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This video discusses optimal nonlinear control using the Hamilton Jacobi Bellman (HJB) equation, and how to solve this using dynamic programming.

Little has been done in the study of these intriguing questions, and I do not wish to give the impression that any extensive set of ideas exists that could be called a theory. What is quite surprising, as far as the histories of science and philosophy are concerned, is that the major impetus for the fantastic growth of interest in brain processes, both psychological and physiological , has come from a device, a machine, the digital computer. In dealing with a human being and a human society, we enjoy the luxury of being irrational, illogical, inconsistent, and incomplete, and yet of coping. In operating a computer, we must meet the rigorous requirements for detailed instructions and absolute precision. If we understood the ability of the human mind to make effective decisions when confronted by complexity, uncertainty, and irrationality, then we could use computers a million times more effectively than we do. Recognition of this fact has been a motivation for the spurt of research in the field of neurophysiology. The more we study the information-processing aspects of the mind, the more perplexed and impressed we become. It will be a very long time before we understand these processes sufficiently to reproduce them. In any case, the mathematician sees hundreds and thousands of formidable new problems in dozens of blossoming areas, puzzles galore, and challenges to his heart's content. He may never resolve some of these, but he will never be bored. What more can he ask?

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