Nonlinear model predictive control with an infinite horizon approximation

Abstract

Current nonlinear model predictive control (NMPC) strategies are formulated as finite predictive horizon nonlinear programs (NLPs), which maintain NMPC stability and recursive feasibility through the construction of terminal cost functions and/or terminal constraints. However, computing these terminal properties may pose formidable challenges with a fixed horizon, particularly in the context of nonlinear dynamic processes. Motivated by these issues, we introduce an alternate moving horizon approach where the final element in the horizon is constructed from an infinite-horizon time transformation. The key feature of this approach lies in solving the proposed NMPC formulation as an extended boundary value problem, using orthogonal collocation on finite elements. Numerical stability is ensured through a dichotomy property for an infinite horizon optimal control problem, which pins down the unstable modes, extending beyond open-loop stable dynamic systems, and leads to both asymptotic and robust stability guarantees. The efficacy of the proposed NMPC formulation is demonstrated on three case studies, which validate the practical application and robustness of the developed approach on real-world problems.