Title :
ℓ∞ worst-case optimal estimators for switched ARX systems
Author :
Cheng, Yuan Bing ; Wang, Yannan ; Sznaier, M.
Author_Institution :
Dept. of Electr. & Comput. Eng., Northeastern Univ., Boston, MA, USA
Abstract :
This paper considers the problem of worst-case estimation for switched piecewise linear models, in cases where the mode-variable is not directly observable. Our main result shows that worst case point wise optimal estimators can be designed by solving a constrained polynomial optimization problem. In turn, this problem can be relaxed to a sequence of convex optimizations by exploiting recent results on moments-based semi-algebraic optimization. Theoretical results are provided showing that this approach is guaranteed to find the optimal filter in a finite number of steps, bounded above by a constant that depends only on the number of data points available and the parameters of the model. Finally, we briefly show how to extend these results to accommodate parametric uncertainty.
Keywords :
autoregressive processes; optimisation; piecewise linear techniques; time-varying systems; ℓ∞ worst-case optimal estimator; constrained polynomial optimization problem; convex optimization; moments-based semialgebraic optimization; optimal filter; parametric uncertainty; switched ARX system; switched piecewise linear model; Estimation; Noise; Noise measurement; Optimization; Polynomials; Switches; Uncertainty;
Conference_Titel :
Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on
Conference_Location :
Firenze
Print_ISBN :
978-1-4673-5714-2
DOI :
10.1109/CDC.2013.6760507