ℓ∞ worst-case optimal estimators for switched ARX systems

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.