2017/05/03 by Daniel E. Miller, Miller, Daniel E. · 1 citation
Engineering · #Adaptive Control of Nonlinear Systems #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1705.01494
openalex publication_date 2017/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Classical discrete-time adaptive controllers provide asymptotic\nstabilization. While the original adaptive controllers did not handle noise or\nunmodelled dynamics well, redesigned versions were proven to have some\ntolerance; however, exponential stabilization and a bounded gain on the noise\nwas rarely proven. Here we consider a classical pole placement adaptive\ncontroller using the original projection algorithm rather than the commonly\nmodifed version; we impose the assumption that the plant parameters lie in a\nconvex, compact set and that the parameter estimates are projected onto that\nset at every step. We demonstrate that the closed-loop system exhibits very\ndesireable closed-loop behaviour: there are linear-like convolution bounds on\nthe closed loop behaviour, which implies exponential stability and a bounded\nnoise gain, as well an easily proven tolerance to unmodelled dynamics and plant\nparameter variation. We emphasize that there is no persistent excitation\nrequirement of any sort.\n