Development and application of a gradient method for solving differential games
A technique for solving n-dimensional games is developed and applied to two pursuit-evasion games. The first is a two-dimensional game similar to the homicidal chauffeur but modified to resemble an airplane-helicopter engagement. The second is a five-dimensional game of two airplanes at constant altitude and with thrust and turning controls. The performance function to be optimized by the pursuer and evader was the distance between the evader and a given target point in front of the pursuer. The analytic solution to the first game reveals that both unique and nonunique solutions exist. A comparison between the gradient results and the analytic solution shows a dependence on the nominal controls in regions where nonunique solutions exist. In the unique solution region, the results from the two methods agree closely. The results for the five-dimensional two-airplane game are also shown to be dependent on the nominal controls selected and indicate that initial conditions are in a region of nonunique solutions.
AIRCRAFT PURSUIT–EVASION PROBLEMS WITH VARIABLE SPEEDS
Aircraft pursuit-evasion encounters in a plane with variable speeds are analysed as a differential game. An engagement-dependent coordinate system confers open-loop optimality on the game. Each aircraft's optimal motion can be represented by extremel trajectory maps which are independent of role, adversary and capture radius. These maps are used in two different ways to construct the feedback solution. Some examples are given to illustrate these features. The paper draws on earlier results and surveys several existing papers on the subject.
SEASONAL AND REGIONAL MPG AS INFLUENCED BY ENVIRONMENTAL CONDITIONS AND TRAVEL PATTERNS
In-use fuel economy shortfall varies regionally and seasonally in response to changing environmental conditions and travel patterns. Shortfall changes by 25 percent or more are associated with variation in miles travelled per day by in-use vehicles. Monthly variations in northern states are twice those in the south; air conditioning penalties also vary by region. Although regional difference in annual levels are relatively small, shortfall can increase by 16 percent in densely populated urban areas. These variations have been quantified in an analysis of time-series mpg data and related to variables commonly reported in fuel economy surveys.