Minimizing integrals of absolute deviations in linear control systems

A criterion function involving time integral of absolute deviations is considered. There are three critical regions in the time behavior of the desired function, r(t), and optimal policies are derived and discussed depending on the behavior of r(t) with respect to these three regions. An algorithm of shifting the origin to appropriate points in the time axis and restarting the process is provided, by which optimal control policies can be constructed successively in the forward direction of time.