The control parameterization method for nonlinear optimal control: A survey

The control parameterization method is a popular numerical technique for solving optimal control problems. The main idea of control parameterization is to discretize the control space by approximating the control function by a linear combination of basis functions. Under this approximation scheme, the optimal control problem is reduced to an approximate nonlinear optimization problem with a finite number of decision variables. This approximate problem can then be solved using nonlinear programming techniques. The aim of this paper is to introduce the fundamentals of the control parameterization method and survey its various applications to non-standard optimal control problems. Topics discussed include gradient computation, numerical convergence, variable switching times, and methods for handling state constraints. We conclude the paper with some suggestions for future research

Neptunism and transformism:Robert Jameson and other evolutionary theorists in early nineteenth-century Scotland

This paper sheds new light on the prevalence of evolutionary ideas in Scotland in the early nineteenth century and establish what connections existed between the espousal of evolutionary theories and adherence to the directional history of the earth proposed by Abraham Gottlob Werner and his Scottish disciples. A possible connection between Wernerian geology and theories of the transmutation of species in Edinburgh in the period when Charles Darwin was a medical student in the city was suggested in an important 1991 paper by James Secord. This study aims to deepen our knowledge of this important episode in the history of evolutionary ideas and explore the relationship between these geological and evolutionary discourses. To do this it focuses on the circle of natural historians around Robert Jameson, Wernerian geologist and professor of natural history at the University of Edinburgh from 1804 to 1854. From the evidence gathered here there emerges a clear confirmation that the Wernerian model of geohistory facilitated the acceptance of evolutionary explanations of the history of life in early nineteenth-century Scotland. As Edinburgh was at this time the most important center of medical education in the English-speaking world, this almost certainly influenced the reception and development of evolutionary ideas in the decades that followed.</p

The Sparrow Question: Social and Scientific Accord in Britain, 1850-1900.

During the latter-half of the nineteenth century, the utility of the house sparrow (Passer domesticus) to humankind was a contentious topic. In Britain, numerous actors from various backgrounds including natural history, acclimatisation, agriculture and economic ornithology converged on the bird, as contemporaries sought to calculate its economic cost and benefit to growers. Periodicals and newspapers provided an accessible and anonymous means of expression, through which the debate raged for over 50 years. By the end of the century, sparrows had been cast as detrimental to agriculture. Yet consensus was not achieved through new scientific methods, instruments, or changes in practice. This study instead argues that the rise and fall of scientific disciplines and movements paved the way for consensus on "the sparrow question." The decline of natural history and acclimatisation stifled a raging debate, while the rising science of economic ornithology sought to align itself with agricultural interests: the latter overwhelmingly hostile to sparrows

Developing a Sense of the Pacific: The 1923 Pan-Pacific Science Congress in Australia

The Australian Congress of 1923 was a determining moment for the Pacific Science Association. In contrast to the Australian meeting of the British Association for the Advancement of Science, held in 1914, this first postwar Congress signaled the emergence of a new scientific nationalism i.n Australia and the advent of a new scientific relationship between Australia and Its great and powerful friend across the Pacific. At the same time, the success of the Congress gave the infant Pan-Pacific movement much-needed visibility and support and led directly to the permanent establishment of the Pacific Science Association and to its continuing presence in international scientific affairs