Stabilization Control for Differentially Flat System under Constant Disturbances

The differentially flat system, a class of nonlinear systems, contains many mechanical systems. However, few control laws for differentially flat systems are tolerant of disturbances despite many mechanical systems suffer from some disturbances. We aim to design a stabilization control law for differentially flat systems under constant disturbances by using its linearizability and the minimum projection method. First, we design a static control Lyapunov function (CLF) that includes a disturbance for the nonlinear system via a CLF for the linearized system. After that, we prove the designed CLF satisfies the condition of an adaptive control Lyapunov function (ACLF). Finally, we demonstrate an example of designing the proposed adaptive controller for a PVTOL system under winds and verify the effectiveness of the proposed method.