A passivity‐based simple adaptive synergetic control for a class of nonlinear systems

Summary For a class of nonlinear systems with the representation {A(x), B(x), C} and where the system parameters and dynamics are unknown, a simple adaptive synergetic controller ensuring the asymptotic convergence of the system to a desired manifold is proposed based on the technique of simple adaptive control (SAC). It is well known that the design of the synergetic control (SC) law requires a thorough knowledge of the system parameters and dynamics. Such problem obstructs the synthesis of the SC law and the designer is prompted to pass through the estimation methods, which, in turn, poses a problem of increasing the computation time of the control algorithm. To cope with this problem, a solution is proposed by modifying the original SC law to develop an SAC‐like adaptive SC law without the need of prior knowledge of the system. The stability of the proposed adaptive controller is formally proven via the Lyapunov approach. Experimental application to a quadrotor system is given to validate the theoretical results.