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Robust adaptive model predictive control: Performance and parameter estimation
Author(s) -
Lu Xiaonan,
Can Mark,
KoksalRivet Denis
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5175
Subject(s) - model predictive control , control theory (sociology) , convergence (economics) , estimation theory , bounded function , mathematical optimization , adaptive control , robust control , mathematics , probabilistic logic , set (abstract data type) , computer science , algorithm , control system , control (management) , statistics , artificial intelligence , engineering , mathematical analysis , programming language , economic growth , electrical engineering , economics
Summary For systems with uncertain linear models, bounded additive disturbances and state and control constraints, a robust model predictive control (MPC) algorithm incorporating online model adaptation is proposed. Sets of model parameters are identified online and employed in a robust tube MPC strategy with a nominal cost. The algorithm is shown to be recursively feasible and input‐to‐state stable. Computational tractability is ensured by using polytopic sets of fixed complexity to bound parameter sets and predicted states. Convex conditions for persistence of excitation are derived and are related to probabilistic rates of convergence and asymptotic bounds on parameter set estimates. We discuss how to balance conflicting requirements on control signals for achieving good tracking performance and parameter set estimate accuracy. Conditions for convergence of the estimated parameter set are discussed for the case of fixed complexity parameter set estimates, inexact disturbance bounds, and noisy measurements.