The Problem of Measurement Output Control under Set-membership Uncertainty

集合成员不确定性下的测量输出控制问题

• 批准号: 0807771
• 负责人: Pravin Varaiya
• 金额: $ 20万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0807771&HistoricalAwards=false
• 关键词: Problem; Measurement; Output; Control; under

A key problem of control theory is to construct feedback control laws based on available data and to determine how the level of uncertainty in the model and in the information arriving on-line, through noisy measurements, would affect the system performance. In the absence of statistical description such problems of Measurement Output Feedback Control (MOFC) were investigated mostly within the H(inf) setting, with soft-type integral costs, while problems with hard bounds on the unknowns were less developed. The present proposal is aimed to produce a fairly complete investigation of the problem of output feedback control constructed through available measurements under unknown but bounded disturbances subject to hard bounds on the uncertain items. The proposal covers topics from basic theoretical problems to computational methods. The novelty of the suggested solution schemes, applicable to nonlinear systems, with greater specifics for the linear case, lies in the combination of dynamic programming, set-valued analysis and minmax approaches. It is well understood that the overall problem under consideration is a combination of two ? a finite-dimensional problem of guaranteed state estimation and an infinite-dimensional problem of feedback control under set-membership uncertainty. The second problem is especially difficult to formalize and solve. In the proposed solution, based on earlier work, the aim is to reduce the second problem to a finite-dimensional one, which would facilitate calculation. For systems with linear structure and convex constraints the computational procedure is to be based on using and also generalizing the ellipsoidal calculus which proved effective for many problems and allows development of complementary software. It is expected that such approach will produce solutions "to the end," with illuminating examples. For the nonlinear case calculations may be facilitated by using the specifics of the problem and applying modifications of the earlier suggested comparison principles that allow one to relax the original equations or variational inequalities of the Hamilton-Jacobi type through simpler, finite-dimensional relations.The Measurement Output Feedback Control (MOFC) problem has been thoroughly studied in a stochastic setting as a combination of stochastic filtering theory within the theory of stochastic control. However a considerable number of problems in control design have to deal with systems subjected to information conditions that are other than stochastic. Such problems of MOFC are increasingly motivated by applied issues, given the progress in design of high-tech complex systems arising in automation, navigation and the cyber-physical field (including hybrid, impulsive, time-lag, multi-agent, communication-oriented processes and the like). They naturally require new techniques, new types of models and their mathematical formalization, as well as new numerical methods, algorithms and software. The present project is designed in response to the indicated demand.

控制理论的一个关键问题是根据可用数据构建反馈控制律，并通过噪声测量确定模型和在线信息中的不确定性水平如何影响系统性能。在缺乏统计描述的情况下，此类测量输出反馈控制（MOFC）问题主要在H（inf）设置内进行研究，具有软型积分成本，而具有硬界的未知问题较少发展。本文的目的是对在未知但有界干扰下的输出反馈控制问题进行较为完整的研究。该提案涵盖了从基本理论问题到计算方法的主题。建议的解决方案的新颖性，适用于非线性系统，更具体的线性情况下，在于动态规划，集值分析和极小极大方法的结合。众所周知，所考虑的整体问题是两个问题的结合。一个有限维的保证状态估计问题和一个集隶属度不确定性下的无限维反馈控制问题。第二个问题尤其难以形式化和解决。在提出的解决方案中，基于早期的工作，其目的是将第二个问题减少到一个有限维的问题，这将有助于计算。对于具有线性结构和凸约束的系统，计算过程基于椭球微积分的使用和推广，椭球微积分被证明对许多问题是有效的，并且允许开发补充软件。预计这种方法将产生“最终”的解决方案，并提供具有启发性的示例。对于非线性情况，可以通过使用问题的特殊性和应用先前建议的比较原则的修改来方便计算，这些比较原则允许人们通过更简单的有限维关系放宽原始方程或汉密尔顿-雅可比型的变分不等式。作为随机控制理论中的随机滤波理论的结合，测量输出反馈控制（MOFC）问题在随机环境下得到了深入的研究。然而，控制设计中有相当多的问题必须处理受非随机信息条件影响的系统。随着自动化、导航和信息物理领域（包括混合、脉冲、时滞、多智能体、面向通信的过程等）高科技复杂系统设计的进步，MOFC的这些问题越来越多地受到应用问题的推动。它们自然需要新技术、新类型的模型及其数学形式化，以及新的数值方法、算法和软件。目前的项目是针对上述需求而设计的。