On mathematical models and the role of the mathematics in knowledge of reality
On minimal realizations and minimal partial realizations of linear time-invariant systems subject to point incommensurate delays.
On modelling dynamic systems excited by the Dirac function
On modelling of large variable systems of higher degree by means of language systems
On monotonicity of solutions of discrete-time nonnegative and compartmental dynamical systems.
On motions with bursting characters for Lagrangian mechanical systems with a scalar control. I. Existence of a wide class of Lagrangian systems capable of motions with bursting characters
In this Note (which will be followed by a second) we consider a Lagrangian system (possibly without any Lagrangian function) referred to coordinates , , with to be used as a control, and precisely to add to a frictionless constraint of the type . Let 's (frictionless) constraints be represented by the manifold generally moving in Hertz's space. We also consider an instant (to be used for certain limit discontinuity-properties), a point of , a value for 's momentum conjugate...
On nearly selfoptimizing strategies for multiarmed bandit problems with controlled arms
Two kinds of strategies for a multiarmed Markov bandit problem with controlled arms are considered: a strategy with forcing and a strategy with randomization. The choice of arm and control function in both cases is based on the current value of the average cost per unit time functional. Some simulation results are also presented.
On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance
We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum...
On network models and the symbolic solution of network equations
This paper gives an overview of the formulation and solution of network equations, with emphasis on the historical development of this area. Networks are mathematical models. The three ingredients of network descriptions are discussed. It is shown how the network equations of one-dimensional multi-port networks can be formulated and solved symbolically. If necessary, the network graph is modified so as to obtain an admittance representation for all kinds of multi-ports. N-dimensional networks are...
On nonlinear equivalence and backstepping observer
An observer design based on backstepping approach for a class of state affine systems is proposed. This class of nonlinear systems is determined via a constructive algorithm applied to a general nonlinear Multi Input–Multi Output systems. Some examples are given in order to illustrate the proposed methodology.
On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces
In this paper we study a general concept of nonuniform exponential dichotomy in mean square for stochastic skew-evolution semiflows in Hilbert spaces. We obtain a variant for the stochastic case of some well-known results, of the deterministic case, due to R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3(1972), 428–445. Our approach is based on the extension of some techniques used in the deterministic case for the study of asymptotic behavior...
On numerical solution of optimal control problems with nonsmooth objectives: Application to economic models
On obtaining the time-invariant associated system of a periodic system through system equivalence
On one algorithm for solving the problem of source function reconstruction
In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations...
On one approach to local surface smoothing
A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.
On one method of analysis of linear systems with random stationary coefficients
On optimal control of systems with interface side conditions
On optimal observability of linear systems with infinite-dimensional states
On optimal stopping of inhomogeneous standard Markov processes.
On option pricing in the multidimensional Cox-Ross-Rubinstein model
Option pricing in the multidimensional case, i.e. when the contingent claim paid at maturity depends on a number of risky assets, is considered. It is assumed that the prices of the risky assets are in discrete time subject to binomial disturbances. Two approaches to option pricing are studied: geometric and analytic. A numerical example is also given.