Robust Asymptotic Stabilization of Nonlinear Systems with Non-Hyperbolic Zero Dynamics

In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to design locally Lipschitz stabilizers under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models.Comment: 30 pages. Preliminary versions accepted at the 47th IEEE Conference on Decision and Control, 200

Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation

Motivated by some recent results on the stabilization of homogeneous systems, we present a gain-scheduling approach for the stabilization of non-linear systems. Given a one-parameter family of stabilizing feedbacks and associated Lyapunov functions, we show how the parameter can be rescaled as a function of the state to give a new stabilizing controller. In the case of homogeneous systems, we obtain generalizations of some existing results. We show that this approach can also be applied to nonhomogeneous systems. In particular, the main application considered in this paper is to the problem of stabilization with magnitude limitations. For this problem, we develop a design method for single-input controllable systems with eigenvalues in the left closed plane

Norm estimators and global output feedback stabilization of nonlinear systems with ISS inverse dynamics

Published versio

Invariance-like theorems and “lim inf” convergence properties

International audienceSeveral theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish “lim inf” convergence results are presented in a unified framework. These properties are useful to “describe” the oscillatory behavior of the solutions of dynamical systems. The theorems resemble “lim inf” Matrosov and Small-gain theorems and are based on a “lim inf” Barbalat's Lemma. Additional technical assumptions to have “lim” convergence are given: the “lim inf”/“lim” relation is discussed in-depth and the role of some of the assumptions is illustrated by means of examples

Optimal controller gain tuning for robust stability of spacecraft formation

The spacecraft formation control problem sets high demands to the performance, especially with respect to positional accuracy. The problem is further complicated due to scarce fuel resources and limited actuation effects, in addition to the many sources of disturbances. This paper addresses the problem of finding the optimal gains of spacecraft formation controllers. By optimal, we mean the gains that minimizes a cost functional which penalizes both the control efforts and the state deviation, while still guaranteeing stability of the closed-loop systems in the presence of disturbances

Adaptive Control Based on Retrospective Cost Optimization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83558/1/AIAA-46741-507.pd

Glucose utilization via glycogen phosphorylase sustains proliferation and prevents premature senescence in cancer cells.

Metabolic reprogramming of cancer cells provides energy and multiple intermediates critical for cell growth. Hypoxia in tumors represents a hostile environment that can encourage these transformations. We report that glycogen metabolism is upregulated in tumors in vivo and in cancer cells in vitro in response to hypoxia. In vitro, hypoxia induced an early accumulation of glycogen, followed by a gradual decline. Concordantly, glycogen synthase (GYS1) showed a rapid induction, followed by a later increase of glycogen phosphorylase (PYGL). PYGL depletion and the consequent glycogen accumulation led to increased reactive oxygen species (ROS) levels that contributed to a p53-dependent induction of senescence and markedly impaired tumorigenesis in vivo. Metabolic analyses indicated that glycogen degradation by PYGL is important for the optimal function of the pentose phosphate pathway. Thus, glycogen metabolism is a key pathway induced by hypoxia, necessary for optimal glucose utilization, which represents a targetable mechanism of metabolic adaptation