Optimal parametric synthesis of continuous/discrete stochastic terminal control systems

We propose an efficient numerical algorithm for computer parametric synthesis of linear continuous/discrete stochastic dynamic terminal control systems. The algorithm is based on the application of the method of inverse-conjugate systems and conjugate variables. Translated fromDinamicheskie Sistemy, Vol. 11, 1992.     

Finite-dimensional discrete linear stochastic accelerated-time systems and their application to quadratic stochastic dynamical systems

The limiting behavior of the trajectories {x ⁽ⁿ⁾ } of linear discrete stochastic systems of the form (K, P ^an+b ) _nN , whereK is the standard simplex in ^N ,P: ^{N N} is a linear operator,PK K,a ft,b ,a+b>0, is described. An application to a class of quadratic stochastic dynamical systems is considered.Translated fromMatematicheskie Zametki, Vol. 59, No. 5, pp. 709–718, May, 1996.     

Convergence of discrete approximation for differential linear stochastic complementarity systems

Numerical Algorithms - We provide a new algorithm to generate images of the generalized fuzzy fractal attractors described recently by Oliveira and Strobin. We also provide some new results on the...     

Mixed model identification for linear time‐invariant systems with mixed noises in frequency domain

In this paper, we present a new method for frequency domain identification of discrete linear time‐invariant systems. We take consideration of the case where the output noises are mixed or unknown. In order to deal with this problem, a new mixed model structure is used correspondingly. The augmented Lagrangian method (ALM) is combined in selection of poles for the shifted Cauchy kernels to get solutions to the optimal problem. Simulations show the proposed method can get efficient approximation to the original systems.     

Design of RLS fixed-lag smoother using covariance information in linear discrete stochastic systems

This paper newly designs the recursive least-squares fixed-lag smoother using the covariance information in linear discrete-time stochastic systems. It is assumed that the signal is observed with additive white observation noise and the signal is uncorrelated with the observation noise. The fixed-lag smoother uses the covariance function of the signal in the semi-degenerate kernel form and the variance of the observation noise. The proposed fixed-lag smoother is suitable for the estimations of stationary or non-stationary stochastic signals generally.     

Design of RLS Wiener fixed-lag smoother using covariance information in linear discrete stochastic systems

In this paper, we propose a new design for the recursive least-squares (RLS) Wiener fixed-lag smoother and filter in linear discrete-time wide-sense stationary stochastic systems. It is assumed that the signal is observed with additive white observation noise. The signal is uncorrelated with the observation noise. The estimators require knowledge of the system matrix, the observation matrix and the variance of the state vector. These quantities can be obtained from the auto-covariance function of the signal. In the estimation algorithms, moreover, the variance of the observation noise is assumed to be known, as a priori information.     

Rapid parameter identification of linear time-delay system from noisy frequency domain data

The technique to identify the system parameters thereof has attracted extensive research interest, since knowing the parameters would enable effective system control strategy and accurate response prediction. In this paper, a novel approach is developed to identify the parameters of the linear time-delay differential system by analyzing the complex system response in the frequency domain. Firstly, the complex frequency response of the time-delay system is expressed as a function of physical parameters and time-delay parameters, forming a typical optimization problem. Subsequently, the sensitivities with respect to the unknown parameters are derived. A novel sensitivity-based algorithm is adopted in the identification procedure. Trust-region constraint is implemented and hence tackled by Tikhonov regularization, which effectively enhances the efficiency of the algorithm. The feasibility and robustness of the identification procedure are evaluated by identifying the parameters of two numerical time-delay systems and an experimental case.     

On discrete stochastic bilinear systems stability

Mean square stability conditions for discrete-time bilinear systems operating in a stochastic environment are given in this paper. Only independence and wide sense stationarity are required for the second order disturbance sequences involved, thus dismissing ergodicity and zero-mean assumptions. Stochastic stability conditions are derived by using a deterministic stability result for a class of separable nonlinear dynamical systems evolving in a Banach space.     

On the regularity of discrete linear systems

In this paper we have introduced a new regularity coefficient of time varying discrete linear system. On the base of this coefficient we have characterized the regularity of homogeneous discrete time varying linear systems by nonhomogeneous ones. Moreover we provided bounds for the regularity coefficient in terms of the existing in the literature regularity coefficients.     

Perturbed linear stochastic dynamical systems

This paper is concerned with a class of stochastic differential equations which arises by adding a nonlinear term involving a small parameter δ to the drift coefficient of a linear stochastic system. First, a stochastic representation of the solutions of a certain class of Cauchy problems is studied. Second, a finite time expansion in powers of δ of the expectations of functions is established. Third, the corresponding ergodic expansions are sought with additional assumptions regarding the existence of a unique ergodic measure.     

Base duality theorem for stochastic and parametric linear programming

Summary Consider the primal and dual bases of a basic optimal solution to a linear-programming problem with a given set of parameters (coefficients of objective function, technology matrix, and restriction vector). For brevity, call those bases themselves optimal. If the parameters are subject to variation (controlled or uncontrolled according as one deals with parametric or stochastic programming, respectively) the initial bases are optimal throughout certain subregions of parameter space, termed optimality regions of the respective bases.It is shown that the optimality regions of primal and dual bases are identical.

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Zusammenfassung Betrachtet werden die Primär- und Dualbasen einer optimalen Basislösung eines linearen Programms mit einer gegebenen Parametermenge (d. h. Koeffizienten der Zielfunktion, Koeffizienten der Matrix und des Beschränkungsvektors). Der Kürze halber seien diese Basen selbst optimal genannt. Die Anfangsbasen bleiben optimal innerhalb gewisser Teilbereiche des Parameterraumes, bezeichnet als Optimalitätsbereiche der jeweiligen Basen, wenn die Parameter gewissen Variationen unterliegen (vorgegeben oder nicht, je nachdem, ob es sich um parametrisches oder stochastisches Programmieren handelt).Es wird gezeigt, daß die Optimalitätsbereiche der Primär- und Dualbasen übereinstimmen.

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This research has been carried out in association with, and with partial support from the National Science Foundation, Project Nr. 401-04-07 at Iowa State University.     

Stability estimates of linear stochastic systems

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 9, pp. 1267–1273, September, 1989.     

On the spectrum of discrete time-varying linear systems

In this paper, we investigate the influence of small perturbations of the coefficients of discrete time-varying linear systems on the Lyapunov exponents. For that purpose we introduce the concepts of central exponents of the system and we show that these exponents describe the possible changes in the Lyapunov exponents under small perturbations. Finally, we present several formulas for the central exponents in terms of the transition matrix of the system and the so-called upper sequences. The results are illustrated by numerical examples.     

On the exponential exponents of discrete linear systems

In this paper we introduce the concepts of exponential exponents of discrete linear time varying systems. It is shown that these exponents describe the possible changes in the Lyapunov exponents under perturbation decreasing at infinity at exponential rate. Finally we present formulas for the exponential exponents in terms of the transition matrix of the system.     

On the Perron exponents of discrete linear systems

This note studies properties of Perron or lower Lyapunov exponents for discrete time varying system. It is shown that for diagonal system of order s there are at most 2^s-1 lower Lyapunov exponents. By example it is demonstrated that in non-diagonal case it is possible to have arbitrarily many different Perron exponents. Finally it is shown that the exponent is almost everywhere equal to the lower Lyapunov exponent of the matrices coefficient sequence.     

Stability of linear systems with time-varying delays: A direct frequency domain approach

The stability of linear systems with uncertain bounded time-varying delays (without any constraints on the delay derivatives) is analyzed. It is assumed that the system is stable for some known constant values of the delays (but may be unstable for zero delay values). The existing (Lyapunov-based) stability methods are restricted to the case of a single non-zero constant delay value, and lead to complicated and restrictive results. In the present note for the first time a stability criterion is derived in the general multiple delay case without any constraints on the delay derivative. The simple sufficient stability condition is given in terms of the system matrices and the lengths of the delay segments. Different from the existing frequency domain methods which usually apply the small gain theorem, the suggested approach is based on the direct application of the Laplace transform to the transformed system and on the bounding technique in _L2$L_2$. A numerical example illustrates the efficiency of the method.     

Spectral theory of discrete linear Hamiltonian systems

This paper is concerned with spectral problems for a class of discrete linear Hamiltonian systems with self-adjoint boundary conditions, where the existence and uniqueness of solutions of initial value problems may not hold. A suitable admissible function space and a difference operator are constructed so that the operator is self-adjoint in the space. Then a series of spectral results are obtained: the reality of eigenvalues, the completeness of the orthogonal normalized eigenfunction system, Rayleigh's principle, the minimax theorem and the dual orthogonality. Especially, the number of eigenvalues including multiplicities and the number of linearly independent eigenfunctions are calculated.