Semi-global stabilization of nonlinear systems via output feedback and sampled-data controls with applications to power systems
It has been known that for nonlinear control systems, global stabilizability by state feedback plus global observability is usually not sufficient for achieving global stabilizability by output feedback. The impossibility of this kind indicates that in the nonlinear case, semi-global, instead of global, stabilization by output feedback is the more realistic control objective to be pursued. This dissertation aims to develop new theories and approaches for designing non-smooth output feedback controllers and sampled-data output feedback controllers which semi-globally stabilize several general classes of nonlinear systems.
First, the problem of semi-global finite-time stabilization by output feedback is considered for a class of uncertain nonlinear systems which contain both higher-order and lower-order terms and therefore cannot be handled by the existing design schemes. Based on the homogeneous domination approach, a scaled homogeneous output feedback controller is constructed to semi-globally stabilize the system in a finite time by choosing an appropriate gain. The proposed approach not only achieves finite-time convergence rather than asymptotic convergence, but also widens the applicability to broader classes of systems with mixed-order nonlinearities and non-triangular structure. Second, semi-global stabilization by nonsmooth output feedback is achieved for a class of planar nonlinear systems with unknown control coefficients and more general nonlinearities. The design approach is based on the construction of a new root Lyapunov function and utilization of a saturation design. The result is applied to solve the problem of Maximum Power Point Tracking (MPPT) in photovoltaic (PV) arrays. Next, a systematic approach is proposed to design non-smooth output feedback controllers to semi-globally stabilize a class of higher-dimensional nonlinear systems without restrictive growth conditions. Compared to the existing results, the approach proposed in this dissertation is able to achieve fast convergence rate and handle uncertain controller coefficients. The final thrust of the dissertation is the development of a new approach to design sampled-data output feedback controllers which semi-globally stabilize a class of nonlinear systems with linear and high-order growth condition. To accomplish this, the output feedback domination approach is redesigned by integrating a sampled-data output feedback controller with a tunable scaling gain and a tunable sampling period. Then the scaling gain is selected to dominate the uncertain nonlinearities and the sampling period is determined to guarantee the overall stability of the systems under sampled-data controller. The proposed output feedback controller consists of a set of linear difference equations and hence is easier to be digitally implemented.
This dissertation has advanced the research of the semi-global output stabilization of nonlinear systems, mainly in three directions: (i) more general nonlinear systems have been stabilized by the proposed methods, (ii) better performance such as finite-time convergence has been achieved, and (iii) more digitally implementable controllers are designed for real world applications.