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Online adaptive optimal control for bilinear systems

Bilinear systems are a special class of nonlinear systems, which have linear characteristic. In this paper, policy iteration (PI) is introduced to solve the optimal control problem of bilinear systems. An online adaptive optimal control method is proposed, which avoids the direct solution of the Hamilton-Jacobi-Bellman (HJB) equation. The convergence is established by proving that it is equivalent to an existing offline iterative method. This PI algorithm can be implemented online, which does not require the knowledge of internal system dynamic. Simulation studies on two examples demonstrate the effectiveness of the proposed method.