In this paper we develop a new finite time optimal control algorithm for the bilinear systems by using the successive approximation method. Hofer and Tibken (1988) and Aganovic and Gajic (1994, 1995) have proposed iterative schemes to solve the optimal control problem for these systems. On the contrary to the results of Aganovic where the optimal solution has been obtained in terms of a sequence of the differential Lyapunov equations based on the results of Hofer, we propose a new method based on the the successive approximation method and the control law is represented by an explicit state feedback form. An example is presented to illustrate the results, and the proof of convergence is provided.
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