Computational Methods of Nonlinear Control and Systems Identification

在这个项目中，我们建议在非线性控制和系统识别领域进行研究。我们的目标是为系统的分析和设计提供计算方法，以统一的方式结合识别和控制。在非线性控制领域，重点将放在开发非线性系统类的计算工具，以限制分析和设计问题的复杂性。我们将在之前的工作的基础上，重点寻找合适的控制李雅普诺夫函数（Lfs），用于类准线性参数变化系统，以获得实现更雄心勃勃的性能目标的系统工具。我们还将进一步探索神经动态规划领域，以研究实时计算控制器的潜力，以及推导适当的clf。我们还建议开发分段线性系统的分析工具，并将其扩展到混合系统（混合连续动态与逻辑）的类别。在系统识别领域，我们建议在之前工作的基础上开发一个完整的理论，用于识别可能复杂的系统的简单模型。该理论应提供可计算的算法与相关的非保守误差界限，实验输入，以及准确识别样本复杂性的估计。我们建议扩展我们以前的工作，以处理更大类别的模型参数化以及某些类别的非线性系统。这种方法将与鲁棒控制方法相结合，并在参数和非参数不确定性之间提供了很好的权衡，这在量化反馈系统的性能时非常重要

In this project, we propose to undertake research in the areas of nonlinear control and system identification. Our objectives is to provide computational methods for analysis and design of systems that incorporates both identification and control in a unified fashion.In the area of nonlinear control, the emphasis will be placed on developing computational tools for classes of nonlinear systems that limit the complexity of the analysis and design problems. We will build on our previous work that focused on finding appropriate control-Lyapunov-functions (Lfs) for the class of quasi-linear-parameter-varying systems to derive systematic tools for achieving more ambitious performance objectives. We will also explore further the area of Neuro-dynamic programming to investigate the potential of computing controllers in real time, as well as deriving appropriate CLFs. We also propose to develop analysis tools for piecewise linear systems and extend that to classes of Hybrid systems (mixed continuous dynamics with logic).In the area of system identification, we propose to build on our previous work to develop a complete theory for identifying simple models of possibly complex systems. This theory should provide computable algorithms with associated non-conservative error bounds, experimental inputs, and estimates of sample complexity for accurate identification. We propose to extend our previous work to handle a larger class of model parametrizations as well as certain classes of nonlinear systems. This approach is will integrated with robust control approaches and provides a nice tradeoff between parametric and non-parametric uncertainty that is quite essential in quantifying the performance of a feedback system