The isopone method in optimal control

The minimum-time problem is a well known problem in optimal control and several methods are available to solve this problem. In this article, an extension of the minimum-time problem will be considered. A specific optimal control problem will be treated and the so-called Isopone method to determine the optimal control is proposed. In this Isopone method, multi dimensional reachable subsets are computed repeatedly. This method is similar to dynamic programming in that it is a recursive algorithm, but is designed to reduce the amount of calculation time. The current algorithm yields, as a degenerate case, also the time optimal route.     

Nash equilibria in risk-sensitive dynamic games

Dynamic games in which each player has an exponential cost criterion are referred to as risk-sensitive dynamic games. In this note, Nash equilibria are considered for such games. Feedback risk-sensitive Nash equilibrium solutions are derived for two-person discrete time linear-quadratic nonzero-sum games, both under complete state observation and shared partial observation     

Comments on `Matrix inequalities applicable to estimating solutionsizes of Riccati and Lyapunov equations'

In the above work by N. Komaroff (see ibid., vol.34, p.97-8 (1989)), the proof of an (almost) correct theorem has been based partly on an incorrectly cited theorem. As the incorrectly cited theorem could abusively be used by unsuspecting readers, accurate theorems and proofs are provided