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.

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