"There are two main approaches to solve optimal control problems. The optimal LQ control problems obtained through indirect methods of recurring open-loop counting and optimal nonlinear control problems which can be acquired by using direct spectral methods. The main reason for using the spectral methods is their high speed in solving such problems; the other reason for the use of spectral methods is to obtain optimal results for optimal control problems. The most important reason for the use of orthogonal functions, ...
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"There are two main approaches to solve optimal control problems. The optimal LQ control problems obtained through indirect methods of recurring open-loop counting and optimal nonlinear control problems which can be acquired by using direct spectral methods. The main reason for using the spectral methods is their high speed in solving such problems; the other reason for the use of spectral methods is to obtain optimal results for optimal control problems. The most important reason for the use of orthogonal functions, especially Chebyshev, is that the output of these methods is a well-posed matrix which minimizes the complexity of the system as much as possible. From another perspective, optimal control problems with interval uncertainties can be solved based on two direct and indirect approaches"--
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