{"title":"优化网络传输以最小化状态估计误差和信道使用","authors":"Sayeh Rezaee, César Nieto, Abhyudai Singh","doi":"10.1109/ICSTCC55426.2022.9931801","DOIUrl":null,"url":null,"abstract":"We consider the problem of transmitting the state value of a dynamical system through a communication network. The dynamics of the error in state estimation is modeled using a stochastic hybrid system formalism, where the error grows exponentially over time. Transmission occurs over the network at specific times to acquire the system's state, and whenever a transmission is triggered, the error is reset to a zero-mean random variable. Our goal is to uncover transmission strategies that minimize a combination of the steady-state error variance and the average number of transmissions per unit of time. We found that a constant Poisson rate of transmission results in a heavy-tailed distribution for the estimation error. Next, we consider a random non-threshold transmission rate that varies as a power law of the error. Finally, we explore a threshold-based rate in which transmission occurs exactly when the error reaches a threshold. Our results show that if the error's variance after transmission is small enough, a threshold-based strategy is the optimal paradigm. On the other hand, if this variance is large, and the error does not grow fast enough, the random non-threshold transmission strategy emerges as optimal. These analytical results are verified by simulations of the stochastic hybrid system.","PeriodicalId":220845,"journal":{"name":"2022 26th International Conference on System Theory, Control and Computing (ICSTCC)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Optimal network transmission to minimize state-estimation error and channel usage\",\"authors\":\"Sayeh Rezaee, César Nieto, Abhyudai Singh\",\"doi\":\"10.1109/ICSTCC55426.2022.9931801\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of transmitting the state value of a dynamical system through a communication network. The dynamics of the error in state estimation is modeled using a stochastic hybrid system formalism, where the error grows exponentially over time. Transmission occurs over the network at specific times to acquire the system's state, and whenever a transmission is triggered, the error is reset to a zero-mean random variable. Our goal is to uncover transmission strategies that minimize a combination of the steady-state error variance and the average number of transmissions per unit of time. We found that a constant Poisson rate of transmission results in a heavy-tailed distribution for the estimation error. Next, we consider a random non-threshold transmission rate that varies as a power law of the error. Finally, we explore a threshold-based rate in which transmission occurs exactly when the error reaches a threshold. Our results show that if the error's variance after transmission is small enough, a threshold-based strategy is the optimal paradigm. On the other hand, if this variance is large, and the error does not grow fast enough, the random non-threshold transmission strategy emerges as optimal. These analytical results are verified by simulations of the stochastic hybrid system.\",\"PeriodicalId\":220845,\"journal\":{\"name\":\"2022 26th International Conference on System Theory, Control and Computing (ICSTCC)\",\"volume\":\"33 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2022 26th International Conference on System Theory, Control and Computing (ICSTCC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICSTCC55426.2022.9931801\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2022 26th International Conference on System Theory, Control and Computing (ICSTCC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICSTCC55426.2022.9931801","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Optimal network transmission to minimize state-estimation error and channel usage
We consider the problem of transmitting the state value of a dynamical system through a communication network. The dynamics of the error in state estimation is modeled using a stochastic hybrid system formalism, where the error grows exponentially over time. Transmission occurs over the network at specific times to acquire the system's state, and whenever a transmission is triggered, the error is reset to a zero-mean random variable. Our goal is to uncover transmission strategies that minimize a combination of the steady-state error variance and the average number of transmissions per unit of time. We found that a constant Poisson rate of transmission results in a heavy-tailed distribution for the estimation error. Next, we consider a random non-threshold transmission rate that varies as a power law of the error. Finally, we explore a threshold-based rate in which transmission occurs exactly when the error reaches a threshold. Our results show that if the error's variance after transmission is small enough, a threshold-based strategy is the optimal paradigm. On the other hand, if this variance is large, and the error does not grow fast enough, the random non-threshold transmission strategy emerges as optimal. These analytical results are verified by simulations of the stochastic hybrid system.