Optimal feedback control problems for a semi-linear neutral retarded integro-differential system

Abstract

This article considers the optimal and time optimal feedback control problems for a semi-linear neutral retarded integro-differential system. The existence of mild solutions and feasible pairs for the considered system is studied by applying theory of resolvent operators for linear neutral integro-differential evolution systems, fractional powers of operators and Schauder fixed point theorem. Then the Lagrange optimal feedback control problem for the system is investigated via limit arguments under some suitable assumptions. The time optimal feedback control problem is proposed and discussed deliberately here as well. An example is presented in the end to illustrate the obtained results.

Keywords:

• Neutral integro-differential system
• resolvent operator
• fractional power operator
• optimal feedback control

AMS:

• 34K30
• 34K40
• 45K05
• 49J20
• 93B52

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work is supported by National Natural Science Foundation of China (No. 12001146), Fundamental Research Funds for the Provincial Universities of Zhejiang (No. GK229909299001-029), Zhejiang Provincial National Natural Science Foundation of China (No. LQ21A010006), Science and Technology Commission of Shanghai Municipality (No. 22DZ2229014).