Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

This paper presents a robust adaptive control solution for linear parameter-varying (LPV) systems with unknown input gain and unmatched nonlinear (state- and time-dependent) uncertainties based on the $\mathcal{L}_1$ adaptive control architecture and peak-to-peak gain (PPG) analysis/minimization from robust control. Specifically, we introduce new tools for stability and performance analysis leveraging the PPG bound of an LPV system that is computable using linear matrix inequality (LMI) techniques. A piecewise-constant estimation law is introduced to estimate the lumped uncertainty with quantifiable error bounds, which can be systematically improved by reducing the estimation sampling time. We also present a new approach to attenuate the unmatched uncertainty based on the PPG minimization that is applicable to a broad class of systems with linear nominal dynamics. In addition, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system as compared to the same signals of a virtual reference system that represents the possibly best achievable performance. Under mild assumptions, we prove that the transient performance bounds can be uniformly reduced by decreasing the estimation sampling time, which is subject only to hardware limitations. The theoretical development is validated by extensive simulations on the short-period dynamics of an F-16 aircraft

A path planning and path-following control framework for a general 2-trailer with a car-like tractor

Maneuvering a general 2-trailer with a car-like tractor in backward motion is a task that requires significant skill to master and is unarguably one of the most complicated tasks a truck driver has to perform. This paper presents a path planning and path-following control solution that can be used to automatically plan and execute difficult parking and obstacle avoidance maneuvers by combining backward and forward motion. A lattice-based path planning framework is developed in order to generate kinematically feasible and collision-free paths and a path-following controller is designed to stabilize the lateral and angular path-following error states during path execution. To estimate the vehicle state needed for control, a nonlinear observer is developed which only utilizes information from sensors that are mounted on the car-like tractor, making the system independent of additional trailer sensors. The proposed path planning and path-following control framework is implemented on a full-scale test vehicle and results from simulations and real-world experiments are presented.Comment: Preprin