Kunihiko Ichikawa

Optimal Design of Incomplete Feedback Control System in the Sense of Mini-max

Although the optimal control theory has been much developed in recent years, the theory requires assumption that all the components of state vector are detected, but detection of all components of state vector is not always possible. The usual application of optimal control theory of incomplete feedback control system leads us to the inconvenience such that the optimal control law varies depending upon the initial point. this paper proposes a design method of incomplete feedback control system, where only the detected components are used to feedback. In order to get rid of dependence of optimal control law on the initial point, the method to optimize incomplete feedback control system in the sense of mini-max is contrived. The design method is explained in detail.

Optimal Problem with Discontinuity

Pontryagins maximum principle is only applicable when right hand side functions in a differential equation of a controlled system and an integrand in criterion function as well as their partial derivatives with respect to x are all continuous for both x and u. The optimal control problem in which any above condition is not satisfied is called a problem with discontinuity. In this case the state space is divided by boundary into some regions in which the maximum principle is applicable. In this paper one approach to find out the optimal control law for the problem is discussed. That is, d optimal backward time trajectories are sought in a whole state space by solving one after another the newly established optimal problem with the maximum principle for each region. Usually, costate vector experiences a jump at the discontinuity point but in our method it arises as the result of the solution and any account for jump condition is not required. The mechanism of jump, however, is also examined in this paper.