Abstract
This paper deals with the optimal control problem of piece-wise linear time-invariant periodic control systems (PLPCS).
This problem can be considered as an application of the optimal control problem for system equations with right-hand side discontinuity of the state. The solution of the optimal control problem is shown to be valid for periodic control processes.
A switching sequence of system equations is denoted by σ, and the σ- invariance of the system is defined.
A sufficient condition is obtained that PLPCS should have a unique periodic solution. It is also shown that when this condition holds and the system is σ-invariant, the PLPCS optimally designed for an integral quadratic P. I. will have a stationary periodic solution obtainable by solving the optimal control problem of PLPCS with the same P. I. and under the periodic condition.
