Optimal syntheses for infinite-dimensional linear delayed state-output systems: A semicausality approach

Quadratic optimal control synthesis for infinite-dimensional delayed dynamical systems with output time delay involved in the cost functional is described. By introducing a truncation operator and associated semicausal trajectory, a new dynamical optimality principle was established. The closed-loop optimal control is given in three parts as a linear feedback: real-time state feedback, retarded state integral feedback, and initial data feedback which effects only a small time interval. The main feedback operator can be determined by solving a linear Fredholm integral equation.This research was supported by the National Science Foundation under Grant No. 8607687 and the Airforce Office of Scientific Research under Grant No. 860088.