Dynamic Surface Control and Its Application to Lateral Vehicle Control

This paper extends the design and analysis methodology of dynamic surface control (DSC) in Song and Hedrick, 2011, for a more general class of nonlinear systems. When rotational mechanical systems such as lateral vehicle control and robot control are considered for applications, sinusoidal functions are easily included in the equation of motions. If such a sinusoidal function is used as a forcing term for DSC, the stability analysis faces the difficulty due to highly nonlinear functions resulting from the low-pass filter dynamics. With modification of input variables to the filter dynamics, the burden of mathematical analysis can be reduced and stability conditions in linear matrix inequality form to guarantee the quadratic stability via DSC are derived for the given class of nonlinear systems. Finally, the proposed design and analysis approach are applied to lateral vehicle control for forward automated driving and backward parallel parking at a low speed as well as an illustrative example.