IMA Journal of Mathematical Control and Information, Vol. 11, pp. 311-319, 1994.

Consider a class of continuous-time, quadratic regulator problems involving a class of nonlinear affine dynamical systems. It is known that the optimal feedback control is directly related to the solution of the Algebraic Riccati Equation (ARE) at every point along the state trajectory. In this paper we propose a new, practical computational method for constructing a suboptimal stabilising feedback controller. To be more specific, the state-space is first partitioned into rectangular regions. The ARE is then solved off-line at the geometric centre of all rectangular regions. On this basis, a suboptimal stabilising feedback control law is constructed. A numerical example is presented to illustrate the proposed method.