Robust Control Design and Analysis Based on Lifting Linearization of Nonlinear Systems Under Uncertain Initial Conditions

This paper presents a robust control synthesis and analysis framework for nonlinear systems with uncertain initial conditions. First, a deep learning-based lifting approach is proposed to approximate nonlinear dynamical systems with linear parameter-varying (LPV) state-space models in higher-dimensional spaces while simultaneously characterizing the uncertain initial states within the lifted state space. Then, convex synthesis conditions are provided to generate full-state feedback nonstationary LPV (NSLPV) controllers for the lifted LPV system. A performance measure similar to the l2-induced norm is used to provide robust performance guarantees in the presence of exogenous disturbances and uncertain initial conditions. The paper also includes results for synthesizing full-state feedback linear time-invariant controllers and output feedback NSLPV controllers. Additionally, a robustness analysis approach based on integral quadratic constraint (IQC) theory is developed to analyze and tune the synthesized controllers while accounting for noise associated with state measurements. This analysis approach characterizes model parameters and disturbance inputs using IQCs to reduce conservatism. Finally, the effectiveness of the proposed framework is demonstrated through two illustrative examples.