Computational Solution To a Class of Optimization Problems.
FRANK J SEILER RESEARCH LAB UNITED STATES AIR FORCE ACADEMY COLO
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Optimum control problems typically involve the minimization with respect to a control input of a performance index subject to a vector differential equation describing the propagation in time of the system states. Application of Pontryagins Minimum Principle results in necessary conditions which the minimizing control must satisfy. Unfortunately, these necessary conditions are expressed as a two-point boundary-value problem TPBVP which must be solved for the optimum control. Many TPBVPs cannot be solved analytically hence, some approximate numerical scheme is necessary. Thus computational solutions occupy a central role in optimum systems control. In some optimization problems, the control which may be applied is constrained. Such constraints may be expressed as in inequality when the allowable control must, for example, be less than some maximum amount. Or such constraints may be expressed by an equality. This report examines the computational solution to the TPBVP which results when the allowable control is constrained to be either zero or one.
- Numerical Mathematics