Shape congruence and guidance control design for a class of nonlinear systems

By using the curve theory in differential geometry, the concepts of shape congruence controllers are proposed for a class of nonlinear systems with binary input. Then, the shape congruence controllers are designed by employing signed curvature. The shape congruence controller can ensure that the shape of the shape curve of system controlled is coincident with the given reference curve in shape. Finally, the guidance controller is also synthesized by using the method of sliding mode variable structure. The usability of the guidance controller and shape congruence controller can complete the shape congruence control task of the system at a given point. The simulation results show the validity of the method in this paper.