Andrea L'Afflitto

Bio: Andrea L'Afflitto is an academic researcher from University of Oklahoma. The author has contributed to research in topics: Lyapunov function & Optimal control. The author has an hindex of 9, co-authored 35 publications receiving 363 citations. Previous affiliations of Andrea L'Afflitto include Georgia Institute of Technology & Virginia Tech.

Finite-Time Stabilization and Optimal Feedback Control

Abstract: Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using continuous Lyapunov functions. In this technical note, we develop a framework for addressing the problem of optimal nonlinear analysis and feedback control for finite-time stability and finite-time stabilization. Finite-time stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that satisfies a differential inequality involving fractional powers. This Lyapunov function can clearly be seen to be the solution to a partial differential equation that corresponds to a steady-state form of the Hamilton-Jacobi-Bellman equation, and hence, guaranteeing both finite-time stability and optimality.

EXPOSE, an Astrobiological Exposure Facility on the International Space Station - from Proposal to Flight

Abstract: Following an European Space Agency announcement of opportunity in 1996 for ”Externally mounted payloads for 1st utilization phase” on the International Space Station (ISS), scientists working in the fields of astrobiology proposed experiments aiming at long-term exposure of a variety of chemical compounds and extremely resistant microorganisms to the hostile space environment. The ESA exposure facility EXPOSE was built and an operations´ concept was prepared. The EXPOSE experiments were developed through an intensive pre-flight experiment verification test program. 12 years later, two sets of astrobiological experiments in two EXPOSE facilities have been successfully launched to the ISS for external exposure for up to 1.5 years. EXPOSE-E, now installed at the balcony of the European Columbus module, was launched in February 2008, while EXPOSE-R took off to the ISS in November 2008 and was installed on the external URM-D platform of the Russian Zvezda module in March 2009.

An Introduction to Nonlinear Robust Control for Unmanned Quadrotor Aircraft: How to Design Control Algorithms for Quadrotors Using Sliding Mode Control and Adaptive Control Techniques [Focus on Education]

Abstract: Quadrotor aircraft are drawing considerable attention for their high mobility and capacity to perform tasks with complete autonomy, while minimizing the costs and risks involved with the direct intervention of human operators. Moreover, several limitations characterizing these rotary-wing unmanned aerial systems (UASs), such as their underactuation, make quadrotors ideal testbeds for innovative theoretical approaches to the problem of controlling mechanical systems. Designing autopilots for autonomous quadrotors is a challenging task, which involves multiple interconnected aspects. Numerous researchers are currently addressing the problem of designing autonomous guidance systems, navigation systems, and control systems for quadrotors. The primary goal of this article is to present an analysis and synthesis of several nonlinear robust control systems for quadrotors, as discussed in “Summary.” First, the article presents and analyzes the equations of motion of quadrotors under three sets of progressively restrictive modeling assumptions: 1) the vehicle’s inertial properties (such as the mass and matrix of inertia) vary in time, 2) the quadrotor’s main frame is a rigid body and the propellers are thin spinning discs, and 3) the pitch and roll angles are small.

Constrained Robust Model Reference Adaptive Control of a Tilt-Rotor Quadcopter Pulling an Unmodeled Cart

Abstract: This article presents an innovative control architecture for tilt-rotor quadcopters with H-configuration transporting unknown, sling payloads. This control architecture leverages on a thorough analysis of the aircraft's equation of motion, which reveals gyroscopic effects that were not fully characterized and were disregarded while synthesizing control algorithms in prior publications. Furthermore, the proposed control architecture employs barrier Lyapunov functions and a novel robust model reference adaptive control law to guarantee a priori user-defined constraints on both the trajectory tracking error and the control input, despite poor information on the aircraft's inertial properties and the presence of unknown, unsteady payloads. Flight tests involving a quadcopter pulling an unmodeled cart by means of a thin rope of unknown length, which is slack at the beginning of the mission, verify the effectiveness of the theoretical results.

Barrier Lyapunov Functions and Constrained Model Reference Adaptive Control

Abstract: In classical model reference adaptive control, the closed-loop system’s ability to track a given reference signal can be tuned by choosing the adaptive rates and parameterizing the solution of an algebraic Lyapunov equation that appears in the adaptive law. The projection operator can be employed to impose user-defined constraints on the adaptive gains. However, using the projection operator and quadratic Lyapunov functions to certify uniform ultimate boundedness of the trajectory tracking error, the bounds on the trajectory tracking error can only be estimated, but not explicitly imposed a priori . In this letter, we provide an adaptive control law for the same class of nonlinear dynamical systems as classical model reference adaptive control. A barrier Lyapunov function guarantees that user-defined constraints on both the trajectory tracking error and the adaptive gains are verified.

Linear systems

Abstract: 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:

Ordinary Differential Equations With Applications

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Singular optimal control problems

Abstract: For the last 30 years the optimization of nonsingular control problems has been an Important part of control engineering, and its mathematical theory is well developed and widely known. On the other hand, singular control problems prove more difficult to analyse and—although necessary conditions for optimality of singular controls have been established over the past decade—It is only recently that sufficient, and necessary and sufficient, conditions have been formulated. The purpose of this book Is to collect together all known results in optimal control theory (as well as appropriate computational methods) which can be applied to the singular problems In optimal control and which up to now have been scattered In numerous journals. Complete and self-contained, the volume begins with an historical survey of singular control problems and leads to the presentation of important, recent results in the field. There are specific real-world applications and the authors discuss those avenues of research which require further Investigation. All those involved In the optimization of dynamical systems will welcome the publication of this book. In addition to advanced students, lecturers and research workers in universities, this will include practising mechanical, chemical and electrical engineers, builders, textile technologists, paper scientists and chemists, and many concerned with non-technical fields such as economics and business management Contents An historical survey of singular control problems Introduction. Singular control in space navigation. Method of Mlele via Green's theorem. Linear systems—quadratic cost Necessary conditions for singular optimal control. Sufficient conditions and necessary and sufficient conditions for optimality. References. Fundamental concepts Introduction. The general optimal control problem. The first variation of J. The second variation of J. A singular control problem. References. Necessary conditions for singular optimal control Introduction. The generalized Legendre-Clebsch condition. Jacobson's necessary condition. References. Sufficient conditions and necessary and sufficient conditions tor non-negativity of nonsingular and singular second variations Introduction. Preliminaries. The nonsingular case. Strong positivlty and the totally singular second variation. A general sufficiency theorem for the second variation. Necessary and sufficient conditions for non-negativity of the totally singular second variation. Necessary conditions for optimality. Other necessary and sufficient conditions. Sufficient conditions for a weak local minimum. Existence conditions for the matrix Rlccati differential equation. Conclusion. References. Computational methods for singular control problems Introduction. Computational application of the sufficiency conditions of theorems in the previous chapter. Computation of optimal singular controls. Joining of optimal singular and non-singular sub-arcs. Conclusion. References. Conclusion The Importance of singular optimal control problems. Necessary conditions. Necessary and sufficient conditions. Computational methods. Switching conditions. Outlook for the future Author index. Sublect index.