There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

/pdf/higher-order-sliding-modes-differentiation-and-output-438zdzb0ld.pdf

Higher-order sliding modes, differentiation and output-feedback control

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

In this paper, the use of a class of robust control technique as a tool to compute the robustness margin for a closed loop multi-agent system is discussed. Our approach is based on a leader/follower structure of the multiple robot systems. It is shown that, for multiple agent system with cyclic, chain and balanced topology of information exchange, the result is achieved. A Lyapunov based robust control design for coordination and trajectory tracking of multiple agent systems with parametric uncertainty is presented. The results are illustrated with examples and simulations.

Robustness Margin for Leader-based Multi-agent Consensus Systems in Presence of Parametric Uncertainty

In this chapter, various results concerning the stability of dissipative systems are presented. First, the input/output properties of several feedback interconnections of passive, negative imaginary, maximal monotone systems are reviewed. Large-scale systems are briefly treated. Then the conditions under which storage functions are Lyapunov functions are given in detail. Results on stabilization, equivalence to a passive system, input-to-state stability, and passivity of linear delay systems are then provided. The chapter ends with an introduction to \(H_{\infty }\) theory for nonlinear systems that is related to a specific dissipativity property, and with a section on Popov’s hyperstability.

Stability of Dissipative Systems

This paper presents a novel autonomous take-off and landing approach which uses a discrete-time finite-horizon suboptimal nonlinear control strategy to achieve a smooth landing on specific colored platform. By color-based tracking we can improve the performance of the position landing by correcting the position given by the GPS. The signal of the GPS is not always reliable since the accuracy strongly depends on the environment situation and the correction by vision servoing is then necessary. Experimental results using the proposed approach show a better performance than those where the GPS signal is only used to perform the take-off and landing tasks in a completely autonomous way in presence of wind gusts.

Rogelio Lozano

Papers

Robustness Margin for Leader-based Multi-agent Consensus Systems in Presence of Parametric Uncertainty

Stability of Dissipative Systems

Autonomous take-off and landing on a colored platform

Control Strategy using vision for the stabilization of the PVTOL aircraft

Toward Vision‐Based Coordination of Quadrotor Platoons