arXiv subjects

Daniel E. Miller

Publications and source records attributed to Daniel E. Miller.

3 recordsLinked to original sources

arXiv2022

A Convolution Bound Implies Tolerance to Time-variations and Unmodelled Dynamics

Recently it has been shown, in several settings, how to carry out adaptive control for an LTI plant so that a convolution bound holds on the closed-loop behavior; this, in turn, has been leveraged to prove robustness of the closed-loop system to time-varying parameters and unmodelled dynamics. The goal of this paper is to show that the same is true for a large class of finite-dimensional, nonlinear plant and controller combinations.

math.OC↗

arXiv2021

Model Reference Adaptive Control with Linear-like Closed-loop Behavior

It is typically proven in adaptive control that asymptotic stabilization and tracking holds, and that at best a bounded-noise bounded-state property is proven. Recently, it has been shown in both the pole-placement control and the $d$-step ahead control settings that if, as part of the adaptive controller, a parameter estimator based on the original projection algorithm is used and the parameter estimates are restricted to a convex set, then the closed-loop system experiences linear-like behavior: exponential stability, a bounded gain on the noise in every $p$-norm, and a convolution bound on the exogenous inputs; this can be leveraged to provide tolerance to unmodelled dynamics and plant parameter time-variation. In this paper, we extend the approach to the more general Model Reference Adaptive Control (MRAC) problem and demonstrate that we achieve the same desirable linear-like closed-loop properties.

eess.SY↗

arXiv2017

Classical Discrete-Time Adaptive Control Revisited: Exponential Stabilization

Classical discrete-time adaptive controllers provide asymptotic stabilization. While the original adaptive controllers did not handle noise or unmodelled dynamics well, redesigned versions were proven to have some tolerance; however, exponential stabilization and a bounded gain on the noise was rarely proven. Here we consider a classical pole placement adaptive controller using the original projection algorithm rather than the commonly modifed version; we impose the assumption that the plant parameters lie in a convex, compact set and that the parameter estimates are projected onto that set at every step. We demonstrate that the closed-loop system exhibits very desireable closed-loop behaviour: there are linear-like convolution bounds on the closed loop behaviour, which implies exponential stability and a bounded noise gain, as well an easily proven tolerance to unmodelled dynamics and plant parameter variation. We emphasize that there is no persistent excitation requirement of any sort.

math.OC↗