KEYWORDS: Monte Carlo methods, Statistical analysis, Computing systems, Engineering, Control systems, Biological samples, Systems modeling, Stochastic processes, Dynamical systems, Tolerancing
The average performance of uncertain dynamic discrete-event systems remains a persistent concern in the field of control engineering. In this paper, we propose to use a Monte Carlo method to analyze uncertain systems by determining whether their average performance exceeds an acceptable level. Specifically, we formulate the performance analysis as a problem of statistical hypothesis testing of mean values. Using a mean-preserving transform, we convert this problem into one of statistical hypothesis testing of probabilities, which can be solved using our adaptive Monte Carlo test. This test is based on Wald’s sequential probability ratio (SPRT). We demonstrate the applicability of our method by investigating the average performance of a control system with parametric uncertainty.
KEYWORDS: Monte Carlo methods, Statistical analysis, Dynamical systems, Control systems, Computing systems, Stochastic processes, Computer simulations, Tolerancing, Systems modeling, Tin
The analysis of uncertain dynamic discrete-event systems is generally intractable by deterministic numeric methods. In this paper, we propose an adaptive Monte Carlo test method to analyze systems. In contrast to the conventional methods of estimating the probability that a system fails to satisfy prespecified requirements, our goal is to determine whether the probability that the system violates the requirements. To accomplish this goal, we exploit a testing method based on the sequential probability ratio (SPRT) method invented by Wald. We demonstrate that such method can result in a substantial reduction of computational complexity as compared to conventional methods. To make the test method rigorous, we develop exact methods for computing the probability of making wrong decisions and the average number of simulations runs. The proposed method can be applied to investigate the stability of a control system with parametric uncertainty.
KEYWORDS: Computer simulations, Error control coding, Error analysis, Monte Carlo methods, Genetic algorithms, Evolutionary algorithms, Control systems design, Control systems, Systems modeling, Computing systems
In this paper develop a novel, quantitative, rigorous and efficient method for risk minimization for control and decision under uncertainty. The crucial components of our approach include a rigorous, efficient risk evaluation method and a stochastic optimization technique. The risk evaluation method is an adaptive Monte Carlo estimation method which is derived from the concept of relative entropy and truncated inverse binomial sampling. The stochastic optimization technique is built upon evolutionary computing methods such as genetic algorithms, where the fitness function is constructed from the adaptive Monte Carlo estimation method. The effectiveness of the proposed method is demonstrated by its applications to the design of PID controllers for uncertain systems, where the probability of performance violation is minimized.
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