A homotopy approach for nonlinear control synthesis

In this paper, the authors propose a control method for nonlinear systems which relies on the homotopy method for solving nonlinear equations and tangent linearized control systems. They present a mathematically rigorous treatment of the theoretical foundations, including a constructive proof of the exponential error decay for the controlled system which contains an explicit control design instruction. For illustration, this design instruction is applied to an example system. The behavior of the controlled system is examined by numerical simulations. To demonstrate the advantages and drawbacks of the proposed method they include a short comparison with two usual nonlinear control techniques by means of the considered example system.