An optimum control problem which can be solved completely is the linear, time-invariant free-terminal-time, regulator problem with unrestricted control function and a quadratic-type performance index. However, if the control function is constrained, the solution of the regulator problem becomes complicated. In the present work, when the control function |u(t)| ≤ 1, the requirements of the existence of an optimal solution and a method for obtaining this solution are outlined.
On a Class of Constrained Control, Linear Regulator Problems
Department of Electrical Engineering, The Johns Hopkins University, Baltimore, Md.
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Tchamran, A. (June 1, 1966). "On a Class of Constrained Control, Linear Regulator Problems." ASME. J. Basic Eng. June 1966; 88(2): 385–391. https://doi.org/10.1115/1.3645865
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