Stabilization, synchronization and tracking of nonlinear systems by feedback domination approach




Yan, Song

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This dissertation presents a series of fundamental and challenging control problems and their solutions for nonlinear systems, including global stabilization for a class of upper-triangular nonlinear systems, global asymptotic synchronization via sampled-data feedback, finite-time control for synchronization and bounded tracking of a variable-speed wind turbine nonlinear system. The problem of global stabilization for a class of upper-triangular nonlinear systems is first discussed in this dissertation. We focus on the nonlinear systems whose linearization around the origin can and cannot be guaranteed to be controllable, respectively and a variety of nonlinearity growth rates which depend on the input are considered. Based on adding a power integrator technique and the homogeneous domination design, the state-feedback controller is recursively constructed such that the closed-loop systems are globally asymptotically stable. We also investigate the problem of using sampled-data feedback to synchronize a slave (driven) system with a master (driver) system. Based on the domination approach, both state-feedback and output-feedback control methods using sampled-data are proposed to make the tracking error converge to zero. This issue is of practical importance since in practice the system state is transmitted as sampled signal, and very often only the output is measurable. The problem of finite-time synchronization is also discussed where a homogeneous nonlinear controller is designed to make the tracking error converge to zero in a finite time. In addition, the finite-time control technique is applied to solve the tracking problem of a variable-speed wind turbine system. A finite-time nonlinear tracking controller has been designed for an obtained variable-speed wind turbine model to achieve finite-time asymptotic tracking control for reference rotor speed signals, in order to capture maximum wind power in the operational mode. The proposed scheme relies on Barrier Lyapunov Functions, with which the output of closed-loop system will remain bounded under a mild condition on the initial output. The comparison between the designed controller and traditional finite-time controller which is based on Quadratic Lyapunov Functions is presented.


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Global asymptotic synchronization, Nonlinear system control



Electrical and Computer Engineering