What is LRE

This chapter states the result of the development of optimal control methods for deterministic discontinuous systems of optimal control problems for deterministic compound dynamical systems (CDS) with branching paths. The necessary conditions for optimality of the CDS branching paths are formulated in the form convenient for subsequent development of algorithms for the operational synthesis of these paths. The optimality conditions developed by the authors allow both preliminary and in real time (on-line) optimization of the CDS branching paths. The need for an operational synthesis of the CDS branching trajectory is caused by the inaccuracy of prior knowledge of information about the factors affecting CDS movement which are critical for the implementation of the CDS end-use. The developed conditions are universal for solving problems with any finite number of branches of a branching trajectory and are focused on the use of artificially intelligent systems which allow analyzing the structure of optimal control of CDS components as they move along the path branches.