The Stabilization Design For Nonlinear Systems Based On The Saturation Method

Actuator saturation phenomena are often found in engineering practice and consequently, saturated designs have been paid attention for a long time. Recently, the related research even becomes a hot issue. In this area, the main works in this paper are stated as follows.1. The use of saturation has been developed as a tool for the stabilization of nonlinear systems. If the closed-loop system is proven to have no finite escape time, the boundedness information in finite time, which is obtained from robust stable subsystems or recursive analysis procedures, is then sufficiently employed to deal with crucial nonlinear terms. The proposed method does not rely on complicated Lyapunov functions, and in some cases can avoid strong growth conditions and complicated small gain analysis. Also, simple saturated control laws are explicitly constructed in an almost unified way.2. The established saturation method is then applied to the well-known planar vertical take-off and landing aircraft and present a new stabilizing control law. The system model is first transformed into its equivalent form, then a control law consisting of a linear term and a saturated term is given for an important subsystem, with the saturation levels being assigned as large as possible. Compared to the existing saturation scheme in which all states are restricted by saturations, the new design brings about a relatively fast convergence.3. Proposed a novel backstepping design technique based on the saturation method. For some cascade systems whose upper subsystems have a feedforward structure and include higher order terms, small control are first assigned to stabilize the upper subsystem, and a simple backstepping procedure is then followed. When dealing with the upper subsystem, we adopt an approach of using small controls to attenuate higher order terms, rather than the usual method in which complicated Lyapunov functions need to be constructed. This is in sharply contrast with previous designs where (involved) Lyapunov functions are utilized. As applications, global stabilization designs are presented for several classical mechanical systems including the inertia wheel pendulum, the translational oscillator with rotating actuator and the cart-pole system.