Stochastic Adaptive Estimation and Control

本研究涉及随机自适应估计与控制领域的几个基本问题。自适应控制问题（包含估计）是设计一个反馈控制器（算法），当过程模型包含未知（由于建模困难）或变化（由于磨损，温度变化等）参数时，最小化给定的性能标准或跟踪某些给定的参考信号。反馈回路中的自适应控制算法试图通过在线参数估计来主动降低参数的不确定性，然后使用这些更新的估计来不断地重新配置或重新调整控制器。提出的研究代表了非线性和/或涉及不完全状态观测的系统的自适应估计和控制的创新方法。正在考虑的问题比迄今已解决的问题更困难。特别是，这项研究应该导致对具有不完全观测值的马尔可夫链的自适应估计和控制的深入理解；这些问题出现在计算机通信网络的控制中，以及工业过程的质量控制、维护、更换和维修中。对随机双线性系统的自适应控制进行了深入的研究；这种动态系统包含状态和控制双线性的项。马库斯教授以他在随机控制方面的研究而闻名。德克萨斯大学奥斯汀分校为该项目提供了良好的研究环境。该奖项更新了以前由NSF资助的研究ECS-8412100。

This research concerns several basic problems in the area of stochastic adaptive estimation and control. The adaptive control problem (with estimation incorporated) is that of designing a feedback controller (algorithm) which minimizes a given performance criterion or tracks some given reference signal when the process model contains unknown (due to modeling difficulties) or changing (due to wear, temperature variations, etc.) parameters. The adaptive control algorithm in the feedback loop attempts to actively reduce the parameter uncertainty by performing on line parameter estimation and then using these updated estimates to continuously reconfigure or retune the controller. The proposed research represents innovative approaches toward the adaptive estimation and control of systems which are nonlinear and/or involve incomplete state observations. The problems being considered are more difficult than problems solved to date. In particular, this research should result in a deep understanding of the adaptive estimation and control of Markov chains with incomplete observations; such problems arise in the control of computer communication networks, as well as in quality control, maintenance, replacement, and repair of industrial processes. A thorough investigation of the adaptive control of stochastic bilinear systems is also proposed; such dynamic systems contain terms which are bilinear in the state and the control. Professor Marcus is well known for his work on stochastic control. The University of Texas at Austin provides a fine research environment for this project. This award renews research previously supported under NSF Grant ECS-8412100.