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LIAPOUNOV'S THEOREM ON THE RANGE OF A VECTOR MEASURE AND PONTRYAGIN'S MAXIMUM PRINCIPLE
STANFORD UNIV CALIF APPLIED MATHEMATICS AND STATISTICS LABS
The necessary condition for the optimal control of a non-linear dynamical system is studied. The system under consideration is described by a canonical system of ordinary differential equations for the state variables. The differential equations depend also on certain parameters called control variables. The problem is to choose the value of these control variables, which can be time dependent, in order to satisfy given initialAND END POINTS CONDITIONS AND TO MAXIMIZE A GIVEN FUNCTIONAL. When there are no restrictions on the values which can be taken by the control variables the problem is relatively simple and equivalent to the Problem of Bolza of the calculus of variations. Such situation however is very unlikely to occur in practice because of the physical limitations of the control devices. Autho