  We consider the problem of designing a machine learning-based model of an
unknown dynamical system from a finite number of (state-input)-successor state
data points, such that the model obtained is also suitable for optimal control
design. We propose a specific neural network (NN) architecture that yields a
hybrid system with piecewise-affine dynamics that is differentiable with
respect to the network's parameters, thereby enabling the use of
derivative-based training procedures. We show that a careful choice of our NN's
weights produces a hybrid system model with structural properties that are
highly favourable when used as part of a finite horizon optimal control problem
(OCP). Specifically, we show that optimal solutions with strong local
optimality guarantees can be computed via nonlinear programming, in contrast to
classical OCPs for general hybrid systems which typically require mixed-integer
optimization. In addition to being well-suited for optimal control design,
numerical simulations illustrate that our NN-based technique enjoys very
similar performance to state-of-the-art system identification methodologies for
hybrid systems and it is competitive on nonlinear benchmarks.
