ON THE CONSTRUCTION OF PROGRAM CONTROL IN THE PROBLEM ON ATTAINABLE VALUES OF ON-TARGET FUNCTIONALS FOR DYNAMIC ECONOMIC MODELS WITH DISCRETE MEMORY

Main constructions and relationships for program control actions are proposed as applied to the problem on attainable prescribed values of on-target functionals for continuous-discrete dynamic economic mathematical model with discrete memory under given polyhedral constrains with respect to control. The form of on-target functionals covers widely used kinds of functionals such as multipoint, integral ones and linear combinations of those. The feature of the control system under consideration is the presence of two kinds of the state variables, namely, a part of them depends on continues time, whereas others depend on discrete time. Aftereffect of the system is defined by its discrete memory located at a given collection of instants. The results are obtained on the basis of the principal statements from the general theory of continuous-discrete systems. In the constructive part of the research, the basic idea is the reduction of the original problem to a variant of the general moment problem with taking into account pointwise polyhedral constraints on controls. This allows us to construct estimates of the attainability set and to build program controls on the base of solutions to a series of linear programming problems. Every such a problem provides us with values of the program control on a partial segment. All these values are used while constructing the program control as a whole. The mentioned procedures use in essence the Cauchy operator to the hybrid system under consideration. The property of this operator are studied in the cited previous papers. The obtained results constitute an instrumental basis for efficient studying and constructing solutions to urgent applied problems with constrained resources of control.

On a class of linear continuous-discrete systems with discrete memory

A class of linear functional differential systems with continuous and discrete times and discrete memory is considered. An explicit representation of the principal components to the general solution representation such as the fundamental matrix and the Cauchy operator is derived. The obtained representation is given in terms of the system parameters and opens a way towards efficient studying general linear boundary value problems and control problems with respect to a fixed collection of linear on-target functionals. In the study of the problems mentioned above outside the class under consideration, the systems with discrete memory can be employed as model or approximating ones. This can be useful as applied to systems with aftereffect under studying rough properties that hold under small perturbations of the parameters.

An improved artificial bee colony algorithm for robust design of power system stabilizers

Purpose Low-frequency oscillations of 0.1 to 3 Hz are prejudicial to the power system stability. Within this context, this study aims to present an improved artificial bee colony (ABC)-based algorithm for optimal setting of multimachine power system stabilizers (PSSs) under several loading conditions simultaneously. Design/methodology/approach The proposed approach symbolized by GCABC incorporates the grenade explosion technique and the Cauchy operator in the employed bee and onlooker bee phases to avoid random search. The parameters of the grenade explosion method and Cauchy operator based ABC(GCABC)-based PSSs (GCABC-PSSs) are tuned to place all undamped and lightly damped electromechanical modes in a prespecified zone in the s-plan. Findings Simulation results based on eigenvalue analysis and nonlinear time-domain simulation show the potential and the dominance of the proposed controllers GCABC-PSSs in the improvement of the system stability under several disturbances and large set of operating points compared with the classical ABC method and genetic algorithm-based PSSs. Originality/value The novelty of the study is to efficiently implement a new optimization method called GCABC for an optimum design of PSSs. The design problem is formulated as a multi-objective optimization problem. In addition, all PSS parameters have been included in the space research.