Recursive approach to the optimal control problems for singularly perturbed bilinear systems

The optimal control problem of a singularly perturbed bilinear system is studied. The authors present a recursive algorithm to solve the corresponding nonlinear algebraic equations. The algorithm removes the ill-conditioning by decomposing the higher order equation into lower order equations and develops a technique that enables obtaining an arbitrary accuracy, i.e., O(ε^k) approximation for this problem. A numerical example that supports the theoretical results is presented