Sub-optimal stabilizing controller design for non-linear slowly varying systems: application in a benchmark system

摘要

In this paper, non-linear time-varying systems with slowly varying parameters are considered. Using slowly varying control Lyapunov function and considering a cost function, a controller (with closed-form structure) is presented which guarantees asymptotic stability of the closed-loop non-linear slowly varying system. Moreover, the Hamilton-Jacobi-Bellman equation is analysed to show that the proposed controller is a sub-optimal controller and the response of the closed-loop system may be very close to its optimal solution. Additionally, in order to show the applicability of the proposed method, it is applied to the time-varying inertia pendulum, which is one of the famous benchmarks among the non-linear time-varying systems. Then, the efficiency of the designed controller is compared with that of a numerical optimal controller, which is called, 'receding horizon generalization of point-wise min-norm controller'. Simulation results demonstrate the applicability and efficiency of the proposed method.