Design of a Switching Controller for Adaptive Disturbance Attenuation with Guaranteed Stability

In this paper, a new algorithm is proposed for the design of a family of controllers to be used within an adaptive switching control scheme. The resulting switching controller is able to attenuate the effects of disturbances having uncertain and possibly time-varying characteristics, as well as to ensure stability under arbitrary switching sequences. Specifically, the stability requirement is addressed within the synthesis of the set of controllers by imposing some constraints in LMI form. The overall synthesis algorithm is formulated in terms of convex optimization problems, which can be solved by means of standard tools. The validity of the proposed solution is underlined by showing simulation results on an adaptive optics case study

Switching Control for Adaptive Disturbance Attenuation

The problem of adaptive disturbance attenuation is addressed in this paper using a switching control approach. A finite family of stabilizing controllers is pre-designed, with the assumption that, for any possible operating condition, at least one controller is able to achieve a prescribed level of attenuation. Then, at each time instant, a supervisory unit selects the controller associated with the best potential performance on the basis of suitably defined test functionals. In the paper, we prove some important properties which are satisfied by the test functionals, and analyze the stability of the overall switched system. Simulation results are provided to show the validity of the proposed method as a solution to the problem

A New Approach to Multi-Model Adaptive Control

Adaptive control is an approach used to deal with systems with uncertain or time-varying parameters. A classical adaptive controller typically consists of a linear time-invariant (LTI) control law together with a tuning mechanism which adjusts its parameters. Usually, though not exclusively, discrete-time adaptive controllers provide only asymptotic stability and possibly bounded-noise bounded-state stability; neither exponential stability nor a bounded noise gain is typically proven. Recently it has been shown that if we employ a parameter estimator based on the original Projection Algorithm together with projecting the parameter estimates onto a given compact and convex set, then the adaptive controller guarantees linear-like closed-loop behavior: exponential stability, a bounded noise gain and a convolution bound on the exogenous inputs. In this thesis, the overarching objective is to show that we can prove these same desirable linear-like properties in a wide range of adaptive control problems without the convexity assumption: the main idea is to use multiple estimators and a switching algorithm. Indeed, we show that those properties arise in a surprisingly natural way. We first prove a general result that exponential stability and a convolution bound on the closed-loop behavior can be leveraged to show tolerance to a degree of time-variations and unmodelled dynamics, i.e. such closed-loop properties guarantee robustness. After reviewing the original Projection Algorithm and introducing the reader to our slightly revised version, we turn our attention to controller design, with a focus on a non-convex set of plant uncertainty. As a starting point, we first consider first-order plants incorporating a simple switching algorithm. We then extend the approach to a class of nonlinear plants (which have stable zero dynamics); we consider both cases of convex and non-convex sets of parameter uncertainty. Afterwards, we turn to possibly non-minimum phase LTI plants; first we consider the stabilization problem for which we have two convex sets of uncertainty; then, we turn to the problem of tracking the sum of a finite number of sinusoids of known frequencies subject to an unknown plant order and a general compact set of uncertainty

Adaptive memory in multi-model switching control of uncertain plants

This paper describes some recent results in multi-model switching control. The scheme here considered embeds a finite family of pre-designed controllers and a high-level unit which selects, at each instant of time, the candidate controller to be placed in feedback to the uncertain plant. The study considers a switching strategy where controller selection is based on windowed cost functions. The key feature of the proposed strategy is that the window (the memory) is not kept constant, but, on the contrary, is adjusted on-line, on the grounds of measured data. The potential benefits of using an adaptive memory switching strategy are discussed and illustrated through a benchmark example. (C) 2013 Elsevier Ltd. All rights reserved