Probabilistic robustness: an RLC circuit realization of the truncation phenomenon

Abstract

A recently developed new paradigm for probabilistic robustness analysis does not require apriori information about the underlying distribution function for the uncertain parameters; only ai mild monotonicity and symme try assumption is involilred. The starting point is exactly the same as in classical robustness theory -a system with uncertain parameters which are only known within given bounds. However, instead of calculating the classical robustness margin for such a system, a risk-adjusted margin is sought. The theory suggests that the "best" way to sample the uncertain parameters is not necessarily the most intuitive way. That is, the sampling distribution to use is riot something obvious such as a normal or uniform distribution. The main objective of this paper is to demonstrate that these "counterintuitive" predictions of the theory are not just mathematical possibilities but actually admit physical realizations.

Distributionally Robust Monte Carlo Simulation: A Tutorial Survey

“…The reader interested in more mathematical detail than that provided here may consult some of the underlying references such as [2], [3], [26], [27], [29] and [30].…”

“…Namely, one simply performs the simulation using uniform That is, in the example below, taken from [30], the Truncation Principle leads to sampling over a subinterval of the range of q i whereas a classical Monte Carlo analysis typically dictates sampling over the entire range of parameter variation. Subsequently, the two methods may lead to dramatically different assessments of performance.…”

“…The RLC circuit of [30] is now studied with random parameters corresponding to independent uncertainties in the interstage capacitors C 1 and C 2 ; see Figure 6. The amplifier has fixed parameters R 1 = 1000, R 2 = 100, L = 0.01 and uncertain parameters 0.755 × 10…”

A universal figure of merit for stochastic first order filters

“…the performance limits which are obtained apply for an entire family of probability distributions F rather than a single assumed distribution .f E F. It often turns out to be the case that this new approach leads to probabilistic assessments of performance which differ considerably from the ones! obtained in a more classical Monte Carlo setting; for example, see [7] for an illustration in the context of circuits. To motivate the problem under consideration, we consider the simple circuit in Figure 1.0.1 below.…”

“…The problem considered in this paper is motivated by a new line of research involving Monte Carlo analysis of electrical circuits; e.g., see [5], [7] and [SI. In contrast to more classical Monte Carlo approaches to simulation such as in [ I ] - [4].…”