper bounds of the differences are also presented, which are O(?T2) and O(?T), respectively.