  Constraint handling during tracking operations is at the core of many
real-world control implementations and is well understood when dynamic models
of the underlying system exist, yet becomes more challenging when data-driven
models are used to describe the nonlinear system at hand. We seek to combine
the nonlinear modeling capabilities of a wide class of neural networks with the
constraint-handling guarantees of model predictive control (MPC) in a rigorous
and online computationally tractable framework. The class of networks
considered can be captured using Koopman operators, and are integrated into a
Koopman-based tracking MPC (KTMPC) for nonlinear systems to track piecewise
constant references. The effect of model mismatch between original nonlinear
dynamics and its trained Koopman linear model is handled by using a constraint
tightening approach in the proposed tracking MPC strategy. By choosing two
Lyapunov functions, we prove that solution is recursively feasible and
input-to-state stable to a neighborhood of both online and offline optimal
reachable steady outputs in the presence of bounded modeling errors under mild
assumptions. Finally, we demonstrate the results on a numerical example, before
applying the proposed approach to the problem of reference tracking by an
autonomous ground vehicle.
