Optimization of Systems with Constant Pure Time Delay,
Abstract
There are many control processes of practical engineering interest which involve nonnegligible time delays in the behavior of the quantities being controlled. These hereditary effects have a considerable importance during the evolution of the process. The mathematical formulation of these processes with time delay can be expressed by a system of differential-difference equations. Necessary conditions of optimality for systems with pure time delay are examined. An outline of the proof of the maximum principle for a special class of time delay systems is presented using the geometrical approach of Pontryagin. The system being considered is linear with respect to the control and the delayed control. A new computational approach for optimization of linear time delay (differential-difference) systems with quadratic performance indices is presented. The method utilizes parameter imbedding, and transforms the advanced-delayed type two point boundary value form of necessary conditions to a sequence of conventional non-delayed linear boundary value problems. The method leads to a truncated Maclaurin series approximation for the optimum control. A theorem concerning the degree of approximation of the truncated Maclaurin series is proved. Computational results for several examples are presented. A suboptimal state feedback control is also considered. Extension of the imbedding method to treat nonlinear systems with constant pure time delay is accomplished when the method is used in conjunction with the quasilinearization technique. A numerical example is presented to demonstrate this approach. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1971
- Accession Number
- AD0732476
Entities
People
- Hing Chun Chan
Organizations
- University of Illinois Urbana–Champaign