On the Hybrid Minimum Principle

Ali Pakniyat, Peter E. Caines

Published 2017-10-16Version 1

The Hybrid Minimum Principle (HMP) is established for the optimal control of deterministic hybrid systems where autonomous and controlled state jumps are allowed at the switching instants and, in addition to running costs, switching between discrete states incurs costs. A feature of special interest in this work is the possibility of state space dimension change, i.e. the hybrid state space is considered as the direct product of a set of discrete state components with finite cardinality and a set of Euclidean spaces whose dimensions depend upon the discrete state components. First order variational analysis is performed on the hybrid optimal control problem via the needle variation methodology and the necessary optimality conditions are established in the form of the HMP. A key aspect of the analysis is the relationship between the Hamiltonian and the adjoint process before and after the switching instants.