Paper Info
Title
Convex Certificates for Model (In)validation of Switched Affine Systems With Unknown Switches
Abstract
Checking validity of a model is a crucial step in the process of system identification. This is especially true when dealing with switched affine systems since, in this case, the problem of system identification from noisy data is known to be generically NP-Hard and can only be solved in practice by using heuristics and relaxations. Therefore, before the identified models can be used for instance for controller design, they should be systematically validated against additional experimental data. In this paper we address the problem of model (in)validation for multi-input multi-output switched affine systems in output error form with unknown switches. As a first step, we prove that necessary and sufficient invalidation certificates can be obtained by solving a sequence of convex optimization problems. In principle, these problems involve increasingly large matrices. However, as we show in the paper by exploiting recent results from semialgebraic geometry, the proposed algorithm is guaranteed to stop after a finite number of steps that can be be explicitly computed from the a priori information. In addition, this algorithm exploits the sparse structure of the underlying optimization problem to substantially reduce the computational burden. The effectiveness of the proposed method is illustrated using both academic examples and a non-trivial problem arising in computer vision: activity monitoring.
Year
DOI
Venue
2014
10.1109/TAC.2014.2351714
Automatic Control, IEEE Transactions  
Keywords
Field
DocType
MIMO systems,affine transforms,control system synthesis,convex programming,time-varying systems,activity monitoring,computer vision,controller design,convex certificates,convex optimization problems,model validation,multiinput multioutput switched affine systems,necessary invalidation certificates,noisy data,semialgebraic geometry,sparse structure,sufficient invalidation certificates,system identification,unknown switches,Convex relaxations,hybrid systems,model validation,switched affine systems
Affine transformation,Data modeling,Mathematical optimization,Control theory,A priori and a posteriori,Heuristics,System identification,Convex optimization,Hybrid system,Optimization problem,Mathematics
Journal
Volume
Issue
ISSN
59
11
0018-9286
Citations 
PageRank 
References 
5
0.49
18
Authors
3
Name
Order
Citations
PageRank
Necmiye Ozay139041.51
Mario Sznaier265656.66
Constantino M. Lagoa316425.38