Adaptive control of wing rock system in uncertain environment using contraction theory

Contraction theory is used to study stability based on differential and incremental behaviour of trajectories of a system with respect to each other. Application of contraction theory provides a platform to analyze the exponential stability of nonlinear systems. This paper considers the design of a control law for wing rock system using contraction theory principles. An adaptive control design approach based on contraction theory is proposed for controlling the dynamics of such systems for the cases with and without uncertainty in parameters. An adaptive control law along with parameter updation law is derived for uncertain wing rock system to achieve convergence of trajectories of actual system to that of desired system. The analysis made in the paper leads to quite simple results avoiding complexities involved with Lyapunov method. Finally numerical simulations are presented to justify the effectiveness of the proposed controller.