On the solution of the open-loop Nash Riccati equations in linear quadratic differential games†

Communicated by Professor J. B. Cruz, Jr. This work was supported in part by the U.S. Air Force under Grant AFOSR-68-1579D, in part by NSF under Grant GK-36276, and in part by the Joint Services Electronics Program. Under Contract DAAB-07-72-C-0259 with the Coordinated Science Laboratory, University of Illinois, Urbana, Illinois

Abstract

A simplified method for solving the asymmetric, coupled, Riccati-type matrix differential equations occurring in the solution of open-loop Nash controls in linear quadratic differential games is discussed m this paper. This method offers considerable savings in the computational requirements of the sampled-data Nash solution in time-invariant linear quadratic differential games where the open-loop Nash Riccati equations must be solved repeatedly several times for different boundary conditions. A simple example is presented to illustrate the results

Notes

Communicated by Professor J. B. Cruz, Jr. This work was supported in part by the U.S. Air Force under Grant AFOSR-68-1579D, in part by NSF under Grant GK-36276, and in part by the Joint Services Electronics Program. Under Contract DAAB-07-72-C-0259 with the Coordinated Science Laboratory, University of Illinois, Urbana, Illinois