Optimal control systems. Part I, Analysis : the methods of Pontryagin in the optimal control of second order oscillatory systems with discontinuities in the state variables
Nevius, William B.
Titus, Harold A.
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It is the purpose of these two reports to demonstrate with very simple systems, several applications of the optimization theory of L. S. Pontryagin (1). An attempt to synthesize the control logic using a modification of dynamic programming is developed,, Part 1 presents the solution to the minimum time problem and the minimum fuel problem for a second order system with one zero c The zero causes discontinuities in the state variables . Control difficulties are encountered when there are discontinuities in the error states, but these are alleviated by a transformation to a system with continuous variables. Optimum control of the transformed system is then accomplished using the methods of Pontryagin „ The control action is then related back to the original plant. Although the investigation is concerned entirely with second order systems , the methods are sufficiently general to be extended to higher order systems with zeros. In part II an example of the extension is given,, Also Part II presents various schemes for the synthesis of optimum controls.
NPS Report NumberNaval Postgraduate School (U.S.) Research paper ; no. 37.
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