A neural network-based approach to hybrid systems identification for control
This work addresses the challenge of efficient optimal control design for hybrid systems, offering a method that simplifies computation by avoiding mixed-integer optimization, though it is incremental as it builds on existing neural network and hybrid system techniques.
The authors tackled the problem of modeling unknown dynamical systems from data for optimal control by developing a neural network architecture that yields a differentiable hybrid system with continuous piecewise-affine dynamics, enabling derivative-based training and strong local optimality guarantees via nonlinear programming instead of mixed-integer optimization. Numerical simulations show it performs similarly to state-of-the-art hybrid system identification methods and is competitive on nonlinear benchmarks.
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 adopt a neural network (NN) architecture that, once suitably trained, yields a hybrid system with continuous piecewise-affine (PWA) 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 favorable when used as part of a finite horizon optimal control problem (OCP). Specifically, we rely on available results to establish that optimal solutions with strong local optimality guarantees can be computed via nonlinear programming (NLP), in contrast to classical OCPs for general hybrid systems which typically require mixed-integer optimization. Besides 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 methods for hybrid systems and it is competitive on nonlinear benchmarks.