Proceedings of the SIAM Conference on Control and Its Applications. SIAM Conference on Control and Its Applications最新文献

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Online Inner Approximation of Reachable Sets of Nonlinear Systems with Diminished Control Authority. 控制权限减小非线性系统可达集的在线内逼近。

Proceedings of the SIAM Conference on Control and Its Applications. SIAM Conference on Control and Its Applications Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976847.2

Hamza El-Kebir, Melkior Ornik

{"title":"Online Inner Approximation of Reachable Sets of Nonlinear Systems with Diminished Control Authority.","authors":"Hamza El-Kebir, Melkior Ornik","doi":"10.1137/1.9781611976847.2","DOIUrl":"https://doi.org/10.1137/1.9781611976847.2","url":null,"abstract":"This work presents a method of efficiently computing inner approximations of forward reachable sets for nonlinear control systems with diminished control authority, given an a priori computed reachable set for the nominal system. The method functions by shrinking a precomputed convex reachable set based on a priori knowledge of the system's trajectory deviation growth dynamics. The trajectory deviation growth dynamics determine an upper bound on the minimal deviation between two trajectories emanating from the same point that are generated by control inputs from the nominal and diminished set of control inputs, respectively. These growth dynamics are a function of a given Hausdorff distance bound between the nominal convex space of admissible controls and the possibly unknown impaired space of admissible controls. Because of its relative computational efficiency compared to direct computation of the off-nominal reachable set, this procedure can be applied to onboard fault-tolerant path planning and failure recovery. We consider the implementation of the approximation procedure by way of numerical integration and a root finding scheme, and we present two illustrative examples, namely an application to a control system with quadratic nonlinearities and aircraft wing rock dynamics.","PeriodicalId":93490,"journal":{"name":"Proceedings of the SIAM Conference on Control and Its Applications. SIAM Conference on Control and Its Applications","volume":"2021 ","pages":"9-16"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8780881/pdf/nihms-1765290.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39730711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Quantitative Resilience of Linear Driftless Systems. 线性无漂移系统的定量复原力。

Proceedings of the SIAM Conference on Control and Its Applications. SIAM Conference on Control and Its Applications Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976847.5

Jean-Baptiste Bouvier, Kathleen Xu, Melkior Ornik

{"title":"Quantitative Resilience of Linear Driftless Systems.","authors":"Jean-Baptiste Bouvier, Kathleen Xu, Melkior Ornik","doi":"10.1137/1.9781611976847.5","DOIUrl":"10.1137/1.9781611976847.5","url":null,"abstract":"This paper introduces the notion of quantitative resilience of a control system. Following prior work, we study linear driftless systems enduring a loss of control authority over some of their actuators. Such a malfunction results in actuators producing possibly undesirable inputs over which the controller has real-time readings but no control. By definition, a system is resilient if it can still reach a target after a partial loss of control authority. However, after a malfunction, a resilient system might be significantly slower to reach a target compared to its initial capabilities. We quantify this loss of performance through the new concept of quantitative resilience. We define such a metric as the maximal ratio of the minimal times required to reach any target for the initial and malfunctioning systems. Naïve computation of quantitative resilience directly from the definition is a complex task as it requires solving four nested, possibly nonlinear, optimization problems. The main technical contribution of this work is to provide an efficient method to compute quantitative resilience. Relying on control theory and on two novel geometric results we reduce the computation of quantitative resilience to a single linear optimization problem. We demonstrate our method on an opinion dynamics scenario.","PeriodicalId":93490,"journal":{"name":"Proceedings of the SIAM Conference on Control and Its Applications. SIAM Conference on Control and Its Applications","volume":"2021 ","pages":"32-39"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8782088/pdf/nihms-1765293.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39730712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0