Self-organized locally linear optimal tracking control for unknown nonlinear systems

This paper considers optimal full state feedback tracking control of unknown nonlinear systems. To deal with the unknown nonlinearities in the system, small learning regions are assigned online along the system trajectory in a manner dictated by a Lyapunov based self-organization method. In each of these regions, a local affine approximation is developed. A state observer-based approach adapts the approximator parameters. With the aid of this state observer, analytic optimal controllers are proposed by solving corresponding linear quadratic control problems in each learning region. To show the effectiveness of the proposed controllers, a numerical example is included.