Computational Methods of Nonlinear Control and Systems Identification

在本项目中，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，将辨识和控制统一起来。在非线性控制领域，重点将放在为限制分析和设计问题复杂性的非线性系统开发计算工具上。 我们将建立在我们以前的工作，重点是找到适当的控制李雅普诺夫函数（LFS）的类准线性参数变化系统，以获得系统的工具，实现更雄心勃勃的性能目标。 我们还将进一步探索神经动力学规划领域，以研究真实的时间计算控制器的潜力，以及获得适当的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。在系统识别领域，我们建议建立在我们以前的工作，以开发一个完整的理论来识别可能复杂的系统的简单模型。 这个理论应该提供可计算的算法与相关的非保守误差界，实验输入，并估计准确识别的样本复杂性。 我们建议扩展我们以前的工作，以处理更大的一类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一个很好的折衷，这在量化反馈系统的性能方面是非常必要的

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