Time-delay systems: an overview of some recent advances and open problems

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Feedback systems: Input-output properties

A geometric formulation of Beard's failure detection filter problem is stated using the concepts of (C, A) -invariant and unobservability subspaces. The notions of output separable and mutually detectable families of subspaces introduced by Beard are also clarified. It is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum. Moreover, it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions. Finally, the complete duality between a generalization of Beard's detection filter problem and the restricted control decoupling problem is illustrated.

A geometric approach to the synthesis of failure detection filters

This paper presents an advanced driver assistance system (ADAS) for lane keeping, together with an analysis of its performance and stability with respect to variations in driver behavior. The automotive ADAS proposed is designed to share control of the steering wheel with the driver in the best possible way. Its development was derived from an H2-Preview optimization control problem, which is based on a global driver-vehicle-road (DVR) system. The DVR model makes use of a cybernetic driver model to take into account any driver-vehicle interactions. Such a formulation allows 1) considering driver assistance cooperation criteria in the control synthesis, 2) improving the performance of the assistance as a cooperative copilot, and 3) analyzing the stability of the whole system in the presence of driver model uncertainty. The results have been experimentally validated with one participant using a fixed-base driving simulator. The developed assistance system improved lane-keeping performance and reduced the risk of a lane departure accident. Good results were obtained using several criteria for human-machine cooperation. Poor stability situations were successfully avoided due to the robustness of the whole system, in spite of a large range of driver model uncertainty.

Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty

We study the problems raised by the implementation of a control law including distributed-delay, i.e. a finite integral over the time, such as /spl int//sub 0//sup 1/ x(t-/spl tau/)d/spl tau/. These delays appear in control laws allowing the finite spectrum assignment for time-delay systems, but cannot be exactly implemented on a digital computer. We study some problems that arise when using numerical quadrature methods to implement such control laws.

Some problems arising in the implementation of distributed-delay control laws

The aim of this paper is to introduce a new list of integers which is invariant under the action of biproper compensation and which plays a key role in the solution of the row-by-row decoupling problem. Several equivalent characterizations are provided within both the geometric and the transfer matrix approaches.

New decoupling invariants: the essential orders

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac11-proceedings/data/html/papers/2349.pdf

Jean-François Lafay

Papers

Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty

Some problems arising in the implementation of distributed-delay control laws

New decoupling invariants: the essential orders

Human-Like Cybernetic Driver Model for Lane Keeping

Memory-resilient gain-scheduled state-feedback control of uncertain LTI/LPV systems with time-varying delays