scholarly journals Mean-field sparse Jurdjevic–Quinn control

2017 ◽  
Vol 27 (07) ◽  
pp. 1223-1253 ◽  
Author(s):  
Marco Caponigro ◽  
Benedetto Piccoli ◽  
Francesco Rossi ◽  
Emmanuel Trélat
Keyword(s):  
Lyapunov Function ◽  
Control Function ◽  
Kinetic Equations ◽  
Mean Field ◽  
Transport Equations ◽  
Control Law ◽  
Time Varying ◽  
Nonlinear Transport ◽  
Lie Derivatives ◽  
Derivatives Of

We consider nonlinear transport equations with non-local velocity describing the time-evolution of a measure. Such equations often appear when considering the mean-field limit of finite-dimensional systems modeling collective dynamics. We address the problem of controlling these equations by means of a time-varying bounded control action localized on a time-varying control subset of small Lebesgue measure. We first define dissipativity for nonlinear transport equations in terms of Lie derivatives of a Lyapunov function depending on the measure. Then, assuming that the uncontrolled system is dissipative, we provide an explicit construction of a control law steering the system to an invariant sublevel of the Lyapunov function. The control function and the control domain are designed in terms of the Lie derivatives of the Lyapunov function. In this sense the construction can be seen as an infinite-dimensional analogue of the well-known Jurdjevic–Quinn procedure. Moreover, the control law presents sparsity properties in the sense that the support of the control is small. Finally, we show that our result applies to a large class of kinetic equations modeling multi-agent dynamics.

Continuous time-varying feedback control of a robotic manipulator with base vibration and load uncertainty

2020 ◽  
pp. 107754632092759
Author(s):  
Xi Wang ◽  
Baolin Hou
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Continuous Time ◽  
Position Control ◽  
Control Method ◽  
Robotic Manipulator ◽  
Control Law ◽  
Time Varying ◽  
Load Uncertainty ◽  
Feedback Control Method

To solve precise and fast position control of a robotic manipulator with base vibration and load uncertainty, a continuous time-varying feedback control method based on the implicit Lyapunov function is studied. This method is proportional–derivative-like in the form of control law, but its proportional and differential coefficients depend on the system Lyapunov function, which are differentiable functions of system error variables. In the motion process of the robotic manipulator, the system performance is influenced by three main nonlinear factors: system friction, balance torque, and base vibration. As the former two factors are available to be modeled and identified through experiments, compensation of the two terms is added to the proposed control law to reduce the effects of system nonlinearities to a certain extent. Experimental results show that the proposed control strategy is robust to base vibration and load uncertainty. Besides, the compensation of system friction and balance torque can shorten the positioning time by 27.3%, from 1.32 s to 0.96 s. Meanwhile, the positioning precision is guaranteed, which verifies the effectiveness of the proposed control scheme.

Finite-time control of uncertain time-varying systems in p-normal form

2020 ◽  
Author(s):  
Kanya Rattanamongkhonkun ◽  
Radom Pongvuthithum ◽  
Chulin Likasiri
Keyword(s):  
Normal Form ◽  
Finite Time ◽  
Control Law ◽  
Time Varying ◽  
Time Control ◽  
Special Cases ◽  
Time Varying Systems ◽  
A Chain ◽  
Uncertain Time ◽  
Power Integrator

Abstract This paper addresses a finite-time regulation problem for time-varying nonlinear systems in p-normal form. This class of time-varying systems includes a well-known lower-triangular system and a chain of power integrator systems as special cases. No growth condition on time-varying uncertainties is imposed. The control law can guarantee that all closed-loop trajectories are bounded and well defined. Furthermore, all states converge to zero in finite time.

Cooperative Networked Control Based on a Time-Varying Lyapunov Function

2021 ◽  
Vol 32 (3) ◽  
pp. 533-542
Author(s):  
Arturo M. Flores ◽  
Lucas N. Egidio ◽  
Grace S. Deaecto
Keyword(s):  
Lyapunov Function ◽  
Networked Control ◽  
Time Varying

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

2021 ◽  
pp. 107754632098598
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Multiple Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Common Lyapunov Function ◽  
Suggested Approach ◽  
Aggregation Techniques

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.

Simultaneous Optimal Design of the Lyapunov-Based Semi-Active Control and the Semi-Active Vibration Control Device: Inverse Lyapunov Approach

2010 ◽  
Author(s):  
Kazuhiko Hiramoto ◽  
Taichi Matsuoka ◽  
Akira Fukukita ◽  
Katsuaki Sunakoda
Keyword(s):  
Optimal Design ◽  
Lyapunov Function ◽  
Vibration Control ◽  
Active Control ◽  
Control Device ◽  
Ball Screw ◽  
Design Parameters ◽  
Resistance Force ◽  
Control Law ◽  
Lyapunov Approach

We address a simultaneous optimal design problem of a semi-active control law and design parameters in a vibration control device for civil structures. The Vibration Control Device (VCD) that is being developed by authors is used as the semi-active control device in the present paper. The VCD is composed of a mechanism of a ball screw with a flywheel for the inertial resistance force and an electric motor with an electric circuit for the damping resistance force. A new bang-bang type semi-active control law referred to as Inverse Lyapunov Approach is proposed as the semi-active control law. In the Inverse Lyapunov Approach the Lyapunov function is searched so that performance measures in structural vibration control are optimized in the premise of the bang-bang type semi-active control based on the Lyapunov function. The design parameters to determine the Lyapunov function and the design parameters of the VCD are optimized for the good performance of the semi-active control system. The Genetic Algorithm is employed for the optimal design.

Robust H∞ control of neutral system for sampled-data dynamic positioning ships

2018 ◽  
Vol 36 (4) ◽  
pp. 1325-1345 ◽  
Author(s):  
Minjie Zheng ◽  
Yujie Zhou ◽  
Shenhua Yang ◽  
Lina Li
Keyword(s):  
Sufficient Conditions ◽  
Control Law ◽  
Dynamic Positioning ◽  
Neutral System ◽  
Time Varying ◽  
Sampled Data ◽  
Stability Theorems ◽  
Data Control ◽  
Conservative Result ◽  
Data Controller

Abstract This study focuses on the robust ${H}_{\infty }$ sampled-data control problem of neutral system for dynamic positioning (DP) ships. Using the input delay approach and a state-derivative control law, the ship DP system is turned into a neutral system with time-varying delays. By incorporating the delay-decomposition technique, Wirtinger-based integral inequality and an augmented Lyapunov–Krasovskii functional, less conservative result is derived for the resulting system. Sufficient conditions are established to determine the system’s asymptotical stability and achieve ${H}_{\infty }$ performance using Lyapunov stability theorems. Then the ${H}_{\infty }$ sampled-data controller is obtained by analyzing the stabilization conditions. Finally, simulation result is shown that the proposed method is effective.

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