Study of several problems in nonlinear control by backstepping

Abstract

Adaptive control is investigated for a class of nonlinearly parameterized systems by backstepping. An adaptive controller is constructed for MIMO nonlinearly parameterized systems with nested triangular form. The design procedure is developed based on the adaptive backstepping design technique. The designed controller guarantees that the corresponding closed-loop system is globally asymptotically stable for any unknown parameters which enter the system nonlinearly. Adaptive control problem is also investigated for MIMO nonlinear DAE systems with unknown parameters appearing linearly in both differential and algebraic equations. The DAE system is converted into an equivalent ODE system. An adaptive controller is designed by the backstepping technique and the asymptotic stability o f the system is guaranteed. A parallel robotic system is studied as a test-bed to illustrate the backstepping control approach. For comparison, PD control is also designed and implemented on the parallel robot. The given simulation and experimental results are satisfactory for both backstepping and PD control approaches.