Global synthesis of nonlinear systems with uncontrollable linearization.

摘要

This dissertation will present some recent advances in the synthesis of a significant class of nonlinear systems that have uncontrollable linearization.; First, a new feedback design tool called adding a power integrator is introduced and used to solve the problem of global robust stabilization, for a class of uncertain nonlinear systems that are neither necessarily feedback linearizable (fully or partially) nor affine in the control input, and therefore cannot be dealt with via conventional approaches. Sufficient conditions are presented under which a globally stabilizing smooth state feedback control law can be explicitly constructed, using repeatedly the adding a power integrator technique. This novel design technique permits removal of the feedback linearizability, linearity of the control input, and triangularity, which have been three common assumptions so far in the literature of nonlinear control.; Later, we consider the more challenging case when the systems have uncontrollable unstable linearization and therefore cannot be dealt with by any smooth state feedback, even locally. We give conditions under which it is possible to prove, while no smooth controllers exist, the existence of continuous state feedback control laws that achieve global strong stability in the sense of Kurzweil. The proof is constructive and carried out by developing a machinery, which combines the theory of homogeneous systems with the idea of adding a power integrator, for the explicit construction of globally stabilizing continuous controllers. A number of challenging benchmark examples, including a class of underactuated unstable mechanical systems, are presented to demonstrated the application aspects of our results.; The power of our design schemes is demonstrated by solving several long-standing open control problems, including global stabilization, almost disturbance decoupling, practical output tracking, and adaptive regulation in the presence of nonlinear parameterization, for nonlinear systems with uncontrollable linearization. The results presented in this dissertation are believed to be a major step toward the development of systematic design methodologies for global control of nonlinear systems having uncontrollable linearization, by using both smooth and non-smooth but continuous state feedback.