The Problem of Measurement Output Control under Set-membership Uncertainty

控制理论的一个关键问题是根据已有的数据构造反馈控制律，并通过噪声测量确定模型和在线信息中的不确定性程度如何影响系统的性能。在缺乏统计描述的情况下，这类测量输出反馈控制(MOFC)问题的研究大多是在H(Inf)设置下进行的，具有软型积分代价，而关于未知数的硬界问题的研究较少。本文的目的是对未知但有界扰动下的输出反馈控制问题进行比较完整的研究，这些扰动对不确定项具有硬界。该提案涵盖了从基本理论问题到计算方法的各种主题。所提出的解决方案的新颖之处在于结合了动态规划、集值分析和极小极大法，适用于非线性系统，对线性情况有更具体的描述。众所周知，正在考虑的总体问题是两个问题的组合？一个有限维的保状态估计问题和一个无限维的集员不确定性反馈控制问题。第二个问题尤其难以形式化和解决。在提出的解决方案中，在前面工作的基础上，目的是将第二个问题简化为有限维问题，这将便于计算。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，并允许开发补充软件。预计这样的方法将产生“彻底”的解决方案，并提供有启发性的例子。对于非线性情况，可以通过利用问题的具体细节和应用先前提出的比较原理的修改来简化计算，这些比较原理允许人们通过更简单的有限维关系来松弛原始的Hamilton-Jacobi型方程或变分不等式。测量输出反馈控制(MOFC)问题作为随机控制理论中的随机滤波理论的组合在随机环境中得到了深入的研究。然而，在控制设计中有相当多的问题必须处理受信息条件约束的系统，而不是随机的。随着自动化、导航和网络物理领域(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。本项目是为满足所指出的需求而设计的。

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.