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, we present a trajectory tracking controller design and its implementation on a mini rotorcraft having four rotors. The dynamic model of the four-rotor rotorcraft is obtained via a Lagrange approach. Trajectory generation algorithm is proposed. The proposed controller is based on Lyapunov analysis using nested saturation control algorithm. Global stability analysis of the closed-loop system is presented. Real-time experiments show that the mini-aircraft is able to track satisfactorily the desired trajectory.

Trajectory tracking for a four rotor mini-aircraft

The design of MRAC for achieving independent tracking and regulation objectives with a unique equilibrium point in the controller parameter space is presented. The corresponding schemes can use either an explicit reference model or an implicit reference model. The design is done from a stability point of view by extending an appropriate control configuration used for the case of known plant parameters. The result of the design is a simple control scheme using a linear constant feedforward controller and a non-linear feedback controller. The stability of the system and boundness of various variables do not require any positivity condition. The performances of the control structure in tracking and regulation are evaluated by simulations.

Redesign of explicit and implicit discrete time model reference adaptive control schemes

A path generator is proposed for a fixed-wing Unmaned Aereal Vehicle (UAV). Assuming that the vehicle maintain a constant altitude, and airspeed, and that the UAV is constrained by a turning rate. The Dubins paths serve as a strategy to find the shortest path for the non-holonomic model of the UAV. Dubins paths consist of three path segments which are based on straight lines or arcs of circle of a given radius. The Dubins path generation is combined with a nonlinear Lypaunov-based path-following control. Finally we present a complete simulation environment in which the path generator and path following strategy are validated. As an example of application we propose the scenario in which a missing person is located in some known area and we use the path generator along with this path-following strategy applied to the fixed wing UAV to search and find this person.

/pdf/dubins-path-generation-for-a-fixed-wing-uav-16ozssalyu.pdf

Dubins path generation for a fixed wing UAV

Stabilization and nonlinear control for a novel trirotor mini-aircraft

Presents some sufficient conditions for a linear system with (point or distributed) delay in the state to be passive. Passivity based (memoryless) stabilization of linear delay systems is also addressed. The proposed approach is based on a Lyapunov-Krasovskii functional construction.

Rogelio Lozano

Papers

Trajectory tracking for a four rotor mini-aircraft

Redesign of explicit and implicit discrete time model reference adaptive control schemes

Dubins path generation for a fixed wing UAV

Stabilization and nonlinear control for a novel trirotor mini-aircraft

On the passivity of linear delay systems