A linear problem of terminal control of composite systems (Q760898)

For the linear control problem of composite systems \[ \dot x=A_ 1x+u,\quad t\in [0,\tau],\quad x(0)=x_ 1,\quad \dot y=A_ 2y+v,\quad t\in [\tau,T],\quad y(\tau)=x(\tau),\quad <a,y(T)>\to \min \] sufficient conditions for optimality are obtained. Here \(A_ 1\), \(A_ 2\) are (n,n) matrices; \(\tau\in [0,T]\), T is a fixed number; \(u\in P\), \(v\in Q\) with P, Q being compact sets; a is a fixed vector.