ON DESIGN OF TIME OPTIMAL SPACE VEHICLE SYSTEMS VIA THE SECOND METHOD OF LYAPUNOV

摘要

Recently much attention has been given to synthesis of time optimal control systems, i.e., systems which are desired to he transferred from one state (such as a set of values for initial position, velocity, etc.) to a new state in minimum time while being operated from a limited source of power. A number of techniques such as Bellman's dynamic programming, Pontryagin's maximum principle and the results of functional analysis have been applied to the solution of this problem. However, in the very few cases where the solutions have been obtained they are of the form of open-loop control and involve tedious computational procedures. In many cases, such as control of space vehicles, the goal is to design a feed¬back system to perform the desired operation while considering the sim¬plicity of the over-all system as a basic requirement.nIn this report a class of systems has been introduced where a parti¬cular application of the second method of Lyapunov leads to a simple time-optimal feedback solution. A much broader class of systems has been identified where a desired time of response can be achieved through the design of appropriate "dead-beat" systems. A number of examples are included to show the simplicity of the application of the suggested techniques to design of space vehicle systems and systems in general.