Robustness analysis for identification and control of nonlinear systems

Abstract

This thesis concerns two problems of robustness in the modeling and control of nonlinear dynamical systems. First, I examine the problem of selecting a stable nonlinear state-space model whose open-loop simulations are to match experimental data. I provide a family of techniques for addressing this problem based on minimizing convex upper bounds for simulation error over convex sets of stable nonlinear models. I unify and extend existing convex parameterizations of stable models and convex upper bounds. I then provide a detailed analysis which demonstrates that existing methods based on these principles lead to significantly biased model estimates in the presence of output noise. This thesis contains two algorithmic advances to overcome these difficulties. First, I propose a bias removal algorithm based on techniques from the instrumental-variables literature. Second, for the class of state-affine dynamical models, I introduce a family of tighter convex upper bounds for simulation error which naturally lead to an iterative identification scheme. The performance of this scheme is demonstrated on several benchmark experimental data sets from the system identification literature. The second portion of this thesis addresses robustness analysis for trajectory-tracking feedback control applied to nonlinear systems. I introduce a family of numerical methods for computing regions of finite-time invariance (funnels) around solutions of polynomial differential equations. These methods naturally apply to non-autonomous differential equations that arise in closed-loop trajectory-tracking control. The performance of these techniques is analyzed through simulated examples.