Optimum control of a class of distributed-parameter systems subject to control signal saturation is studied. The system performance is optimized with respect to an integral criterion function. This problem is solved by making use of coordinate transformation and Butkovskii's maximum principle. For this class of systems with distinct characteristic roots, the optimum control law is found to be the solution of a Fredholm integral equation of the second kind, subject to the condition of bounded signal.
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Yeh et al. (1967) studied this question.
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