Published 2012
“…Thus,the rotational controller stabilizes all the attitudes of the X4-ALJV at a desired (x-, y- or z-) position of the vehicle.The stability of the corresponding closed-loop system is proved by imposing a suitable Lyapunov function and then using LaSalles's invariance principle.The second stabilization strategy is based on a discontinuous control law,involving the a-process for exponential stabilization of nonholonomic system.This technique is applied to the system by two different approaches.The first approach does not necessitate 11 any conversion of the system model into a
chained form, and thus not rely on any special transformation techniques.The system is written in a control-affine form by applying a partial linearization technique and a dynamic controller based on Astolfi's discontinuous control is derived to stabilize all the states of the system to the desired equilibrium point exponentially.Motivated by the fact that the discontinuous dynamic-model without using a
chained form transformation assures only a local stability (or controllability) of the dynamics based control system, instead of guaranteeing a global stability of the system, the conversion of system model into a second-order
chained form is
implemented in the second approach.The second-order
chained form consisting of a dynamical model is obtained by separating the original dynamical model into three subsystems so as to use the standard canonical form with two inputs and three states second-order
chained form.Here,two subsystems are subject to a second-order nonlinear model with two inputs and three states,and the other subsystem is subject to a linear second-order model with two inputs and two states. …”
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Thesis
