Leonid Fridman

Bio: Leonid Fridman is an academic researcher from National Autonomous University of Mexico. The author has contributed to research in topics: Sliding mode control & Observer (quantum physics). The author has an hindex of 60, co-authored 569 publications receiving 16927 citations. Previous affiliations of Leonid Fridman include university of lille & Instituto Politécnico Nacional.

Sliding Mode Control and Observation

Abstract: The sliding mode control methodology has proven effective in dealing with complex dynamical systems affected by disturbances, uncertainties and unmodeled dynamics. Robust control technology based on this methodology has been applied to many real-world problems, especially in the areas of aerospace control, electric power systems, electromechanical systems, and robotics. Sliding Mode Control and Observation represents the first textbook that starts with classical sliding mode control techniques and progresses toward newly developed higher-order sliding mode control and observation algorithms and their applications.The present volume addresses a range of sliding mode control issues, including:*Conventional sliding mode controller and observer design*Second-order sliding mode controllers and differentiators*Frequency domain analysis of conventional and second-order sliding mode controllers*Higher-order sliding mode controllers and differentiators*Higher-order sliding mode observers *Sliding mode disturbance observer based control *Numerous applications, including reusable launch vehicle and satellite formation control, blood glucose regulation, and car steering control are used as case studiesSliding Mode Control and Observation is aimed at graduate students with a basic knowledge of classical control theory and some knowledge of state-space methods and nonlinear systems, while being of interest to a wider audience of graduate students in electrical/mechanical/aerospace engineering and applied mathematics, as well as researchers in electrical, computer, chemical, civil, mechanical, aeronautical, and industrial engineering, applied mathematicians, control engineers, and physicists. Sliding Mode Control and Observation provides the necessary tools for graduate students, researchers and engineers to robustly control complex and uncertain nonlinear dynamical systems. Exercises provided at the end of each chapter make this an ideal text for an advanced coursetaught in control theory.

Second-order sliding-mode observer for mechanical systems

Abstract: The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems. The finite time convergence of the observer is proved. Thus, the observer can be designed independently of the controller. A discrete version of the observer is considered and the corresponding accuracy is estimated.

Higher order sliding modes

Abstract: One of the most important control problems is control under heavy uncertainty conditions. While there are a number of sophisticated methods like adaptation based on identification and observation, or absolute stability methods, the most obvious way to withstand the uncertainty is to keep some constraints by "brutal force". Indeed any strictly kept equality removes one " uncertainty dimension". The most simple way to keep a constraint is to react immediately to any deviation of the system stirring it back to the constraint by a sufficiently energetic effort. Implemented directly, the approach leads to so-called sliding modes, which become main operation modes in the variable structure systems (VSS) [55]. Having proved their high accuracy and robustness with respect to various internal and external disturbances, they also reveal their main drawback: the so-called chattering effect, i.e., dangerous high-frequency vibrations of the controlled system. Such an effect was considered as an obvious intrinsic feature of the very idea of immediate powerful reaction to the minutest deviation from the chosen constraint. Another important feature is proportionality of the maximal deviation from the constraint to the time interval between the measurements (or to the switching delay).

Analysis and design of integral sliding manifolds for systems with unmatched perturbations

Abstract: The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if integral sliding-mode control is to be combined with other methods to further robustify against unmatched perturbations. H/sub /spl infin// is taken as a special case. Simulations support the general analysis and show the effectiveness of this particular combination.

Uniform Robust Exact Differentiator

Abstract: The differentiators based on the Super-Twisting Algorithm (STA) yield finite-time and theoretically exact convergence to the derivative of the input signal, whenever this derivative is Lipschitz. However, the convergence time grows unboundedly when the initial conditions of the differentiation error grow. In this technical note a Uniform Robust Exact Differentiator (URED) is introduced. The URED is based on a STA modification and includes high-degree terms providing finite-time, and exact convergence to the derivative of the input signal, with a convergence time that is bounded by some constant independent of the initial conditions of the differentiation error. Strong Lyapunov functions are used to prove the convergence of the URED.

I and i

Abstract: 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 …

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

Abstract: 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...

Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

Abstract: Two types of nonlinear control algorithms are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.

Adaptive Control

Abstract: This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.