In this paper, we study the control of the dynamic system governed by the matrix differential equation, x˙ = Fx + Du, x(0) = −c, where the input vector u is constrained in amplitude. It is shown that in the discrete (sampled data) case: (a) The general optimal control problem can be formulated as a nonlinear programming problem amenable to treatment by techniques developed in the operation research field. (b) The specific time optimal control problem originally studied by Kalman is treated here using a different approach which yields well-known as well as new results.
Solution Space Approach to Optimal Control Problems
Harvard University, Cambridge, Mass.
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Ho, Y. (March 1, 1961). "Solution Space Approach to Optimal Control Problems." ASME. J. Basic Eng. March 1961; 83(1): 53–58. https://doi.org/10.1115/1.3658890
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