Constrained Optimal Control Theory for Differential Linear Repetitive Processes

Abstract

Differential repetitive processes are a distinct class of continuous-discrete twodimensional linear systems of b o th systems theoretic and applications interest. These processes complete a series of sweeps termed passes th rough a set of dynamics defined over a finite duration known as th e pass length, and once th e end is reached th e process is reset to its s ta rtin g position before th e next pass begins. Moreover th e o u tp u t or pass profile produced on each pass explicitly contributes to th e dynamics of th e next one. Applications are as include iterative learning control and iterative solution algorithms, for classes of dynamic nonlin ear optimal control problems based on th e maximum principle, and th e modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In th is paper we develop su b stan tia l new results on optimal control of these processes in th e presence of constraints where th e cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and o th er electromechanical systems. The analysis is based on generalizing th e well-known maximum and e-maximum principles to them.