Accession Number:

AD0753675

Title:

Maximum Principle for Systems with Delay Depending on State, Control and Time,

Descriptive Note:

Corporate Author:

BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s):

• Manitius,Andrzej
• Fijalkowski,Stanislaw

Report Date:

1972-12-08

Pagination or Media Count:

52.0

Abstract:

Optimal control problems for systems described by differential equations with a delayed argument depending on state, control and time are considered. Unlike previous work in this area, there is no restrictive assumption on the monotonicity of the delayed argument with respect to time. The class of admissible controls consists of bounded measurable functions. The terminal point of the trajectory is assumed to be free or constrained by an inequality. Necessary conditions for optimality in the form of a maximum principle are derived via Gabasovs method. The problem of discontinuity of the adjoint variables, as well as other essential features of the maximum principle, are discussed. An example given in the Appendix shows that the optimal behavior of the delay need not necessarily consist in zeroing the delay on the whole time interval. Author

Descriptors:

• (*ADAPTIVE CONTROL SYSTEMS
• MATHEMATICAL MODELS)
• PARTIAL DIFFERENTIAL EQUATIONS
• INEQUALITIES
• MEASURE THEORY
• MATRICES(MATHEMATICS)
• TRAJECTORIES
• INTEGRAL EQUATIONS
• THEOREMS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE