The paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the effectiveness...

Some special selections theorems for stochastic set-valued integrals with respect to the Lebesgue measure are given.

We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors). The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect...

We present the concepts of set-valued stochastic integrals in a plane and prove the existence of a solution to stochastic integral inclusions of the form $z_{s,t}\in {\phi }_{s,t}+{\int }_0^s{\int }_0^t{F}_{u,v}\left(z_{u,v}\right)dudv+{\int }_0^s{\int }_0^t{G}_{u,v}\left(z_{u,v}\right)d{w}_{u,v}$

The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.

This article provides an introduction to Simultaneous Localization And Mapping (SLAM), with the focus on probabilistic SLAM utilizing a feature-based description of the environment. A probabilistic formulation of the SLAM problem is introduced, and a solution based on the Extended Kalman Filter (EKF-SLAM) is shown. Important issues of convergence, consistency, observability, data association and scaling in EKF-SLAM are discussed from both theoretical and practical points of view. Major extensions...

The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.

In this paper we are exploiting some similarities between Markov and Bellman processes and we introduce the main concepts of the paper: comparison of performance measures, and monotonicity of Bellman chains. These concepts are used to establish the main result of this paper dealing with comparison of Bellman chains.

This paper is concerned with the problem of the exponential stability in mean square moment for neutral stochastic systems with mixed delays, which are composed of the retarded one and the neutral one, respectively. Based on an integral inequality, a delay-dependent stability criterion for such systems is obtained in terms of linear matrix inequality (LMI) to ensure a large upper bounds of the neutral delay and the retarded delay by dividing the neutral delay interval into multiple segments. A new...

The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector $(u_1,x_1,...,u_T,x_T)$ on a sample space of $2T$ dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of $x_{\tau }$ given $u_1,x_1,...,u_{\tau -1},x_{\tau -1},u_{\tau }$ are known for $\tau =1,...,T$. Our objective is to determine the remaining conditional probability distributions of $u_{\tau }$ given $u_1,x_1,...,u_{\tau -1},x_{\tau -1}$ such...

A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated...

Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under...

The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.

The definition and some existence theorems for stochastic differential inclusion dZₜ ∈ F(Zₜ)dXₜ, where F and X are set valued stochastic processes, are given.

Existence of strong and weak solutions to stochastic inclusions $x_t-x_s\in {\int }_s^t{F}_{\tau }\left(x_{\tau }\right)d\tau +{\int }_s^t{G}_{\tau }\left(x_{\tau }\right)d{w}_{\tau }+{\int }_s^t{\int }_{{ℝ}^n}{H}_{\tau ,z}\left(x_{\tau }\right)q(d\tau ,dz)$ and $x_t-x_s\in {\int }_s^t{F}_{\tau }\left(x_{\tau }\right)d\tau +{\int }_s^t{G}_{\tau }\left(x_{\tau }\right)d{w}_{\tau }+{\int }_s^t{\int }_{\left|z\right|\le 1}{H}_{\tau ,z}\left(x_{\tau }\right)q(d\tau ,dz)+{\int }_s^t{\int }_{\left|z\right|>1}{H}_{\tau ,z}\left(x_{\tau }\right)p(d\tau ,dz)$, where p and q are certain random measures, is considered.