Optimal Cooperative State Rendezvous and Pontryagin's Maximum Principle†

In the discussion of the theory of optimal cooperative rendezvous, it is shown that the problem of obtaining the optimal control of two independently controlled systems having a common goal may be solved using the maximum principle of Pontryagin. This will be accomplished provided certain special boundary conditions are obtained for the Hamiltonian system of differential equations. It is further demonstrated that the requirement that two state variables be equal at the rendezvous time implies that the adjoint variables associated with them are negatives of each other at that time. Using this result, a first-order time-optimal rendezvous problem is solved and the results discussed. Indications for further work are also shown.