Stability of a Class of Piezoelectric State-Switching Methods

2000 ◽  
Author(s):  
Andrew J. Kurdila ◽  
William W. Clark ◽  
Weijian Wang ◽  
Dwayne E. McDaniel
Keyword(s):  
Lyapunov Functions ◽  
Closed Loop ◽  
Control Strategies ◽  
Short Circuit ◽  
Open Circuit ◽  
Hybrid Dynamical Systems ◽  
Multiple Lyapunov Functions ◽  
Control Laws ◽  
State Switching ◽  
The Stability

Abstract Experimental and anecdotal evidences have shown that state-switched control strategies for piezoelectric actuators can be advantageous. However, most discussions of the stability of these systems has relied on heuristic, or physically motivated, arguments. In this paper, we show that recent open-circuit/short-circuit state-switching control laws can be viewed as hybrid dynamical systems of Witsenhausen type. Within this framework, the closed-loop stability of OC/SC switching is rigorously established using the method of multiple Lyapunov functions.

scholarly journals Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
V. Nosov ◽  
J. A. Meda-Campaña ◽  
J. C. Gomez-Mancilla ◽  
J. O. Escobedo-Alva ◽  
R. G. Hernández-García
Keyword(s):  
Stability Analysis ◽  
Finite Number ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Switched System ◽  
Linear Functions ◽  
Asymptotically Stable ◽  
Multiple Lyapunov Functions ◽  
Stability Theorems ◽  
The Stability

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

scholarly journals Control strategies for the Fokker−Planck equation

2018 ◽  
Vol 24 (2) ◽  
pp. 741-763 ◽  
Author(s):  
Tobias Breiten ◽  
Karl Kunisch ◽  
Laurent Pfeiffer
Keyword(s):  
Closed Loop ◽  
Control Strategies ◽  
Planck Equation ◽  
Control Laws ◽  
Closed Loop Systems ◽  
Associated Solutions ◽  
Fokker Planck Equation ◽  
Speed Up ◽  
Double Well Potential ◽  
Fokker Planck

Using a projection-based decoupling of the Fokker−Planck equation, control strategies that allow to speed up the convergence to the stationary distribution are investigated. By means of an operator theoretic framework for a bilinear control system, two different feedback control laws are proposed. Projected Riccati and Lyapunov equations are derived and properties of the associated solutions are given. The well-posedness of the closed loop systems is shown and local and global stabilization results, respectively, are obtained. An essential tool in the construction of the controls is the choice of appropriate control shape functions. Results for a two dimensional double well potential illustrate the theoretical findings in a numerical setup.

Stability of a class of nonlinear fractional order impulsive switched systems

2016 ◽  
Vol 39 (5) ◽  
pp. 781-790 ◽  
Author(s):  
Guopei Chen ◽  
Ying Yang
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Multiple Lyapunov Functions ◽  
Unstable Subsystems ◽  
Impulsive Switched Systems ◽  
The Stability ◽  
Work First ◽  
Periodic Switching

This paper considers the asymptotic stability of a class of nonlinear fractional order impulsive switched systems by extending the result of existing work. First, a criterion is given to verify the stability of systems by using the Mittag–Leffler function and fractional order multiple Lyapunov functions. Second, by combining the methods of minimum dwell time with fractional order multiple Lyapunov functions, another sufficient condition for the stability of systems is given. Third, by using a periodic switching technique, a switching signal is designed to ensure the asymptotic stability of a system with both stable and unstable subsystems. Finally, two numerical examples are provided to illustrate the theoretical results.

scholarly journals Performance Analysis of Mixed Natural Dye and Nanostructured Tio2 based DSSC

2020 ◽  
Vol 9 (7) ◽  
pp. 453-456
Keyword(s):  
Short Circuit ◽  
Electron Flow ◽  
Sol Gel ◽  
Short Circuit Current ◽  
Open Circuit ◽  
Natural Dye ◽  
Nanostructured Tio2 ◽  
Beet Root ◽  
The Stability ◽  
The Individual

The performance of the mixed natural dye based DSSC has been evaluated in this paper. The mixture of beet root, spinach and turmeric are used with nanostructured TiO2 are used for the fabrication of DSSC. TiO2 is synthesized by sol-gel technique and considered as semiconductor metal oxide (SMO) to act as photo anode here. Nano wire type of morphology of TiO2 is found from the FESEM image which exhibits unidirectional and uniform electron flow. The XRD study reveals anatase and rutile phases of TiO2 that ensure the stability of synthesized TiO2 . The mixed dye made of beet root, spinach and turmeric shows their congruent characteristics with the broad light absorption spectra, lower diffused reflectance spectra after anchoring with SMO and better I-V characteristics in comparison with the individual one. The mixed dye-based DSSC provides the open-circuit voltage of 0.755V, short circuit current of 2.05mA, voltage and current at maximum power equal to 0.51V and 1.7mA, respectively with the efficiency of 0.867 %, in comparison to the efficiency of the individual dyes 0.305%, 0.266% and 0.473% with beet root, spinach and turmeric, respectively.

Sliding Mode Control Laws Design by the ADAR Method with Subsequent Invariant Manifolds Aggregation

2019 ◽  
Vol 20 (8) ◽  
pp. 451-460 ◽  
Author(s):  
A. A. Kolesnikov ◽  
A. A. Kuz’menko
Keyword(s):  
Robust Control ◽  
Invariant Manifolds ◽  
Closed Loop ◽  
Sliding Mode ◽  
Design Procedure ◽  
Sliding Surface ◽  
Closed Loop System ◽  
External Disturbances ◽  
Control Laws ◽  
The Stability

Sliding mode control (SMC) laws are commonly used in engineering to make a system robust to parameters change, external disturbances and control object unmodeled dynamics. State-of-the-art capabilities of the theory of adaptive and robust control, the theory of fuzzy systems, artificial neural networks, etc., which are combined with SMC, couldn’t resolve current issues of SMC design: vector design and stability analysis of a closed-loop system with SMC are involved with considerable complexity. Generally the classical problem of SMC design consists in solving subtasks for transit an object from an arbitrary initial position onto the sliding surface while providing conditions for existence of a sliding mode at any point of the sliding surface as well as ensuring stable movement to the desired state. As a general rule these subtasks are solved separately. This article presents a methodology for SMC design based on successive aggregation of invariant manifolds by the procedure of method of Analytical Design of Aggregated Regulators (ADAR) from the synergetic control theory. The methodology allows design of robust control laws and simultaneous solution of classical subtasks of SMC design for nonlinear objects. It also simplifies the procedure for closed-loop system stability analyze: the stability conditions are made up of stability criterions for ADAR method functional equations and the stability criterions for the final decomposed system which dimension is substantially less than dimension of the initial system. Despite our paper presents only the scalar SMC design procedure in details, the ideas are also valid for vector design procedure: the main difference is in the number of invariant manifolds introduced at the first and following stages of the design procedure. The methodology is illustrated with design procedure examples for nonlinear engineering systems demonstrating the achievement of control goals: hitting to target invariants, insensitivity to emerging parametric and external disturbances.

scholarly journals Hybrid velocity/force control for robot navigation in compliant unknown environments

Robotica ◽  
2006 ◽  
Vol 24 (6) ◽  
pp. 745-758 ◽  
Author(s):  
Dushyant Palejiya ◽  
Herbert G. Tanner
Keyword(s):  
Lyapunov Functions ◽  
Closed Loop ◽  
Position Control ◽  
Dynamic Control ◽  
Control Law ◽  
Closed Loop System ◽  
Multiple Lyapunov Functions ◽  
Unknown Environments ◽  
Control Scheme ◽  
Novel Method

We combine a “hybrid” force-/position-control scheme with a potential field approach into a novel method for collision recovery and navigation in unknown environments. It can be implemented both on manipulators and mobile robots. The use of force sensors allows us to locally sense the environment and design a dynamic control law. Multiple Lyapunov functions are used to establish asymptotic stability of the closed-loop system. The switching conditions and stability criteria are established under reasonable assumptions on the type of obstacles present in the environment. Extensive simulation results are presented to illustrate the system behavior under the designed control scheme, and verify its stability, collision recovery, and navigation properties.

scholarly journals Controlling reversible cell differentiation for labor division in microbial consortia

2021 ◽  
Author(s):  
Davide Salzano ◽  
Davide Fiore ◽  
Mario di Bernardo
Keyword(s):  
Control Strategies ◽  
Analytical Framework ◽  
Microbial Consortia ◽  
External Control ◽  
Toggle Switch ◽  
Memory Element ◽  
Control Laws ◽  
Memory Mechanism ◽  
Labor Division ◽  
The Stability

We address the problem of regulating and keeping at a desired balance the relative numbers between cells exhibiting a different phenotype within a monostrain microbial consortium. We propose a strategy based on the use of external control inputs, assuming each cell in the community is endowed with a reversible, bistable memory mechanism. Specifically, we provide a general analytical framework to guide the design of external feedback control strategies aimed at balancing the ratio between cells whose memory is stabilized at either one of two equilibria associated to different cell phenotypes. We demonstrate the stability and robustness properties of the control laws proposed and validate them in silico implementing the memory element via a genetic toggle-switch. The proposed control framework may be used to allow long term coexistence of different populations, with both industrial and biotechnological applications. Examples include consortia where each population produces a compound of interest or where one population supports the growth of the other which has the role of producing a desired molecule. As a representative example we consider the realistic agent-based implementation of our control strategy to enable cooperative bioproduction in microbial consortia.

Robust integral sliding mode control strategy under designed switching rules for uncertain switched linear systems via multiple Lyapunov functions

2019 ◽  
Vol 41 (12) ◽  
pp. 3536-3549 ◽  
Author(s):  
Xiaoyu Zhang
Keyword(s):  
Sliding Mode Control ◽  
Lyapunov Functions ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Multiple Lyapunov Functions ◽  
Integral Sliding Mode Control ◽  
Integral Sliding Mode ◽  
Mode Control ◽  
The Stability ◽  
Stable Matrix

This paper puts forward a switching rule stabilization design of the robust integral sliding mode control for uncertain switched systems. A kind of common robust integral sliding mode (CRISM) is firstly designed and the system matrices of subsystems under the sliding mode comprise a robust stable matrix set. The stability of the switched system (SS) under the sliding mode is then analyzed by multiple Lyapunov functions (MLF) method. Based on the presented design of CRISM, a sliding mode controller is devised so that the sliding mode can be reached. Finally, the correctness of the proposed method is verified through results of numerical and application simulations.

Exponential stability of memristor-based synchronous switching neural networks with time delays

2015 ◽  
Vol 09 (01) ◽  
pp. 1650016 ◽  
Author(s):  
Yinlu Jiang ◽  
Chuandong Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Lyapunov Functions ◽  
Time Delays ◽  
Memristive Neural Networks ◽  
Multiple Lyapunov Functions ◽  
Synchronous Switching ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results

In this paper, we study the existence, uniqueness and stability of memristor-based synchronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural networks, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.

scholarly journals An Impulsive Three-Species Model with Square Root Functional Response and Mutual Interference of Predator

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Zhen Wang ◽  
Yuanfu Shao ◽  
Xianjia Fang ◽  
Xiangmin Ma
Keyword(s):  
Comparison Theorem ◽  
Lyapunov Functions ◽  
Floquet Theory ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Mutual Interference ◽  
Square Root ◽  
Functional Responses ◽  
Multiple Lyapunov Functions ◽  
Predator Model

An impulsive two-prey and one-predator model with square root functional responses, mutual interference, and integrated pest management is constructed. By using techniques of impulsive perturbations, comparison theorem, and Floquet theory, the existence and global asymptotic stability of prey-eradication periodic solution are investigated. We use some methods and sufficient conditions to prove the permanence of the system which involve multiple Lyapunov functions and differential comparison theorem. Numerical simulations are given to portray the complex behaviors of this system. Finally, we analyze the biological meanings of these results and give some suggestions for feasible control strategies.

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