Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems

The gradient projection anti-windup (GPAW) scheme was recently proposed as an anti-windup method for nonlinear multi-input-multi-output systems/controllers, the solution of which was recognized as a largely open problem in a recent survey paper. This report analyzes the properties of the GPAW scheme applied to an input constrained first order linear time invariant (LTI) system driven by a first order LTI controller, where the objective is to regulate the system state about the origin. We show that the GPAW compensated system is in fact a projected dynamical system (PDS), and use results in the PDS literature to assert existence and uniqueness of its solutions. The main result is that the GPAW scheme can only maintain/enlarge the exact region of attraction of the uncompensated system. We illustrate the qualitative weaknesses of some results in establishing true advantages of anti-windup methods, and propose a new paradigm to address the anti-windup problem, where results relative to the uncompensated system are sought.DSO National Laboratories, Singapore and AFOSR grant FA9550-08-1-008

Equivalence between Approximate Dynamic Inversion and Proportion-Integral Control

Approximate Dynamic Inversion (ADI) has been established as a method to control minimum-phase, nonaffine-in-control systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller admits a linear Proportional-Integral (PI) realization that is largely independent of the nonlinear function that defines the system. In this report, we first present an extension of the ADI method for single-input nonaffine-in-control systems that renders the closed-loop error dynamics independent of the reference model dynamics. The equivalent PI controller will be derived and both of these results are then extended to multi-input nonaffine-in-control systems.DSO National Laboratories (Singapore), AFOSR grant FA9550-08-1-0086

Corrections to "Geometric Properties of Gradient Projection Anti-windup Compensated Systems"

In a conference paper titled "Geometric Properties of Gradient Projection Anti-windup Compensated Systems," two main results were presented. The first is the controller state-output consistency property of gradient projection anti-windup (GPAW) compensated controllers. The second is a geometric bounding condition relating the vector fields of the uncompensated and GPAW compensated closed-loop systems with respect to a star domain. While the controller state-output consistency property stands without modifications, the proof of the geometric bounding condition depends on two lemmas, the proofs of which were found to be faulty. In this report, we present a new proof of the geometric bounding condition using concepts from convex analysis, together with minor miscellaneous corrections.DSO National Laboratories, Singapore, AFOSR grant FA9550-08-1-008

On Approximate Dynamic Inversion

Approximate Dynamic Inversion has been established as a method to control minimum-phase, nonaffine-in-control systems [1]. In this report, we re-state the main results of [1], clarify some minor notational errors, and prove the same results in an expanded form. In the large, the main results of [1] still stand. The development follows [1] closely, and no novelty is claimed herein. The purpose of this report is mainly to supplement our existing results in [2]–[4] that rely heavily on the results of [1].DSO National Laboratories (Singapore), AFOSR grant FA9550-08-1-008

On the absolutely continuous spectrum of generalized indefinite strings II

We continue to investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two more model examples of generalized indefinite strings under rather wide perturbations. In particular, one of these results allows us to prove that the absolutely continuous spectrum of the isospectral problem associated with the two-component Camassa-Holm system in a certain dispersive regime is essentially supported on the set $(-\infty,-1/2]\cup [1/2,\infty)$.Comment: 27 page

On approximate dynamic inversion and proportional-integral control

Approximate dynamic inversion (ADI) has been established as a method to control minimum-phase, nonaffine-in-control systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller admits a linear proportional-integral (PI) realization that is largely independent of the nonlinear function that defines the system. This paper extends these previous results in three ways. First, we present an extension of ADI that renders the closed loop error dynamics independent of the reference model dynamics. It is then shown that the equivalence between the ADI and PI controllers only holds for the time response when applied to the exact system. Finally, key robustness properties of the two control approaches are compared using linear system techniques. These results indicate that the PI realization is preferable when accurate knowledge of the nonlinear system dynamics is not available, and that the ADI realization would be preferred if time delays are the major limitations in the system

How can firms motivate users to innovate on their platforms?

Atreyi Kankanhalli, Hock-Hai Teo and Hua (Jonathan) Ye studied the motivations of both existing and potential user

A Rare Case of Cholecystitis Caused by Raoultella planticola

A 62-year-old female presented with right upper quadrant pain. Clinical examination and ultrasound scan were consistent with gallstones and acute cholecystitis. She received 3 days of intravenous Co-amoxiclav and was discharged with 5-days of oral antibiotics with arrangements to return for an elective cholecystectomy. This was performed 5 months later which revealed an inflamed gallbladder and a localised abscess secondary to gallbladder perforation. Fluid from the gallbladder was taken which cultured Raoultella planticola, a gram-negative, nonmotile environmental bacteria (Bagley et al. (1981)). This is the first report of biliary sepsis with a primary infection by R. planticola. This patient was treated with a 5-day course of oral Co-amoxiclav and made a full recovery

Critical Thinking: Definition and Structure

The development of critical thinking as an essential skill in 21st century learning is uncontested within educational and professional settings. The degree to which it is operationally defined, taught and assessed, however, remain at large. This incongruence complicates efforts to develop critical thinking in students, as well as devise intervention techniques and assessment tools. This framework has been developed to address the challenges associated with teaching and assessing critical thinking. While there are many definitions of the skill, as outlined in the first part of this document, few definitions provide a means to operationalise critical thinking in the classroom. The framework outlines critical thinking processes along prescribed strands and aspects informed by a sound evidentiary basis. The aspects contained within the framework are designed to provide foci for teaching and the basis of assessment

Drugs, frontier capitalism and illicit peasantries: towards a comparative research agenda

A defining character of drugs-affected frontier regions is their dynamic instability and their boom-and-bust cycles. These are violent and disturbed landscapes, in which illicit drug economies play a transformative role. But not all frontiers are the same, and nor are the ‘illicit peasantries’ who inhabit the ‘narco-frontier’. In this article we explore the complex dialectical relations between frontiers, drug economies, illicit peasantries and peasant politics. In doing so we develop a new comparative framework, that provides a heuristic for studying the commonalities and differences across narco-frontiers and the mechanisms behind these differences