LECTURE SERIES IN DIFFERENTIAL EQUATIONS, SESSION I. CONTROL THEORY
Abstract
The Scientific report summarizes the three lectures presented at the First Session of the Lecture Series in Differential Equations. Professor Dantzig illustrated how mathematical programming, and in particular a generalized linear program, can be applied to a linear control process. The 'problem' takes the form of minimizing the 'cost' of moving an 'object' from one convex domain to another by proper choice of a control vector and boundary conditions. Professor Lefschetz dealt with the Lurie problem on nonlinear controls, i.e., the determination of necessary and sufficient conditions such that all solutions of a set of general nonlinear control differential equations are absolutely stable in the large whatever the choice of the admissible (function) characteristic of the control. Professor Markus discussed the 'bang-bang' theory of control as a physical concept and as a collection of precise mathematical theorems. The bang- bang principal states that any response of a controlled system which can be achieved by an arbitrary controller restricted to the extreme values of the control domains. Theorems presented relate both to linear and nonlinear control processes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1965
- Accession Number
- AD0828318
Entities
People
- George Bernard Dantzig
- Lawrence Markus
- Solomon Lefschetz
Organizations
- Georgetown University