Problems of Optimal Control for a Class of Linear and Nonlinear Systems of the Economic Model of a Cluster

Zainelkhriet Murzabekov, Marek Miłosz, Kamshat Tussupova, Gulbanu Mirzakhmedova

2020

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DOI 10.1142/s2196888820500062

Data confidence 70 medium

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Abstract

For the mathematical model of a three-sector economic cluster, the problem of optimal control with fixed ends of trajectories is considered. An algorithm for solving the optimal control problem for a system with a quadratic functional is proposed. Control is defined on the basis of the principle of feedback. The problem is solved using the Lagrange multipliers of a special form, which makes it possible to find a synthesizing control. The problem of optimal stabilization for a class of nonlinear systems with coefficients that depend on the state of the control object is considered. The results obtained for nonlinear systems are used in the construction of control parameters for a three-sector economic cluster on an infinite time interval.