A control problem with structural choices

The case is considered in which, during the operation of an optimal control system, the optimizer, in addition to applying his usual control, may switch structures. Necessary and sufficient conditions are derived and emphasis is placed on the special characteristics of this problem. Continuous and discrete time set-ups are considered and the separation principle is shown not to hold for the linear quadratic case in the presence of noise.     

Dimensions of R&D location in the United States

R&D activities in the United States, as in other advanced economies, are geographically concentrated in certain types of locations. This study presents data on the location of four dimensions of R&D in the U.S.: industrial R&D laboratories, scientists and engineers engaged in R&D, scientists and engineers employed by the federal government, and research universities. Industrial R&D is much more concentrated in large urban areas than the other dimensions, and appears to locate more in response to the location of manufacturing activity than to the location of research universities and federal research facilities. The location of R&D employment, which includes government university, and industrial employees, is associated with facilities for all three types of R&D. Because of these factors, R&D in the U.S. is found on a significant per capita basis in 44 of 177 urban areas, most of them in the northeastern portion of the country. When two dimensions, industrial R&D laboratories and R&D employees, are combined as a measure of R&D concentration, the locational pattern is less clustered regionally. Ten urban areas in all regions of the U.S. are identified as important complexes of R&D. Since the location of R&D is a major indicator of comparative advantage for technological activities and the economic potential of urban regions, only a few areas of the U.S. are likely to remain important in the generation of innovations.     

The physics of brass wind instruments

The design of musical instruments owes more to art than to science and assessment of their quality is essentially subjective. Nevertheless, the physical principles of their operation are very interesting and may be of practical importance. This article reviews the acoustics of brass wind instruments, regarding the player and his instrument as an entity, and compares experimental and theoretical results.     

New projects in particle physics

Recent results in the field of particle physics raise many questions on the elementary constituents of matter and their interactions. These cannot be answered, nor the latest theoretical predictions verified, without accelerators operating at higher energies. Pending world-wide collaboration for the construction of a gigantic accelerator, individual nations are engaged in an increasingly competitive race to construct such machines. The author describes the main assemblies under construction or currently planned in Western Europe, the USA and the USSR, and discusses the technical, financial, political, and, by no means least, human problems involved.     

Structural aspects of controllability and observability—I. tensorial aggregation

The classical criteria for controllability and observability are given a tensorial formulation which is then extended into Boolean form directly related to a digraph interpretation of system structure. This is examined in detail with particular reference to group theoretic aspects, invariant properties under transformation, the term rank test and the existence of zero eigenvalues.Within this framework the structural design concepts of potential controllability and observability are presented in generalised terms.     

Structural aspects of controllability and Sobservability—II. digraph decomposition

The graph theoretic aspects of controllability and observability are examined and related to the tensorial formulation of Part I of the paper. Particular emphasis is given to the significance of the system digraph decomposition and the relevance of this to certain system algebraic properties of interest in control theory.     

Three-axis platform simulation: Bond graph and Lagrangian approach

A bond graph model is derived for the geometric constraints of a three-axis flight table. Gimbal dynamics are easily added even in asymmetrical and unbalanced cases. A method is introduced to make the local dependent inertias computable. The bond graph compares favourably to the Lagrangian approach as to modelling effort and accessibility of intermediate variables as well as having computational advantages.     

The graph-theoretic field model—I. Modelling and formulations

The Graph-Theoretical Field Model provides a unifying approach for developing numerical models of field and continuum problems. The methodology examines the field problem from the first stages of conceptualization without recourse to the governing differential equations of the field problem; this is accomplished by deriving discrete statements of the physical laws which govern the field behaviour. There are generally three laws, and these are modelled by the “cutset equations”, the “circuit equations”, and the “terminal equations”. In order to establish these three sets of equations it is expedient first to spatially discretize the field in a manner similar to the finite difference method and then to associate a linear graph (denoted as the field graph) with the spatial discretization. The concept of “through” and “across” variables, which underlies the cutset and circuit equations respectively, enables one to define the graph in an unambiguous manner such that each “edge” of the graph identifies a pair of complementary variables. From a knowledge of the constitutive properties and the boundary conditions of the field it is possible to associate terminal equations with sets of edges. Since the resulting sets of equations represent the field equations, these equations provide the basis for a complete (but approximate) solution to the field or continuum problem. In fact, this system approach uses a two part model: one for the components and another for the interconnection pattern of the components which renders the formulation procedures totally independent of the solution procedure.This paper presents the theoretical basis of the model and several graph-theoretic formulations for steady-state problems. Examples from heat conduction and small- deformation elasticity are included.