Design of a controller using successive approximation for singularly perturbed bilinear systems

The infinite time optimum to regulate the problem of singularly perturbed bilinear systems with a quadratic performance criterion is obtained by a sequence of algebraic Lyapunov equations. The new approach is based on successive approximations. In particular, the order reduction is achieved by using a suitable state transformation so that the original Lyapunov equations are decomposed into the reduced-order local Lyapunov equations. In addition, the slow part of the solution and the fast part solution are now completely decoupled so that the numerical ill-conditioning is removed. The proposed algorithms not only solve the optimal control problems in singularly perturbed bilinear systems but also reduce the computation time. This paper also includes an example to demonstrate the procedures.