Dual-Objective NMPC: Considering Economic Costs Near Manifolds

This paper presents a dual-objective nonlinear model predictive control (NMPC) algorithm for stabilizing a target neighborhood of a state-space manifold of a nonlinear dynamical system and for concurrently optimizing an economic objective in this neighborhood. The control design is based on the transverse normal form description of the system dynamics. The NMPC scheme solves two optimal control problems (OCPs) in sequence, the first (transversal) OCP provides conditions for the convergence to the target neighborhood. The second (tangential) OCP optimizes the economic objective without compromising the convergence. The stability and performance properties of the resulting control scheme are discussed and its efficacy is illustrated in a tutorial example.