Guidance theory and extremal fields

A guidance concept employing properties of optimal flight paths is developed on the basis of Jacobi's accessory minimum problem for the second variation. The analysis is equivalent to construction of a field of extremals in the neighborhood of a predetermined extremal serving as a "nominal" trajectory. In the absence of inequality constraints on the control variables, a linear terminal control scheme with time-varying gains is realized. The addition of inequality constraints leads to nonlinear control behavior. Certain propulsion system parameters are characterized as state variables as a convenient means for providing adaptive behavior in respect to in-flight changes in propulsion system performance. An application is given to an intercept problem sufficiently simple to allow analytical solution, and some numerical results comparing optimal and approximately optimal guidance in their effects on flight performance are presented. Treatment of a certain type of problem arising in rocket applications is discussed.