Synthesis of optimal controls for real-time linear digital systems

The solution of the problem of optimizing linear digital systems which are optimal in terms of sum of squares performance criteria leads to Riccati's difference equation. The problem of the analytical construction of controls which are optimum with respect to the generalized work criterion, consisting of solving a linear difference equation in reverse time, has been solved for the class of digital systems. An algorithm with a prediction model based on this criterion which allows controls to be synthesized in real time is proposed.