An optimal control model for a system of degenerate parabolic integro-differential equations

An initial-boundary-value problem for a system of degenerate parabolic integro-differential equations is considered. The sufficient conditions for the existence and uniqueness of its generalized solution and for the existence of at least one optimal control for a given performance functional are obtained. A stable numerical solution to the initial-boundary-value problem is derived for a locally one-dimensional case and conditions are formulated for constructing a stable numerical algorithm of the optimal control problem on a class of piecewise-smooth control functions. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 90–102, November–December 2007.     

Genomic control of agent morphogenesis in a physically correct virtual environment

Based on the analysis of the morphogenesis process of real biological organisms, the basic principles are formulated for the simulation of genomic control of the morphogenesis of a virtual agent in a physically correct environment. A model of the genome of a compound agent’s body composed of different functional subsystems is developed. A timing algorithm for genetically conditioned processes of regeneration and division of agent’s microcells is developed. The problem of forming agents with a morphology that is locally optimal for a given environment is formulated as a multi-generation optimization problem in a genetic algorithm. The fitness function is defined as the life duration of agents. Constraints are connected with the physical correctness of an environment and an energy deficit in the environment. Agent genomes are considered as chromosomes in the genetic algorithm. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 42–54, March–April 2008.     

Solving Optimal Control Problems on the Class of Step Functions

Linear optimal control problems with multipoint non-separated conditions with a quadratic performance criterion of control are analyzed. An approach with a violation of intermediate conditions is proposed. The original problem is reduced to the classical quadratic programming problem with the dimension determined by the number of intermediate points. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 153–162, July–August 2005.     

Some Continuous Models of Inventory Control

The problem of optimal control of a manufacturing process is investigated. The dynamics of the process is described by a stochastic differential equation. Two methods of solution of this problem are considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 175–178, May–June 2005.     

On the asymptotics of solution of one problem of optimal control of the small-parameter parabolic equation

For the singularly perturbed parabolic problem, a regularized asymptotics of the solution of the problem of optimal control was constructed. The solution asymptotics involves parabolic boundary-layer functions obeying a special function called the “complementary probability integral.”     

Asymptotic efficiency of kernel support vector machines (SVM)

The paper analyzes the asymptotic properties of Vapnik’s SVM-estimates of a regression function as the size of the training sample tends to infinity. The estimation problem is considered as infinite-dimensional minimization of a regularized empirical risk functional in a reproducing kernel Hilbert space. The rate of convergence of the risk functional on SVM-estimates to its minimum value is established. The sufficient conditions for the uniform convergence of SVM-estimates to a true regression function with unit probability are given. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 81–97, July–August 2009     

Mathematical modeling and optimization of intratumor drug transport

A pseudohyperbolic problem of optimal control of intratumoral drug distribution is formulated. It takes into account the heterogeneity of tumor tissues and effects of convection diffusion in a fissured porous medium. A mathematical model constructed and the corresponding optimal control problem are shown to be correct. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 147–154, November–December 2007.     

The FEM optimization of active vibration control in structures by solving the corresponding two-point-boundary-value problem

An algorithm for solving optimal active vibration control problems by the finite element method (FEM) is presented. The optimality equations for the problem are derived from Pontryagin’s principle in the form of a set of the fourth order ordinary differential equations that, together with the initial and final boundary conditions, constitute the boundary value problem in the time domain, which in control is referred to as a two-point-boundary-value problem. These equations decouple in the modal space and can be solved by the FEM technique. An analogy between the optimality equations and the governing equations for a set of certain static beams permits obtaining numerical solutions to the optimal control problem with the help of standard ‘structural’ FEM software. The optimal action of actuators is automatically calculated by applying the independent modal space control concept. The structure’s response to actuation forces is also determined and can independently be verified for spillover effects. As an illustration, the algorithm is used for the analysis of optimal action of actuators to attenuate vibrations of an elastic fin.     

Control–structural design optimization for vibration of piezoelectric intelligent truss structures

Based on the design sensitivity analysis for structural dynamics in time domain, an integrated control–structural design optimization method is proposed to the vibration control of piezoelectric intelligent truss structure. In this investigation, the objective function and constraint functions include not only the conventional design indexes of structure but also the vibration control indexes and the feedback control variables. The structural design variables are optimized simultaneously with the vibration control system. The sensitivity relations for the control–structure optimization model are derived by using a new method, and the sequential linear programming algorithm is used to solve this kind of optimization problem. The numerical examples given in the paper demonstrate the effectiveness of methods and the program.     

Optimal strategies for an inventory system with cost functions of general form

For an inventory system with a continuous compact phase state and control set, the existence of the optimal (S, s)-policy is proved and an algorithm for determination of this policy based on stochastic approximation is presented. The cost functions are monotone, continuous, and of a rather general form. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 106–123, July–August, 1999.     

Realization of a bounded feedback in a nonlinear control problem

We substantiate a method for design of a limited feedback to control a system whose mathematical model includes a nonlinear state function. Designing such a feedback is based on a positional solution of auxiliary optimal control problems which provides the transition from the vicinity of one equilibrium state to the vicinity of a new equilibrium state and stabilization of the system in the new state. Preassigned additional constrains on the trajectory of the control system are satisfied. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 108–116, January–February 2009.     

Active identification and control given bounded noise (disturbances)

Problems of active identification and control with bounded disturbances are considered for two classes of plants: dynamic plants and those without memory. Performance criteria of set-membership identification are proposed for each of the classes. For controlled plants without memory, an algorithm of optimal design of experiments is developed which provides a minimum of performance criterion of set-membership identification. Only a suboptimal solution of the problem is obtained for the class of dynamic systems. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 147–157, January–February, 2000. This work has been carried out with support from the State Fund for Fundamental Studies (Project 1.4/370) and Grant FWF (Austria) (Project 13706/MAT).     

Synthesis of optimal control of dynamic systems with infinite aftereffect,a small parameter,and poisson perturbations

A methodology is obtained that makes it possible to synthesize an optimal control for stochastic systems of functional-differential equations with the entire prehistory and a small parameter and takes into account continuous Wiener-type and discontinuous Poisson-type perturbations. It is proved that the sought-for control can be found as an optimal control of some auxiliary problem. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 181–186, May–June 2007.     

A model of optimal control over a nonlinear multidimensional innovation diffusion process

A model of competitive innovation diffusion is considered. The model is based on the Lotka-Volterra system and an initial-boundary problem for a system of quasilinear parabolic equations. The maximum principle is proved for the problem of diffusion of two competitive innovations, and sufficient conditions of existence of optimum control are obtained for the system. A numerical algorithm is constructed for solving optimum control problems, and numerical results for a model example are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 120–133, July–August 2008.     

Optimization of advertising activity of an insurance company and an algorithm for its solution

The problem of optimization of advertising activity of an insurance company consisting of n divisions (branches) is considered. For each branch, an optimal control is found in a closed form (an analytic solution) under constraints on advertising expenses. The quality of behavior of optimal controls and phase coordinates is illustrated by a numerical experiment. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 159–165, March–April 2009.     

Scenarios of optimal control of transregional migration processes under risk

Scenarios of migration are considered as applied to the problem of optimal control of transregional migration with zero risk of overpopulation or insufficient population and migration with obtaining the minimum of the objective functional and minimizing risk. Numerical algorithms for the scenarios considered are developed. The algorithms are implemented in an applied geoinformation decision-support system for control of transregional migration of population. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 16–33, January–February 2007.     

Moving Mesh Finite Element Methods for an Optimal Control Problem for the Advection-Diffusion Equation

An optimal control problem for the advection-diffusion equation is studied using a Lagrangian-moving mesh finite element method. The weak formulation of the model advection–diffusion equation is based on Lagrangian coordinates, and semi–discrete (in space) error estimates are derived under minimal regularity assumptions. In addition, using these estimates and Brezzi-Rappaz-Raviart theory, symmetric error estimates for the optimality system are derived. The results also apply for advection dominated problems     

Equivalent optimal compensation problem in the delta domain for systems with white stochastic parameters

The equivalent representation in the delta domain of the digital optimal compensation problem is provided and computed in this article. This problem concerns finding digital optimal full and reduced-order output feedback controllers for linear time-varying and time-invariant systems with white stochastic parameters. It can subsequently be solved in the delta domain using the strengthened optimal projection equations that we recently formulated in this domain as well. If the sampling rate becomes high, stating and solving the problem in the delta domain becomes necessary because the conventional discrete-time problem formulation and solution become ill-conditioned. In this article, by means of several numerical examples and compensator implementations, we demonstrate this phenomenon. To compute and quantify the improved performance when the sampling rate becomes high, a new delta-domain algorithm is developed. This algorithm computes the performance of arbitrary digital compensators for linear systems with white stochastic parameters. The principle application concerns nonconservative robust digital perturbation feedback control of nonlinear systems with high sampling rates.     

The worst-case analysis of the Garey–Johnson algorithm

The Garey–Johnson algorithm is a well known polynomial-time algorithm constructing an optimal schedule for the maximum lateness problem with unit execution time tasks, two parallel identical processors, precedence constraints and release times. The paper is concerned with the worst-case analysis of a generalization of the Garey–Johnson algorithm to the case of arbitrary number of processors. In contrast to other algorithms for the maximum lateness problem, the tight performance guarantee for the even number of processors differs from the tight performance guarantee for the odd number of processors.     

Simulation of Diversified Economic Growth

An optimal growth algorithm is developed for a diversified economic growth model with piecewise-linear production functions. Numerical results are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 147–155, September–October 2005.