  This paper proposes a Lyapunov-based economic MPC scheme for nonlinear sytems
with non-monotonic Lyapunov functions. Relaxed Lyapunov-based constraints are
used in the MPC formulation to improve the economic performance. These
constraints will enforce a Lyapunov decrease after every few steps. Recursive
feasibility and asymptotical convergence to the steady state can be achieved
using Lyapunov-like stability analysis. The proposed economic MPC can be
applied to minimize energy consumption in HVAC control of commercial buildings.
The Lyapunov-based constraints in the online MPC problem enable the tracking of
the desired set-point temperature. The performance is demonstrated by a virtual
building composed of two adjacent zones.
