Nonlinear Horizon-One Model Predictive Control for Resource-Limited Applications

To reduce the computational footprint of model predictive control during online computation, a horizon-one scheme based on pre-computed inner-approximations of reach-able sets is proposed. The inner-approximated reachable set allows to virtually predict the future system behavior over the full-horizon instead of repeatedly solving potentially large-scale optimal control problems. We provide theoretical proofs for recursive feasibility and asymptotic stability under mild assumptions. Furthermore, we illustrate how methods for sum-of-squares reachability analysis can be extended to meet these assumptions. The presented approach is demonstrated in simulation for functional verification and compared to other real-time methods from the literature.