THE PROBLEM OF CONFLICTING CONTROL WITH MIXED CONSTRAINTS

The control problem for a linear dynamical system is considered at a m inimax of the terminal quality index. Feasible controls are simultaneo usly restricted by geometrical constraints and by integrated momentum constraints, the latter being thought of as a store of control resourc es. The problem is formalized as a differential game [1-4] using conce pts [5-8] developed at Ekaterinburg. Here, because of the geometrical constraints, the momentum formulation and its associated difficulties [2-4] do not appear. On the other hand the presence of the integral re strictions leads to the appearance of additional variables whose evolu tion describes the dynamics of the expenditure of the control resource s. These variables are subject to phase restrictions, which is a pecul iarity of the problem. A reasonably informative picture and a class of strategie's for which the given game has a value and a saddle point a re given. A constructive method for computing the value function of th e game and constructing optimal strategies is presented. This method i s conceptually related to the construction of a stochastic programming synthesis [5] and is based on the recursive construction of upper-con vex envelopes for certain auxiliary functions. The possibility of exch anging the minimum and maximum operations over the resource parameters when calculating the value of the game using these procedure is estab lished.