Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
43
5
2011
Discrete Optimal Control of Descriptor Systems with Variable Parameters
1-9
10.1615/JAutomatInfScien.v43.i5.10
Mikhail F.
Bondarenko
Kharkov National University of Radioelectronics, Ukraine
Larisa A.
Vlasenko
V. N. Karazin Kharkov National University, Ukraine
Anatoliy G.
Rutkas
Kharkov National University of Radio and Electronics, Kharkov
lumped and distributed control systems
discrete time
linear statement
nontrivial kernels
conditions of unique solvability
sets of initial vectors and solutions
the problem of optimal control with quadratic performance criterion
We consider lumped and distributed control systems with discrete time, which dynamics is described by linear relations with unbounded operator coefficients in the Hilbert spaces. The systems are of descriptor type in the sense that in their relations operators at unknown vectors can have nontrivial kernels. Conditions of unique solvability are established, sets of initial vectors and solutions are described, the problem of optimal control with quadratic performance criterion was studied.
Analysis of the Conditions of Controllability and Stabilizability of Nonlinear Dynamical Systems
10-22
10.1615/JAutomatInfScien.v43.i5.20
Sergey M.
Onishchenko
Institute of Mathematics of National Academy of Sciences of Ukraine, Kiev
nonlinear dynamic systems
relationship between the controllability and stabilizability
controllability as a sufficient condition of the stabilizability
stabilizability and Lyapunov functions
The relationship between the controllability and stabilizability in nonlinear systems of an arbitrary order is discussed.
Geometrical Model of Control System Presented on Complex Error Surface
23-39
10.1615/JAutomatInfScien.v43.i5.30
Oleg N.
Agamalov
Tashlykskaya .Hydroelectric Accumulative Station, Yuzhnoukrainsk, Nikolaev region, Ukraine
automatic control system
complex error
geodetic curve
stability condition
Consideration has been given to a mathematical model based on calculating a complex error allowing one to design an optimal control law of an object as an equation of the geodetic curve on a complex error surface. The stability condition of automatic control system on the complex error surface (space) has been determined.
Some Approaches to Regularization of Nonlinear Optimization Problems
40-51
10.1615/JAutomatInfScien.v43.i5.40
Yuriy P.
Laptin
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
Tamara A.
Bardadym
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
convex optimization problems with constraints
transformation
equivalent problems with better numerical properties
conic approximations
conic prolongation of objective functions
problem of convex programming without constraints
efficient procedures
peculiarities of software
We consider ways of transformation of convex optimization problems with constraints to equivalent problems with better computational properties. Sufficient attention is paid to use of conic approximations and conic prolongation of objective functions from admissible domain of optimization problem on the whole space of variables. The problem of convex programming without constraints (regularized problem), which solution coincides with solution of the initial problem, is the result of usage of the suggested approach. The considered approaches have special significance when the objective function is not defined outside the admissible domain. We suggested efficient procedures for calculation of auxiliary functions, consider peculiarities of software support of algorithms, results of computational experiments.
Iterative Method for Solving Combinatorial Optimization Problems of the Game-type on Arrangements
52-63
10.1615/JAutomatInfScien.v43.i5.50
Oleg A.
Yemets
Poltava University of Economics and Trade, Poltava
Elena V.
Olkhovskaja
Poltava University of Economics and Trade, Ukraine
combinatorial optimization of the game-type on arrangements
iterative method
quadratic dependence of computation time on the dimension of the problem
numerical experiments
A new class of problems — the problems of combinatorial optimization of the game-type on arrangements is considered. In these problems, the strategies of one of the players are superimposed with combinatorial constraints. The iterative method for solving such problems is proposed. Numerical experiments have shown a quadratic dependence of computation time on the dimension of the problem and solution convergence.
Optimal Control Problems of Sources in Distributed Systems on the Classes of Impulsive, Piecewise Constant and Heaviside Functions
64-82
10.1615/JAutomatInfScien.v43.i5.60
Kamil Rajab ogly
Aida-zade
Institute of Cybernetics of National Academy of Sciences of Azerbaijan, Baku (Azerbaijan)
Yegana R.
Ashrafova
Institute of Cybernetics of National Academy of Sciences of Azerbaijan, Baku
optimal control problems
distributed systems
optimality condition
piecewise constant function
gradient of functional
Problems of optimal control of movable lumped sources in distributed systems when controls are determined by impulsive piecewise constant and Heaviside functions are considered. The optimal control problems are investigated for various cases according to the position of the sources. The necessary conditions of optimality are obtained with respect to all considered problems of optimal control on these classes, which consists in deriving constructive analytical formulas for the gradient of a functional in the space of optimized parameters. The results of some numerical experiments are also given.