Methods of constructing optimal stabilizers (Q1339574)

The problem of transforming a linear dynamical system of the form \(\dot x= Ax\) in the neighbourhood of a state equilibrium is solved using the special problem of the damping of the system \[ \dot x= Ax+ bu,\quad t\geq 0,\quad x(0)= x_ 0, \] by controls of minimum intensity after a finite time interval. The system is called dampened if the property \(| x_ i(\theta)|\leq \varepsilon\), \(i\in I= \{1,2,\dots,n\}\) is satisfied for each initial state \(x_ 0\) (\((0,\theta)\) is the finite time interval of programmed damping). The proposed method is based on the constructive theory of optimal control. An example is given.