Robust L2–L∞ control of uncertain differential linear repetitive processes

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdFor two-dimensional (2-D) systems, information propagates in two independent directions. 2-D systems are known to have both system-theoretical and applications interest, and the so-called linear repetitive processes (LRPs) are a distinct class of 2-D discrete linear systems. This paper is concerned with the problem of L2–L∞ (energy to peak) control for uncertain differential LRPs, where the parameter uncertainties are assumed to be norm-bounded. For an unstable LRP, our attention is focused on the design of an L2–L∞ static state feedback controller and an L2–L∞ dynamic output feedback controller, both of which guarantee the corresponding closed-loop LRPs to be stable along the pass and have a prescribed L2–L∞ performance. Sufficient conditions for the existence of such L2–L∞ controllers are proposed in terms of linear matrix inequalities (LMIs). The desired L2–L∞ dynamic output feedback controller can be found by solving a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

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