  This paper is concerned with the construction and convergence analysis of
novel implicit Peer triplets of two-step nature with four stages for nonlinear
ODE constrained optimal control problems. We combine the property of
superconvergence of some standard Peer method for inner grid points with
carefully designed starting and end methods to achieve order four for the state
variables and order three for the adjoint variables in a
first-discretize-then-optimize approach together with A-stability. The notion
triplets emphasizes that these three different Peer methods have to satisfy
additional matching conditions. Four such Peer triplets of practical interest
are constructed. Also as a benchmark method, the well-known backward
differentiation formula BDF4, which is only $A(73.35^o)$-stable, is extended to
a special Peer triplet to supply an adjoint consistent method of higher order
and BDF type with equidistant nodes. Within the class of Peer triplets, we
found a diagonally implicit $A(84^o)$-stable method with nodes symmetric in
$[0,1]$ to a common center that performs equally well. Numerical tests with
three well established optimal control problems confirm the theoretical
findings also concerning A-stability.
