An Optimal Control Approach to National Settlement System Planning

In this paper, an optimal control approach to a problem in national settlement system planning is presented. The problem description is the same as considered by MacKinnon [6] and by Evtushenko and MacKinnon [4]. It is shown how the special structure of the model and the singular nature of the control can be used to reduce the solution of a nonlinear programming problem to the solution of sets of linear equations. A branch and bound integer programming algorithm is used to handle inequality constraints on the control variables. The organization of the paper is as follows. Section I considers problem formulation and an optimal control solution is discussed in Section II. A branch and bound technique for determining active constraints is presented in Section III. A more general problem is considered in Section IV and conclusions are stated in Section V

Credibility Theory and Kalman Filtering with Extensions

In this paper it is shown that the estimate and prediction problems considered in credibility theory are similar to those considered in Kalman filtering theory. The state vector of the risk model consists of the average risk variables such as the number of claims, cost of claims, etc. for a particular risk from the collective of risks. The observed data consists of the risk variables for the collective and for the individual risks. It is required to predict the values of risk variables in the next time period based on this data and to adjust the individual premiums based on claims experience in such a way as to converge to their true values

Chemical Kinetics and Catastrophe Theory

In this paper a continuous stirred tank reactor (CSTR) model of a first-order, exothermic reaction is examined and the existence of a cusp catastrophe is shown. Analytical solutions are developed for the ignition and quenching boundaries. The significance of the results and further extensions are discussed

On the Dynamics of the Ignition of Paper and Catastrophe Theory

The purpose of this note is to study the phenomenon of ignition of paper considered by Shivadev and Emmons from the viewpoint of stability theory and catastrophe theory. It is shown that ignition results from a sudden or catastrophic change of the kinetics governing temperature from a locally stable to a locally unstable equation. Using the model of Shivadev and Emmons and the above criterion, equations for the ignition temperature and the corresponding heat flux are derived. These equations are shown to provide a good match to the experimental data of Reference. Further extensions of this work to combustion and the appearance of cusp catastrophes are also discussed

Optimization of Measurement Schedules and Sensor Designs for Linear Dynamic Systems

This paper presents new results on the problem of measurement scheduling, sensor location and design for linear dynamic systems. Both time-invariant and time-varying systems are considered and different norms of the Observability and Information matrices are maximized with respect to the structural parameters of the system. A close connection is established between these problems and the Kiefer-Wolfowitz Theory of Experimental Design for Regression problems. Both randomized and nonrandomized designs are considered. It is shown that the optimal designs obey certain minmax properties that lead to rapidly convergent algorithms. The results are illustrated by an analytical and a numerical example