Nonlinear control design method based on state-dependent Riccati equation (SDRE) via quasi-Newton method

The state-dependent Riccati equation (SDRE) method is a recently emerging technique for the control design of nonlinear systems (Cloutier et al., 1996). Nonlinear regulator problems could be solved approximately, by applying a linear control theory to the nonlinear control design. However, one of the bottlenecks is that the SDRE based design method should require real-time computation of the algebraic Riccati equations. It is well known that Schur-decomposition of Hamiltonian and Kleinman algorithm are useful tools for solving the Riccati equations (Menon et al., 2002). The former is noniterative, and the latter is iterative. Generally speaking, the noniterative approach is faster computationally than the iterative approach. However, as far as computation and storage burden are concerned, the iterative method is superior. In this paper, we focus on the iterative approach, and propose a new technique to solve in real-time the algebraic Riccati equation. A key idea is a fusion of the vectorization of the SDRE and the quasi-Newton method. We demonstrate the practicability of the proposed fusion method through experiments of the swing control of a crane.