Stabilizing a nonlinear system by using feedback control

Abstract

This dissertation considers how to stabilize a nonlinear system by using feedback control. To stabilize a nonlinear system, we first need to find the unstable steady state. Then we consider the linearized problem at this steady state and solve the Riccati equation using the linear quadratic regulator (lqr). We then design the feedback controller on the linearized system,. Finally, we apply the feedback controller on the original nonlinear system. We use the forward Euler method, backward Euler method and Trapezoidal method to consider the discretization of the nonlinear system. We design the algorithm and consider two numerical examples of ecological models and verify that the results obtained are in accordance with theoretical results.