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Backstepping And Sequential Predictors For Control Systems, Jerome Avery Weston
Backstepping And Sequential Predictors For Control Systems, Jerome Avery Weston
LSU Doctoral Dissertations
We provide new methods in mathematical control theory for two significant classes of control systems with time delays, based on backstepping and sequential prediction. Our bounded backstepping results ensure global asymptotic stability for partially linear systems with an arbitrarily large number of integrators. We also build sequential predictors for time-varying linear systems with time-varying delays in the control, sampling in the control, and time-varying measurement delays. Our bounded backstepping results are novel because of their use of converging-input-converging-state conditions, which make it possible to solve feedback stabilization problems under input delays and under boundedness conditions on the feedback control. Our …
Topological Dynamics On Compact Phase Spaces, Lieth Abdalateef Majed
Topological Dynamics On Compact Phase Spaces, Lieth Abdalateef Majed
LSU Doctoral Dissertations
Our main focus will be to investigate the various facets of what are commonly called dynamical systems or flows, which are triples $(S,X,\pi)$, where $X$ is a compact Hausdorff space and $\pi:S \times X \longrightarrow X$ is a separately continuous action of a semigroup $S$ on $X$. Historically, as was introduced by R.Ellis 1960, the enveloping semigroup, which is a closure of the set of continuous functions on a compact space $X$, was discovered to be an important tool to study dynamical systems. Soon, a realization of the existence of a universal compactification of a phase semigroup with an extended …
Some Tracking Problems For Aerospace Models With Input Constraints, Aleksandra Gruszka
Some Tracking Problems For Aerospace Models With Input Constraints, Aleksandra Gruszka
LSU Doctoral Dissertations
We study tracking controller design problems for key models of planar vertical takeoff and landing (PVTOL) aircraft and unmanned air vehicles (UAVs). The novelty of our PVTOL work is the global boundedness of our controllers in the decoupled coordinates, the positive uniform lower bound on the thrust controller, the applicability of our work to cases where the velocity measurements may not be available, the uniform global asymptotic stability and uniform local exponential stability of our closed loop tracking dynamics, the generality of our class of trackable reference trajectories, and the input-to-state stability of the controller performance under actuator errors of …