1,721,062 research outputs found
A counterexample to the uniqueness of the asymptotic estimate in ARMAX model identification via the correlation approach
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A simulation-based approach to the approximation of stochastic hybrid systems
No full textWe study the problem of approximating a stochastic, possibly hybrid, system by means of some abstracted model to the purpose of simplifying the analysis of properties such as probabilistic safety and reachability. We suppose that the property to be analyzed depends on the behavior of some output signal of the system and that the model is designed in order to reproduce that signal as close as possible, for the different possible realizations of the stochastic input affecting the system. The idea developed in this paper is to assess the quality of a model as an approximation of a stochastic system by testing how close are their output signals over a finite number of input realizations. Under suitable assumptions, we show that, with high confidence, the quality assessed on a few input realizations is guaranteed to hold also for all the unseen ones except for a set of pre-defined probability epsilon. The proposed approach can be applied to an arbitrary system, the only requirement being to be able to run multiple simulations of its behavior for different input realizations
The exact feasibility of randomized solutions of robust convex programs
No full textMany optimization problems are naturally delivered in an uncertain framework, and one would like to exercise prudence against the uncertainty elements present in the problem. In previous contributions, it has been shown that solutions to uncertain convex programs that bear a high probability to satisfy uncertain constraints can be obtained at low computational cost through constraint randomization. In this paper, we establish new feasibility results for randomized algorithms. Specifically, the exact feasibility for the class of the so-called fully-supported problems is obtained. It turns out that all fully-supported problems share the same feasibility properties, revealing a deep
kinship among problems of this class. It is further proven that the feasibility of the randomized solutions for all other convex programs can be bounded based on the feasibility for the prototype class of fully-supported problems. The feasibility result of this paper outperforms previous bounds and is not improvable because it is exact for fully-supported problems
New results on the asymptotic theory of system identification for the assessment of the quality of estimated models
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