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<p><i>The problem of optimal impulse stabilization is studied for an autonomous linear delay differential system. A method for constructing approximate optimal impulse stabilizing controls is proposed. The approach uses a formulation in the function state space, together with Krasovskii’s approximation of the delayed system by ordinary differential equations. Generalized controls are constructed via an auxiliary nonimpulse stabilization problem for a linear autonomous system of ordinary differential equations. Although the solution of the matrix Riccati equation for this auxiliary problem is high-dimensional, a system of algebraic equations is derived that directly yields the coefficients of the optimal control.</i></p>

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CONSTRUCTION OF APPROXIMATIONS OF OPTIMAL IMPULSE STABILIZING CONTROL FOR SYSTEMS WITH DELAY

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Yuriy Dolgii,
  • Alexander Sesekin

摘要

The problem of optimal impulse stabilization is studied for an autonomous linear delay differential system. A method for constructing approximate optimal impulse stabilizing controls is proposed. The approach uses a formulation in the function state space, together with Krasovskii’s approximation of the delayed system by ordinary differential equations. Generalized controls are constructed via an auxiliary nonimpulse stabilization problem for a linear autonomous system of ordinary differential equations. Although the solution of the matrix Riccati equation for this auxiliary problem is high-dimensional, a system of algebraic equations is derived that directly yields the coefficients of the optimal control.