Distributed trajectory tracking by control contraction theory with learning-based model compensation

In this paper, the contraction theory is used to solve the robust trajectory tracking control method for distributed complex nonlinear systems. The controller designed by the contraction theory can make the system track any trajectory and get rid of the assumption of the stable point of the Lyapunov method. For complex nonlinear systems, parts with unknown parameters or difficult to model will have a great impact on controller design. Neural network is used to compensate the uncertainties of the model, and a global linear matrix inequality (LMI) which satisfies distributed robust trajectory tracking is proposed. A decomposition method of global linear matrix inequalities (LMIS) is presented to meet the solving requirements of distributed controllers. The rationality of the matrix inequality proposed in this paper is verified by theoretical analysis.