Feedback control of nonlinear systems based on tangent linearisation using the multiple shooting method

In this paper we propose a design method for a feedback stabilisation of a nonlinear system which is based on the tangential linearisation of the resulting solution curve in state space. The solution is found by treating a linear control problem for a linear time-varying system together with the original nonlinear system equation. For the linear control design any standard technique can be used, e.g. LQ optimal control. The closed-loop stability of the resulting system is mathematically proved. Also the numerical algorithm for solving the resulting boundary value problem which is based on the multiple shooting method is sketched. A highly unstable nonlinear example system is used to show the practical application of the proposed method and the results are compared to the standard optimal controller.