Contraction based adaptive control of a class of nonlinear systems

Adaptive control problem of nonlinear systems having dynamics in parametric strict feedback form is addressed here. Effort is made to derive adaptive methodology for controller design in contraction framework. General results and conditions for stabilization are derived using backstepping. At each step of recursive design, system is made contracting by suitable selection of control inputs. As contraction property is not intrinsic to the systems, so proposed strategy helps in identifying a coordinate transformation along with controller to establish contracting nature of the system. Contracting dynamics ensures exponential convergence of state trajectories to each other. Results are further extended to address control problem of systems having uncertain parameters. Tracking control problem of single link manipulator with actuator dynamics is addressed using the proposed scheme. Numerical simulations justify the effectiveness of the proposed methodology.