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

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

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.

https://hal.inria.fr/hal-00757561/document

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

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.

Adaptive Control

Stability analysis is developed for uncertain nonlinear switched systems. While being asymptotically stable and homogeneous of degree q < 0, these systems are shown to approach the equilibrium point in finite time. Restricted to second order systems, this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations. Based on this fundamental property, switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m-vector relative degree (2,...,2)T. The controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. The proposed synthesis procedure is illustrated via application to a friction servo-motor.

Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems

Mathematical Tools.- Mathematical Models.- Stability Analysis.- Finite-time Stability of Uncertain Homogeneous and Quasihomogeneous Systems.- Synthesis.- Quasihomogeneous Design.- Unit Feedback Design.- Disturbance Attenuation via Nonsmooth ??-design.- Unit Feedback Control of Infinite-dimensional Systems.- Global Asymptotic Stabilization of Uncertain Linear Systems.- Asymptotic Stabilization of Minimum-phase Semilinear Systems.- Global Asymptotic Stabilization of Uncertain Time-delay Systems.- Electromechanical Applications.- Local Nonsmooth ??-synthesis Under Friction/Backlash Phenomena.- Quasihomogeneous Stabilization of Fully Actuated Systems with Dry Friction.- Hybrid Control of Underactuated Manipulators with Frictional Joints.

Discontinuous Systems: Lyapunov Analysis and Robust Synthesis under Uncertainty Conditions

Brief paper: Exponential stability of linear distributed parameter systems with time-varying delays

In this paper, a novel discrete-time implementation of sliding-mode control systems is proposed, which fully exploits the multivaluedness of the dynamics on the sliding surface. It is shown to guarantee a smooth stabilization on the discrete sliding surface in the disturbance-free case, hence avoiding the chattering effects due to the time-discretization. In addition, when a disturbance acts on the system, the controller attenuates the disturbance effects on the sliding surface by a factor h (where h is the sampling period). Most importantly, this holds even for large h . The controller is based on an implicit Euler method and is very easy to implement with projections on the interval [-1, 1] (or as the solution of a quadratic program). The zero-order-hold (ZOH) method is also investigated. First- and second-order perturbed systems (with a disturbance satisfying the matching condition) without and with dynamical disturbance compensation are analyzed, with classical and twisting sliding-mode controllers.

/pdf/chattering-free-digital-sliding-mode-control-with-state-af3lzcfy08.pdf

Yury Orlov

Papers

Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems

Discontinuous Systems: Lyapunov Analysis and Robust Synthesis under Uncertainty Conditions

Brief paper: Exponential stability of linear distributed parameter systems with time-varying delays

Chattering-Free Digital Sliding-Mode Control With State Observer and Disturbance Rejection

Brief paper: An LMI approach to H ∞ boundary control of semilinear parabolic and hyperbolic systems