Computation of the structural invariants of linear multivariable systems with an extended version of the program

The structural invariants like finite and infinite zeros play an important role in many problems in the analysis of linear systems. In [1] Emami-Naeini and Van Dooren presented the program for computing the finite zeros of a linear system, which in the author's opinion is at present the best commonly available program for this problem. Such a program does not exist for computing the other structural invariants, like the infinite zeros and the Kronecker indices. This paper presents an extended version of the program , which computes the finite zeros as well as the other structural invariants.     

Computation of the structural invariants of linear multivariable systems with an extended version of the program zeros

The structural invariants like finite and infinite zeros play an important role in many problems in the analysis of linear systems. In [1] Emami-Naeini and Van Dooren presented the program zeros for computing the finite zeros of a linear system, which in the author's opinion is at present the best commonly available program for this problem. Such a program does not exist for computing the other structural invariants, like the infinite zeros and the Kronecker indices. This paper presents an extended version of the program zeros, which computes the finite zeros as well as the other structural invariants.     

On controllability and observability for a class of impulsive systems

Many dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes. These complex dynamic behaviors can be modeled by impulsive differential systems. This paper studies the controllability and observability for a class of time-varying impulsive control systems. Several sufficient and necessary conditions for state controllability and state observability of such systems are established and the corresponding criteria for time-invariant impulsive control systems are also obtained. Meanwhile, several new results associated with variation of parameters for time-varying impulsive control systems are derived.     

On parametrizations for the minimal partial realization problem

The paper considers parametrizations for minimal partial realizations of a finite sequence of Markov parameters. First it is shown that all minimal partial realizations have the same set of input and output Kronecker indices. A parametrization is obtained formulated in terms of a minimal set of extension entries. Then an I/O canonical form is used as a parametrization for the set of minimal partial realizations. It is shown that this allows to define the invariants of the problem. Moreover, the I/O canonical form is shown to contain a set of parameters that can be chosen such that any minimal partial realization can be represented.     

On the stability of a general polynomial in the space of Markov parameters

Markov parameters and the associated stability criterion were first introduced for continuous-time real polynomials. Recently, robust stability of such polynomials was considered in Markov parameters space, where efficient robust stability tests were obtained based on the Markov theorem. This has motivated the authors to extend the above idea to more general types of polynomials, and develop Markov parameters and the associated stability criterion for complex continuous-time as well as real and complex discrete-time polynomials. Moreover, for each polynomial type, we present compact relations in order to recover the coefficients of a polynomial corresponding to a given set of Markov parameters. The stability results presented here may be useful for 1-D and 2-D filtering and control applications.     

Stability of diffusion stochastic functional differential equations with Markov parameters

The paper justifies the second Lyapunov method for diffusion stochastic functional differential equations with Markov parameters, which generalize stochastic diffusion equations without aftereffect. Analogs of Lyapunov stability theorems, which generalize the results for systems with finite aftereffect, are proved. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 74–88, January–February 2008.     

On the detectability and observability of discrete-time Markov jump linear systems

This paper presents a new detectability concept for discrete-time Markov jump linear systems with finite Markov state, which generalizes the MS-detectability concept found in the literature. The new sense of detectability can similarly assure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is a stabilizing solution. In addition, the paper introduces a related observability concept that also generalizes previous concepts. A test for detectability based on a coupled matrix equation is derived from the definition, and a test for observability is presented, which can be performed in a finite number of steps. The results are illustrated by examples, including one that shows that a system may be detectable in the new sense but not in the MS sense.     

Transition to canonical principal parameters on minimal surfaces

Ganchev has recently proposed a new approach to minimal surfaces. Introducing canonical principal parameters for these surfaces, he has proved that the normal curvature determines the surface up to its position in the space. Here we prove a theorem that permits to obtain equations of a minimal surface in canonical principal parameters and we make some applications on parametric polynomial minimal surfaces. Thus we show that Ganchev's approach implies an effective method to prove the coincidence of two minimal surfaces given in isothermal coordinates by different parametric equations.     

Vertex vulnerability parameters of Kronecker products of complete graphs

Let G₁ and G₂ be two graphs. The Kronecker product G₁×G₂ of G₁ and G₂ has vertex set V(G₁×G₂)=V(G₁)×V(G₂) and edge set and v₁v₂∈E(G₂)}. In this paper, we determine some vertex vulnerability parameters of the Kronecker product of complete graphs Km×Kn for n?m?2 and n?3.     

Hamiltonian realizations of nonlinear adjoint operators

This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of controllability, observability and Hankel operators are derived from this analysis. The state-space realizations of such adjoint operators provide new insights on singular value analysis and duality issues in nonlinear control systems theory. Finally, a duality between the controllability and observability energy functions is proved.     

Controllability and observability of Boolean control networks

The controllability and observability of Boolean control networks are investigated. After a brief review on converting a logic dynamics to a discrete-time linear dynamics with a transition matrix, some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix. Based on the discrete-time dynamics, the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely. Then the problem of observability is also solved by giving necessary and sufficient conditions.     

On the stabilization of controllable and observable systems by an output feedback law

For control systems which can be locally stabilized in small time by means of a dynamic periodic time-varyingstate feedback law, we give a sufficient condition on Lie derivatives of the output for local stabilization in small time by means of a dynamic periodic time-varyingoutput feedback law. If the system is analytic our sufficient condition is also necessary.     

Observability of real analytic vector fields on compact manifolds

A smooth vector field on a smooth compact manifold is said to be observable if there exists a smooth output function that distinguishes initial states on any time interval. In this paper we prove that a real analytic vector field on a compact manifold is observable if and only if its singularities are isolated. The result remains true for functions. In this case one has to assume that the set of singular points is (p − 1)-dimensional.     

Identification of Boolean control networks

In this paper the identification of Boolean control networks is addressed. First, necessary and sufficient conditions are obtained for the identification of state equation from input-state data. Then a necessary and sufficient condition for a controllable Boolean network to be observable is presented. Based on these two results, a necessary and sufficient condition for the identification from input–output data is achieved. To practically identify the model, a numerical algorithm is proposed. Two particular cases: (i) identification of systems with a known network graph; (ii) identification of a higher order Boolean network, are also investigated. Finally, the approximate identification for large size networks is explored.     

A minimal representation of Markov arrival processes and a moments matching method

The paper investigates the problem of minimal representation of Markov arrival processes of order n (MAP(n)). The minimal representation of MAPs is crucial for developing effective fitting methods. It seems that all existing MAP fitting methods are based on the , representation which is known to be redundant. We present the minimal number of parameters to define a MAP(n) and provide a numerical moments-matching method based on a minimal representation.

The discussion starts with a characterization of phase type (PH) distributions and then the analysis of MAPs follows a similar pattern. This characterization contains essential results on the identity of stationary behaviour of MAPs and on the number of parameters required to describe the stationary behaviour.

The proposed moments matching method is also applicable for PH distributions. In this case it is a unique method that fits a general PH distribution of order n based on 2n−1 parameters.     

可分解马尔可夫网络参数学习中的噪声平滑

对于存在噪声的可分解马尔可夫网络参数学习.目前可通过调整可分解马尔可夫网络的结构来增强其抗噪声能力,但调整后的结构往往会降低网络的有效性和可靠性,而且不能从源头上减少噪声对参数的影响.针对该问题,首先建立基于可分解马尔可夫网络理论的邻域最优预测;然后以变量为基本单位,使用预测值平滑噪声.实验结果显示,使用平滑后的数据进行参数学习,其可靠性能够得到显著的改进.     

Robust Control of Uncertain Markov Jump Singularly Perturbed Systems

In this paper,we study the robust control for uncertain Markov jump linear singularly perturbed systems(MJLSPS),whose transition probability matrix is unknown.An improved heuris- tic algorithm is proposed to solve the nonlinear matrix inequalities.The results of this paper can apply not only to standard,but also to nonstandard MJLSPS.Moreover,the proposed approach is independent of the perturbation parameter and therefore avoids the ill-conditioned numerical prob- lems.     

马尔可夫及隐马尔可夫模型在数据挖掘中的应用

随着用户对于数据挖掘的精确度与准确度要求的日益提高,马尔可夫模型与隐马尔可夫模型被广泛用于数据挖掘领域。本文阐述了马尔可夫模型和隐马尔可夫模型数据挖掘领域的应用,以及隐马尔可夫模型可解决的问题,以供其他研究者借鉴。