On the optimal control systems with multiple controllers (Q2735072)

The paper deals with the class of discrete-time autonomous linear-quadratic optimal regulator problems such that the cost depends on the pair input-trajectory only through the trajectory. NEWLINENEWLINENEWLINEThe author gives a sufficient condition for the system to be equivalent to a pair of non-interacting linear-quadratic regulators. This makes possible to compute the optimal regulator for the original problem as a linear time-invariant feedback whose gain is a linear combination of the optimal gains for the new problems. The optimal gain for each of the new problems can be computed from the solution to an appropriate Riccati matrix equation. NEWLINENEWLINENEWLINEA principal component approach is used to obtain a special type of decoupling in which the regulator of the first decoupled system accounts for most of the performance of the original system. Hence the regulator that results from taking this regulator and ignoring the regulator of the second decoupled system is ``near optimal'' for the original system. NEWLINENEWLINENEWLINEThe results are illustrated with an example.NEWLINENEWLINEFor the entire collection see [Zbl 0962.00004].