Stability Margin Scaling Laws for Distributed Formation Control as a Function of Network Structure

We consider the problem of distributed formation control of a large number of vehicles. An individual vehicle in the formation is assumed to be a fully actuated point mass. A distributed control law is examined: the control action on an individual vehicle depends on (i) its own velocity and (ii) the relative position measurements with a small subset of vehicles (neighbors) in the formation. The neighbors are defined according to an information graph. In this paper we describe a methodology for modeling, analysis, and distributed control design of such vehicular formations whose information graph is a D-dimensional lattice. The modeling relies on an approximation based on a partial differential equation (PDE) that describes the spatio-temporal evolution of position errors in the formation. The analysis and control design is based on the PDE model. We deduce asymptotic formulae for the closed-loop stability margin (absolute value of the real part of the least stable eigenvalue) of the controlled formation. The stability margin is shown to approach 0 as the number of vehicles N goes to infinity. The exponent on the scaling law for the stability margin is influenced by the dimension and the structure of the information graph. We show that the scaling law can be improved by employing a higher dimensional information graph. Apart from analysis, the PDE model is used for a mistuning-based design of control gains to maximize the stability margin. Mistuning here refers to small perturbation of control gains from their nominal symmetric values. We show that the mistuned design can have a significantly better stability margin even with a small amount of perturbation. The results of the analysis with the PDE model are corroborated with numerical computation of eigenvalues with the state-space model of the formation.Comment: This paper is the expanded version of the paper with the same name which is accepted by the IEEE Transactions on Automatic Control. The final version is updated on Oct. 12, 201

Comments on characterizing demand flexibility to provide power grid services

Many loads have flexibility in demand that can be used to provide ancillary services to power grids. A large body of literature exists on designing algorithms to coordinate actions of many loads to provide such a service. The topic of characterizing the flexibility of one or a collection of loads - to determine what kinds of demand deviation from the baseline is feasible - has also been studied. However, there is a large diversity in definitions of flexibility and methods proposed to characterize flexibility. As a result there are several gaps in the literature on flexibility characterization. Some approaches on flexibility characterization are based on ad-hoc approximations that lead to highly conservative estimates. In this paper we point out some of these issues and their implications, with the hope to encourage additional research to address them.Comment: 9 pages, a shorter version will be presented at the 2024 American Control Conferenc

The Flexural Design of Pretensioned Bent Caps

The use of pretensioned bent caps has brought the opportunity to utilize the advantages of accelerated construction and increased worker safety. At the same time they offer the benefits of enhanced performance. To facilitate a widespread implementation of pretensioned bent caps, this research seeks to develop flexural design procedures and recommendations on design and detailing that can benefit design engineers with readily available guidelines. A design procedure for pretensioned bent caps is proposed in this work. In this procedure, the bent caps will be primarily designed to achieve zero tension under dead load, to provide adequate strength under design load combinations and to satisfy the stress limits specified in the American Association of State Highway and Transportation Officials (AASHTO) LRFD Bridge Design specifications. To evaluate the design procedure, a bridge inventory comprising standard Texas Department of Transportation (TxDOT) bridges with I-girders, box beams and X-beams, as well as non-standard bridges have been considered. Design results indicate no cracking expected under service loads and limited cracking expected under ultimate loads. End region detailing of the pretensioned bent caps, for resistance against tensile stresses during prestress transfer, have been reviewed from previous investigations. The pocket connections, used between pretensioned bent caps and columns, offer benefits in the use of concrete instead of grout and in the availability of large construction tolerance. A medium pocket size formed by corrugated pipe is preferable for accommodating accidental misalignment of column. The connection provides resistance to vehicle collision loads. Optimization of bridges with pretensioned bent caps has been assessed with modifications to the prestressing layout and the reconfiguration of the arrangement of columns. Change in strand design and geometry contributed in reduction of flexural cracking and increasing performance. Elimination of the column is expected to result in economic benefits

History from the Margins: Literary Culture and Manuscript Production in Western India in the Vernacular Millennium

Scholars of South Asia have long known of praśastis, eulogistic verses often composed in the transregional Sanskrit language on copperplates, stone slabs, and temple walls, from the early centuries of the Common Era. They have traditionally sieved these documents to recover dynastic histories and have supposed that as a genre, it faded away in the second millennium CE when Islamic polities were established across the subcontinent and new genres of history writing were popularized. In making this supposition they have overlooked the fact that praśastis continued to be frequently composed and written. Yet, their appearance was neither in public spaces nor in public documents, but frequently at the ends of palm-leaf and paper manuscripts. In this paper, I carefully analyze a corpus of hitherto un-translated praśastis and other scribal remarks written at the end of oft illustrated sumptuous Jaina manuscripts prepared between c. 1000 –1600 in western India. This was a period during which manuscript culture and literary production burgeoned in the region. Through my close reading of these genealogical micro histories, I shed new light on the emergence of new power elites, literati associations, centers of manuscript production, the rise of professional authors and scribes, and formation of kinship. I also consider the aesthetics and poetics of patronage in the region and ask why patrons in the early centuries of the second millennium CE sought to legitimize their family histories using an archaic genre