Sum-of-Squares Data-driven Robustly Stabilizing and Contracting Controller Synthesis for Polynomial Nonlinear Systems

This work presents a computationally efficient approach to data-driven robust contracting controller synthesis for polynomial control-affine systems based on a sum-of-squares program. In particular, we consider the case in which a system alternates between periods of high-quality sensor data and low-quality sensor data. In the high-quality sensor data regime, we focus on robust system identification based on the data informativity framework. In low-quality sensor data regimes we employ a robustly contracting controller that is synthesized online by solving a sum-of-squares program based on data acquired in the high-quality regime, so as to limit state deviation until high-quality data is available. This approach is motivated by real-life control applications in which systems experience periodic data blackouts or occlusion, such as autonomous vehicles undergoing loss of GPS signal or solar glare in machine vision systems. We apply our approach to a planar unmanned aerial vehicle model subject to an unknown wind field, demonstrating its uses for verifiably tight control on trajectory deviation.