Stability and Performance Analysis of NMPC: Detectable Stage Costs and General Terminal Costs

• 成果类型: Article
• 署名作者: Kohler, Johannes; Zeilinger, Melanie N.; Gruene, Lars
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Bayreuth
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3235244
• 发表日期: 2023
• 页码: 6114-6129
• 关键词: costs; stability analysis; Numerical stability; cost function; asymptotic stability; performance analysis; CONTROLLABILITY; Linear programming analysis; optimal control; Predictive control; stability of nonlinear systems

摘要

We provide a stability and performance analysis for nonlinear model predictive control (NMPC) schemes subject to input constraints. Given an exponential stabilizability and detectability condition w.r.t. the employed state cost, we provide a sufficiently long prediction horizon to ensure asymptotic stability and a desired performance bound w.r.t. the infinite-horizon optimal controller. Compared to existing results, the provided analysis is applicable to positive semidefinite (detectable) cost functions, provides tight bounds using a linear programming analysis, and allows for a seamless integration of general positive-definite terminal cost functions in the analysis. The practical applicability of the derived theoretical results is demonstrated with numerical examples.