scholarly journals Robust Time-Varying Output Formation Control for Swarm Systems with Nonlinear Uncertainties

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xiaofeng Chai ◽  
Qing Wang ◽  
Yao Yu ◽  
Changyin Sun
Keyword(s):  
Stability Problem ◽  
Formation Control ◽  
Directed Network ◽  
Control Problems ◽  
Time Varying ◽  
Robust Controller ◽  
Nonlinear Uncertainties ◽  
The Stability ◽  
High Order Time ◽  
Time Invariant

Time-varying output formation control problems for high-order time-invariant swarm systems are studied with nonlinear uncertainties and directed network topology in this paper. A robust controller which consists of a nominal controller and a robust compensator is applied to achieve formation control. The nominal controller based on the output feedback is designed to achieve desired time-varying formation properties for the nominal system. And the robust compensator based on the robust signal compensator technology is constructed to restrain nonlinear uncertainties. The time-varying formation problem is transformed into the stability problem. And the formation errors can be arbitrarily small with expected convergence rate. Numerical examples are provided to illustrate the effectiveness of the proposed strategy.

scholarly journals Leader–follower formation with reduction of the off-tracking and velocity estimation under visibility constraints

2021 ◽  
Vol 18 (6) ◽  
pp. 172988142110576
Author(s):  
C. Mauricio Arteaga-Escamilla ◽  
Rafael Castro-Linares ◽  
Jaime Álvarez-Gallegos
Keyword(s):  
Formation Control ◽  
Kinematic Model ◽  
Velocity Estimation ◽  
Lyapunov Theory ◽  
Time Varying ◽  
Absolute Position ◽  
Nonholonomic Mobile Robots ◽  
The Stability ◽  
Time Invariant ◽  
Explicit Communication

This article addresses the time-varying leader–follower formation control problem for nonholonomic mobile robots, under communication and visibility constraints. Although the leader–follower formation control under visibility constraints has been studied, the elimination of the off-tracking effect has not been widely addressed yet. In this work, a new method to eliminate the off-tracking effect, considering the time-invariant formation as a tractor–trailer system, for unknown and circular tractor paths, taking into account the visibility constraints, is proposed. For a time-varying formation with not circular tractor’s path, the proposed method significantly reduces the off-tracking. Only the relative position and the relative orientation, provided by the on board monocular camera, are required. Thus, both the leader robot’s absolute position and the leader robot’s velocities are not needed. Furthermore, to avoid explicit communication among the robots, an extended state observer is implemented to estimate both the translational and the rotational leader’s velocity. In this way, the desired tasks are executed and achieved in a decentralized manner. For a time-varying formation, with constant leader robot’s velocities, the proposed control strategy, based on the kinematic model, guarantees that the formation errors asymptotically converge to the origin. Based on the Lyapunov theory, the stability proof of the formation errors dynamics is shown. Simulation results, considering time-varying leader robot’s velocities, show the efficiency of the proposed scheme.

Robust Controller Synthesis of Multivariable System Subjected to Noises and Nonlinear Time-Varying Plant Perturbations

1988 ◽  
Vol 110 (3) ◽  
pp. 336-340
Author(s):  
Feng-Hsiag Hsiao ◽  
Bor-Sen Chen
Keyword(s):  
Robust Stability ◽  
Function Class ◽  
Controller Synthesis ◽  
Schur Function ◽  
Time Varying ◽  
Multivariable System ◽  
Feedback Systems ◽  
Robust Controller ◽  
Stabilizing Controller ◽  
The Stability

A new robust stability criterion is developed to guarantee the stability of the feedback systems subjected to noises and nonlinear time-varying plant perturbations. The main contribution of this paper is an extension of the results of robust stability for the class of feedback systems containing nonlinear time-varying plant perturbations to the class of systems with unstable plants and noises. The generally parameterized stabilizing controller, advanced by Youla et al., is combined with Schur function (class S) to synthesize the robust stabilizers of the feedback systems subjected to noises and nonlinear time-varying plant perturbations.

Time-varying output formation control for high-order linear time-invariant swarm systems

2015 ◽  
Vol 298 ◽  
pp. 36-52 ◽  
Author(s):  
Xiwang Dong ◽  
Zongying Shi ◽  
Geng Lu ◽  
Yisheng Zhong
Keyword(s):  
Formation Control ◽  
Linear Time ◽  
High Order ◽  
Time Varying ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Time Invariant

The determinants of parental childrearing behavior trajectories: The effects of parental and child time-varying and time-invariant predictors

2012 ◽  
Vol 36 (3) ◽  
pp. 186-196 ◽  
Author(s):  
Isabelle Roskam ◽  
Jean Christophe Meunier
Keyword(s):  
Self Efficacy ◽  
Externalizing Behavior ◽  
Efficacy Beliefs ◽  
Time Varying ◽  
Child Externalizing Behavior ◽  
Parental Educational Level ◽  
The Stability ◽  
Evidence Based Programs ◽  
Time Invariant ◽  
The Way

“Why do parents parent the way they do?” remains an important question since it concerns both scientific issues, such as the stability or change of childrearing behavior, and clinical issues, such as the way to promote positive parenting in evidence-based programs. Using an accelerated design, the aim of this study was to examine several parental and child predictors of childrearing behavior trajectories among 373 mothers and 356 fathers of 2- to 9-year-old children. Hypotheses were drawn from Belsky (1984) and subsequent studies of the determinants of parenting. The parental and child predictors were assessed and analyzed as time-varying (parental self-efficacy beliefs and child externalizing behavior) or time-invariant (parental educational level and personality traits) predictors, according to their conceptual properties. The results show a linear decrease in both supportive and controlling childrearing behavior in mothers and an improvement in supportive but a decrease in controlling childrearing behavior in fathers over time. Moreover, the results support the idea that childrearing behavior is determined by multiple factors, in particular the parents’ self-efficacy beliefs and the child’s behavior. Finally, the results confirm the hypothesis of a greater influence of child predictors than of parental ones in the case of mothers, while the reverse hypothesis of a greater predictive power of parental variables than of child ones is confirmed for fathers. The results are discussed both for research and clinical purposes.

Active Control of Linear Time-Varying Structures by Confinement of Vibrations

2005 ◽  
Vol 11 (1) ◽  
pp. 89-102 ◽  
Author(s):  
S. Choura ◽  
A. S. Yigit
Keyword(s):  
Control Strategy ◽  
Linear Time ◽  
Steady States ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Slowing Down ◽  
Rapid Removal ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Time Invariant

We propose a control strategy for the simultaneous suppression and confinement of vibrations in linear time-varying structures. The proposed controller has time-varying gains and can also be used for linear time-invariant systems. The key idea is to alter the original modes by appropriate feedback forces to allow parts of the structure reach their steady states at faster rates. It is demonstrated that the convergence of these parts to zero is improved at the expense of slowing down the settling of the remaining parts to their steady states. The proposed control strategy can be applied for the rapid removal of vibration energy in sensitive parts of a flexible structure for safety or performance reasons. The stability of the closed-loop system is proven through a Lyapunov approach. An illustrative example of a five-link manipulator with a periodic follower force is given to demonstrate the effectiveness of the method for time-varying as well as time-invariant systems.

scholarly journals Stability Analysis of Pulse-Width-Modulated Feedback Systems with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhong Zhang ◽  
Huahui Han ◽  
Qiling Zhao ◽  
Lixia Ye
Keyword(s):  
Stability Analysis ◽  
Stability Problem ◽  
Pulse Width ◽  
Time Varying ◽  
Stability Criteria ◽  
Feedback Systems ◽  
Stochastic Perturbations ◽  
Pulse Width Modulated ◽  
The Stability ◽  
Moment Exponential Stability

The stability problem of pulse-width-modulated feedback systems with time-varying delays and stochastic perturbations is studied. With the help of an improved functional construction method, we establish a new Lyapunov-Krasovskii functional and derive several stability criteria aboutpth moment exponential stability.

scholarly journals A Robust Formation Control Strategy for Multi-Agent Systems with Uncertainties via Adaptive Gain Robust Controllers

2021 ◽  
Vol 11 (2) ◽  
pp. 71-87
Author(s):  
Shun Ito ◽  
Kaoru Ohara ◽  
Yoshikatsu Hoshi ◽  
Hidetoshi Oya ◽  
Shunya Nagai
Keyword(s):  
Formation Control ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Multi Agent System ◽  
Matrix Inequalities ◽  
Multi Agent Systems ◽  
Robust Controller ◽  
Multi Agent

This paper deals with a design problem of an adaptive gain robust controller which achieves consensus for multi-agent system (MAS) with uncertainties. In the proposed controller design approach, the relative position between the leader and followers are considered explicitly, and the proposed adaptive gain robust controller consisting of fixed gains and variable ones tuned by time-varying adjustable parameters can reduce the effect of uncertainties. In this paper, we show that sufficient conditions for the existence of the proposed adaptive gain robust controller are reduced to solvability of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed robust formation control system is verified by simple numerical simulations. A main result of this study is that the proposed adaptive gain robust controller can achieve consensus and formation control giving consideration to relative distance in spite of uncertainties.

scholarly journals Explicit Commutativity and Stability for the Heun's Linear Time-Varying Differential Systems

2021 ◽  
Author(s):  
Salisu Ibrahim
Keyword(s):  
Differential System ◽  
Stability Problem ◽  
Significant Contribution ◽  
Initial Conditions ◽  
Linear Time ◽  
Time Varying ◽  
Differential Systems ◽  
System Sensitivity ◽  
System Robustness ◽  
The Stability

This paper studies the commutativity and stability for the Heun’s linear time-varying system (LTVS) with both zero and non-zero initial conditions(ICs). Given a LTVS A of order 2 , we find it’s commutative pair, that is a new LTVS B of order m ≤ n . Explicit commutative theories and conditions for second-order LTVSs are derived and solved to simplify and guarantee the equivalency between the connected input-output of systems A B and B A . The explicit results obtained are juxtaposed by simulation in order to investigate the commutativity of Heun’s differential system, sensitivity of Heun’s system, effects due to disturbance on Heun’s system, robustness on Heun’s system and problems regarding the stability of Heun’s system. This findings will help to fill the gap on stability problem, system behaviors, commutativity theory, and general theory for solutions of differential equations, which has significant contribution to science and unlimited application in engineering, our results are verify using Heun’s differential system as well as authenticated by Wolfrom Mathematica 1 1 and Matlab.

Analytical Stability Prediction and Design of Variable Pitch Cutters

1999 ◽  
Vol 121 (2) ◽  
pp. 173-178 ◽  
Author(s):  
Y. Altıntas¸ ◽  
S. Engin ◽  
E. Budak
Keyword(s):  
Time Delay ◽  
Depth Of Cut ◽  
Analytical Prediction ◽  
Time Varying ◽  
Chatter Stability ◽  
Variable Pitch ◽  
Analytical Stability ◽  
The Stability ◽  
Time Invariant ◽  
Regenerative Phase

An analytical prediction of stability lobes for milling cutters with variable pitch angles is presented. The method requires cutting constants, number of teeth, and transfer function of cutter mounted on the machine tool as inputs to a chatter stability expression. The stability is formulated by transforming time varying directional cutting constants into time invariant constants. Constant regenerative time delay in uniform cutters is transformed into nonuniform multiple regenerative time delay for variable pitch cutters. The chatter free axial depth of cut is solved from the eigenvalues of stability expression, whereas the spindle speed is identified from regenerative phase delays. The proposed technique has been verified with extensive cutting tests and time domain simulations. The practical use of the analytical solution is demonstrated by an optimal tooth spacing design application which increases the chatter free depth of cuts significantly.

scholarly journals Global Stability of Polytopic Linear Time-Varying Dynamic Systems under Time-Varying Point Delays and Impulsive Controls

2010 ◽  
Vol 2010 ◽  
pp. 1-33 ◽  
Author(s):  
M. de la Sen
Keyword(s):  
Dynamic System ◽  
Linear Systems ◽  
Dynamic Systems ◽  
Linear Time ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Impulsive Controls ◽  
The Stability ◽  
Time Invariant ◽  
Point Delays

This paper investigates the stability properties of a class of dynamic linear systems possessing several linear time-invariant parameterizations (or configurations) which conform a linear time-varying polytopic dynamic system with a finite number of time-varying time-differentiable point delays. The parameterizations may be timevarying and with bounded discontinuities and they can be subject to mixed regular plus impulsive controls within a sequence of time instants of zero measure. The polytopic parameterization for the dynamics associated with each delay is specific, so that(q+1)polytopic parameterizations are considered for a system withqdelays being also subject to delay-free dynamics. The considered general dynamic system includes, as particular cases, a wide class of switched linear systems whose individual parameterizations are timeinvariant which are governed by a switching rule. However, the dynamic system under consideration is viewed as much more general since it is time-varying with timevarying delays and the bounded discontinuous changes of active parameterizations are generated by impulsive controls in the dynamics and, at the same time, there is not a prescribed set of candidate potential parameterizations.

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