Computational Methods of Nonlinear Control and Systems Identification

在这个项目中，我们计划在非线性控制和系统辨识方面进行研究。我们的目标是以统一的方式提供分析和设计系统的计算方法。在非线性控制领域，重点将放在为一类非线性系统开发计算工具，以限制分析和设计问题的复杂性。我们将在以前工作的基础上，为这类拟线性参数变化系统寻找合适的控制李雅普诺夫函数(LFS)，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(带逻辑的混合连续动态)的类别。在系统辨识方面，我们建议在以前工作的基础上，建立一个完整的理论来辨识可能复杂系统的简单模型。这一理论应该为精确识别提供相关的非保守误差界、实验输入和样本复杂性估计的可计算算法。我们建议扩展我们以前的工作，以处理更大类的模型参数化以及某些类型的非线性系统。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一种很好的折衷，这在量化反馈系统的性能时是非常重要的。

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