The problem of computing the value of a differential game for a positional functional (Q2714653)

The paper deals with the system NEWLINE\[NEWLINE \frac{dx}{dt} = A(t)x + f(t,u,v),\quad t_0\leq t\leq \vartheta, NEWLINE\]NEWLINE where \( x\in R^n\), \( u\in P\subset R^r\), \( v\in Q\subset R^s\), \(t_0\) and \(v\) are given moments of time, \(P\) and \(Q\) are known compacts and \(A(t)\) and \(f(t,u,v)\) are piecewise continuous in \(t\). For any \( m\in R^n \) and \( t\in[t_0,\vartheta] \) it is assumed that NEWLINE\[NEWLINE \min\limits_{u\in P} \max\limits_{v\in Q} \langle m,f(t,u,v)\rangle = \max\limits_{v\in Q} \min\limits_{u\in P} \langle m,f(t,u,v)\rangle. NEWLINE\]NEWLINE The author substantiates the calculation procedure for the value of the corresponding differential game. Examples of application are not given.