Efficient prioritization in explicit adaptive NMPC through reachable-space search

Abstract

This paper presents a computationally tractable explicit nonlinear model predictive control (NMPC) strategy that models and adapts to changes in plant dynamics. Explicit NMPC techniques enumerate all controllers derived from an NMPC formulation. However, the resulting database is exponential in the number of constraints and prohibitive for fast, online queries. Therefore, we propose to construct a database that is restricted to operation within the system’s reachable set under NMPC. To identify this reduced controller set, we construct a randomized search tree to explore the set of trajectories within the reachable set and apply the Experience-driven Predictive Control (EPC) algorithm to construct the database incrementally during the search. Additionally, we model transitions between controllers as a Markov chain with transition probabilities that inform a partial ordering on successors for each controller, thus enabling efficient search of the database at runtime. The resulting Explicit EPC algorithm thus consists of two phases: 1) offline generation of a simplified controller database and 2) efficient online application of the stored controllers. A set of simulation studies, including attitude control of a quadrotor micro air vehicle, demonstrate that the proposed approach enables the use of explicit adaptive NMPC for problems that would otherwise yield prohibitively large databases. We also present experimental evaluation of the proposed Explicit EPC algorithm implemented onboard a nano-quadrotor, thereby demonstrating that this approach enables adaptive NMPC on severely compute-constrained platforms.