Date of Award

Summer 1969

Document Type

Dissertation - Restricted

Degree Name

Doctor of Philosophy (PhD)


Electrical and Computer Engineering

First Advisor

Wu, Sherman H.

Second Advisor

Lade, Robert W.

Third Advisor

Bender, Philip R.


With the advent of high speed digital computers, both discrete systems and continuous systems whose controllers are digital have received extensive study. Because the controls themselves can be considered as either discrete or piecewise constant, much of the theory concerning the optimization of systems is no longer relevant. The early attempts at deriving analogues to the continuous theory met with limited success until the works of Halkin and Canon, Cullum and Polak. They in essence solved the analogue to the continuous system's problem of Mayer. In stating the necessary conditions that an optimal control and trajectory sequence must satisfy, they made use of a discrete Hamiltonian which the optimal solution must extremize. This is in contrast to the other principles in which the Hamiltonian merely has a local extremum or stationary point along the optimal solution. However the maximum principles of both Halkin and Canon, Cullum and Polak admit only initial and terminal state constraints. The purpose of this dissertation is to extend their works to admit parameter constraints, mixed state and control constraints, and trajectory constraints similar to those imposed on a continuous system. In all cases a maximum principle is desired to reject as many candidate sequences as possible.



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