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

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

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

Homelessness and COVID-19

The COVID-19 pandemic has exacerbated the struggle of people experiencing homelessness (PEH) and presented new challenges to those serving this vulnerable population. To better understand and articulate how COVID has impacted both PEH and their ecosystem of support, we compared the national response - aggregated via a literature review of both gray and academic literature - to the statewide response in Indiana and the local response in Tippecanoe County. Local homelessness providers emphasized that organizational partnerships are key - policy changes in one organization can have malignant effect extending throughout and putting additional strain on other organizations within the local homelessness ecosystem Moreover, building community awareness and engagement with organizations serving PEH during normal times can have beneficial effects in times of crisis - calls to the community for help may prove to be more fruitful if they are to existing contacts and not de facto cold calls. Considering the problems elucidated by various homeless providers, certain governmental policies and provisions native to Tippecanoe County and Indiana could be beneficial to export elsewhere in the event of another public health crisis of this scope. Providers relayed that a close relationship with the local department of health and hotels helped expedite the placement and facilitate the extended stay of homeless COVID positive individuals

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

Isolation and characterization of 16 polymorphic microsatellite loci for the Asian green mussel Perna viridis (Mollusca, Mytilidae)

The Asian green mussel Perna viridis is an abundant and important ecological and economical species across its native range. However, outside its native range, this species has been considered invasive and concerns have been raised worldwide regarding its potential impacts. Despite this, little work has been done to investigate the genetics of native and/or introduced populations of this species. In the present study, we developed 16 new polymorphic microsatellite markers using the Illumina MiSeq Platform. Four to 15 alleles per locus were detected. There was no evidence of linkage disequilibrium between pairs of loci and all loci were in Hardy-Weinberg equilibrium

Gradient projection anti-windup scheme

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 205-217).It is a well-recognized fact that control saturation affects virtually all practical control systems. It leads to controller windup, which degrades/limits the system's closed-loop performance, and may cause catastrophic failures if it induces instability. Anti-windup compensation is one of two main approaches to mitigate the effects of windup, and is conceptually and practically attractive. For the idealized case of constrained linear time invariant (LTI) plants driven by LTI controllers, numerous anti-windup schemes exist. However, most practical control systems are inherently nonlinear, and anti-windup compensation for nonlinear systems remains largely an open problem. To this end, we propose the gradient projection anti-windup (GPAW) scheme, which is an extension of the conditional integration method to multi-input-multi-output (MIMO) nonlinear systems, using Rosen's gradient projection method for nonlinear programming. It achieves controller state-output consistency by projecting the controller state onto the unsaturated region induced by the control saturation constraints. The GPAW-compensated controller is a hybrid controller defined by the online solution to either a combinatorial optimization subproblem, a convex quadratic program, or a projection onto a convex polyhedral cone problem. We show that the GPAW-compensated system is obtained by modifying the uncompensated system with a passive operator. Qualitative weaknesses of some existing anti-windup results are established, which motivated a new paradigm to address the anti-windup problem. It is shown that for a constrained first order LTI plant driven by a first order LTI controller, GPAW compensation can only maintain/enlarge its region of attraction (ROA). In this new paradigm, we derived some ROA comparison and stability results for MIMO nonlinear as well as MIMO LTI systems. The thesis is not that the GPAW scheme solves a centuries-old open problem of immense practical importance, but rather, that it provides a potential path to a solution. We invite the reader to join us in this quest at the confluence of nonlinear systems, hybrid systems, projected dynamical systems, differential equations with discontinuous right-hand sides, combinatorial optimization, convex analysis and optimization, and passive systems.by Chun Sang Justin Teo.Sc.D

Fractional oscillator process with two indices

We introduce a new fractional oscillator process which can be obtained as solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short range dependence of the process are studied by considering the asymptotic properties of its covariance function. The fluctuation--dissipation relation of the process is investigated. The fractional oscillator process can be regarded as one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique.Comment: 32 page

Team MIT Urban Challenge Technical Report

This technical report describes Team MITs approach to theDARPA Urban Challenge. We have developed a novel strategy forusing many inexpensive sensors, mounted on the vehicle periphery,and calibrated with a new cross-­modal calibrationtechnique. Lidar, camera, and radar data streams are processedusing an innovative, locally smooth state representation thatprovides robust perception for real­ time autonomous control. Aresilient planning and control architecture has been developedfor driving in traffic, comprised of an innovative combination ofwell­proven algorithms for mission planning, situationalplanning, situational interpretation, and trajectory control. These innovations are being incorporated in two new roboticvehicles equipped for autonomous driving in urban environments,with extensive testing on a DARPA site visit course. Experimentalresults demonstrate all basic navigation and some basic trafficbehaviors, including unoccupied autonomous driving, lanefollowing using pure-­pursuit control and our local frameperception strategy, obstacle avoidance using kino-­dynamic RRTpath planning, U-­turns, and precedence evaluation amongst othercars at intersections using our situational interpreter. We areworking to extend these approaches to advanced navigation andtraffic scenarios