Higher-order approximations of linear control systems via Runge-Kutta schemes (Q1362832)

The author considers a generalization of Runge-Kutta schemes for control systems when the control is not smooth with respect to time: (1) \(y'(t)=Ay(t)+Bu(t)\), \(y(0)=x\), where \(u(t): [0,\infty) \to [0,1]^M\) is the control, \(A\) and \(B\) are constant matrices. There are results concerning higher-order approximations for system (1) and second-order approximations for systems of a more general form.