Solutions to Point-to-Point Control Problems Using Laplace Transform Technique

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Abstract
Using finite-time Laplace transform, the governing differential equations of linear, time invariant point-to-point control problems are converted into an equivalent set of linear algebraic equations embedded with the desired boundary conditions, characterizing the entire set of optimal and sub-optimal solutions. A linear programming technique for synthesizing the control inputs using selected sets of basis functions is presented. A new concept of feedback control which involves a recursive evaluation of the open-loop input is also developed.

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