scholarly journals NonlinearL2-Gain Analysis of Hybrid Systems in the Presence of Sliding Modes and Impacts

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
T. Osuna ◽  
O. E. Montano ◽  
Y. Orlov
Keyword(s):  
Sliding Mode ◽  
Numerical Study ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Sliding Modes ◽  
Time Dynamics ◽  
Attenuation Level ◽  
Disturbance Factor ◽  
Disturbance Attenuation Level ◽  
The Impact

TheL2-gain analysis is extended towards hybrid mechanical systems, operating under unilateral constraints and admitting both sliding modes and collision phenomena. Sufficient conditions for such a system to be internally asymptotically stable and to possessL2-gain less than ana priorigiven disturbance attenuation level are derived in terms of two independent inequalities which are imposed on continuous-time dynamics and on discrete disturbance factor that occurs at the collision time instants. The former inequality may be viewed as the Hamilton-Jacobi inequality for discontinuous vector fields, and it is separately specified beyond and along sliding modes, which occur in the system between collisions. Thus interpreted, the former inequality should impose the desired integral input-to-state stability (iISS) property on the Filippov dynamics between collisions whereas the latter inequality is invoked to ensure that the impact dynamics (when the state trajectory hits the unilateral constraint) are input-to-state stable (ISS). These inequalities, being coupled together, form the constructive procedure, effectiveness of which is supported by the numerical study made for an impacting double integrator, driven by a sliding mode controller. Desired disturbance attenuation level is shown to satisfactorily be achieved under external disturbances during the collision-free phase and in the presence of uncertainties in the transition phase.

scholarly journals RobustH∞Filtering for Networked Control Systems with Random Sensor Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shenping Xiao ◽  
Liyan Wang ◽  
Hongbing Zeng ◽  
Lingshuang Kong ◽  
Bin Qin
Keyword(s):  
Networked Control Systems ◽  
Filter Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Attenuation Level ◽  
Exponentially Stable ◽  
Disturbance Attenuation Level ◽  
Filter Design Method

The robustH∞filtering problem for a class of network-based systems with random sensor delay is investigated. The sensor delay is supposed to be a stochastic variable satisfying Bernoulli binary distribution. Using the Lyapunov function and Wirtinger’s inequality approach, the sufficient conditions are derived to ensure that the filtering error systems are exponentially stable with a prescribedH∞disturbance attenuation level and the filter design method is proposed in terms of linear matrix inequalities. The effectiveness of the proposed method is illustrated by a numerical example.

scholarly journals H∞Filtering for a Class of Piecewise Homogeneous Markovian Jump Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Yucai Ding ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang ◽  
Yong Zeng
Keyword(s):  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Attenuation Level ◽  
Stochastically Stable ◽  
Error System ◽  
Disturbance Attenuation Level ◽  
Filtering Problem

H∞filtering problem for a class of piecewise homogeneous Markovian jump nonlinear systems is investigated. The aim of this paper is to design a mode-dependent filter such that the filtering error system is stochastically stable and satisfies a prescribedH∞disturbance attenuation level. By using a new mode-dependent Lyapunov-Krasovskii functional, mixed mode-dependent sufficient conditions on stochastic stability are formulated in terms of linear matrix inequalities (LMIs). Based on this, the mode-dependent filter is obtained. A numerical example is given to illustrate the effectiveness of the proposed main results.

scholarly journals Stabilization Strategies of Supply Networks with Stochastic Switched Topology

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Shukai Li ◽  
Jianxiong Zhang ◽  
Wansheng Tang
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Supply Networks ◽  
Attenuation Level ◽  
Disturbance Attenuation Level

In this paper, a dynamical supply networks model with stochastic switched topology is presented, in which the stochastic switched topology is dependent on a continuous time Markov process. The goal is to design the state-feedback control strategies to stabilize the dynamical supply networks. Based on Lyapunov stability theory, sufficient conditions for the existence of state feedback control strategies are given in terms of matrix inequalities, which ensure the robust stability of the supply networks at the stationary states and a prescribedH∞disturbance attenuation level with respect to the uncertain demand. A numerical example is given to illustrate the effectiveness of the proposed method.

scholarly journals Integral Sliding Modes with NonlinearH∞-Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Roger Miranda-Colorado ◽  
Carlos Chavez ◽  
Luis T. Aguilar
Keyword(s):  
Nonlinear System ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Disturbance Attenuation ◽  
Underactuated Systems ◽  
Time Varying ◽  
Minimum Phase ◽  
Sliding Modes ◽  
Tracking Tasks ◽  
Disturbance Attenuation Level

This paper presents a methodology for controlling nonlinear time-varying minimum-phase underactuated systems affected by matched and unmatched perturbations. The proposed control structure consists of an integral sliding mode control coupled together with a global nonlinearH∞-control for rejecting vanishing and nonvanishing matched perturbations and for attenuating the unmatched ones, respectively. It is theoretically proven that, using the proposed controller, the origin of the free-disturbance nonlinear system is asymptotically stabilized, while the matched disturbances are rejected whereas theL2-gain of the corresponding nonlinear system with unmatched perturbation is less than a given disturbance attenuation levelγwith respect to a given performance output. The capability of the designed controller is verified through a flexible joint robot manipulator typically affected by both classes of external perturbations. In order to assess the performance of the proposed controller, an existing sliding modes controller based on a nonlinear integral-type sliding surface is also implemented. Both controllers are then compared for trajectory tracking tasks. Numerical simulations show that the proposed approach exhibits better performance.

Dual-finite distributed H∞ filtering in sensor networks

2021 ◽  
pp. 095965182199758
Author(s):  
Changshuo Wang ◽  
Jiwei Wen ◽  
Xiaoli Luan
Keyword(s):  
Sensor Networks ◽  
Disturbance Attenuation ◽  
Time Interval ◽  
Frequency Range ◽  
Frequency Scale ◽  
Attenuation Level ◽  
Exogenous Noise ◽  
Disturbance Attenuation Level ◽  
Reference Input ◽  
Filtering Approach

Generally, distributed H∞ filtering approach achieves a certain disturbance attenuation level in the full frequency range. However, the energy of system noise or reference input usually limits in a specified frequency range. To reduce such a design conservatism, this article develops a distributed filtering approach based on dual scale, that is, filtering over a finite-time interval from time scale and also on a specified finite-frequency region from the frequency scale. Our target is to make the filtering error under sensor networks monitoring be relaxed into an ellipsoid bound rather than asymptotically converging to zero for exogenous noise in a specified frequency range. Finally, two illustrative examples demonstrate the strength of the developed filtering approach.

Robust Delay-Dependent H∞ Control for Uncertain Structural Systems With Actuator Delay

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Hakan Yazici ◽  
Rahmi Guclu ◽  
Ibrahim B. Kucukdemiral ◽  
M. N. Alpaslan Parlakci
Keyword(s):  
Optimization Technique ◽  
Time History ◽  
Disturbance Attenuation ◽  
Structural Systems ◽  
Attenuation Level ◽  
Uncertainty Bound ◽  
Disturbance Attenuation Level ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper is concerned with the design of a robust, state-feedback, delay-dependent H∞ controller for an active vibration control of seismic-excited structural systems having actuator delay, norm bounded uncertainties, and L2 disturbances. The norm bounded uncertainties are assumed to exist in variations of structural stiffness and damping coefficients. Based on the selection of Lyapunov–Krasovskii functional, first a bounded real lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, time-delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay-dependent criteria are developed for a stabilizing H∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm-bounded uncertainties, both the BRL and H∞ stabilization criteria are easily extended by employing a well-known bounding technique. Then, a cone complementary algorithm is also utilized to solve the nonconvex optimization problem. By use of the proposed method, a suboptimal controller with maximum allowable delay bound, uncertainty bound and minimum allowable disturbance attenuation level can be easily obtained by solving the proposed convex optimization technique. A four-degree-of-freedom uncertain structural system subject to seismic excitations is used to illustrate the effectiveness of the approach through simulations. Simulation results, obtained by using real time-history data of Kobe and Kocaeli earthquakes show that the proposed controller is very effective in reducing vibration amplitudes of storeys and guarantees stability at maximum actuator delay and parametric uncertainty bound.

scholarly journals Discrete variable structure system with pseudo-sliding mode

1991 ◽  
Vol 32 (4) ◽  
pp. 365-376 ◽  
Author(s):  
R. B. Potts ◽  
X. Yu
Keyword(s):  
Numerical Solutions ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Continuous System ◽  
Variable Structure ◽  
Sliding Modes ◽  
Discrete Variable ◽  
Variable Structure Systems ◽  
Variable Structure System ◽  
Necessary And Sufficient

AbstractVariable structure systems with sliding modes have been widely discussed and used in many different fields of applications. The precise behaviour at a switching surface is complicated because there the system is non-analytic. The damped simple harmonic oscillator with a nonlinear variable structure is discretised and analysed in detail, revealing the occurrence and structure of pseudo-sliding modes which give insight to the corresponding sliding modes for the continuous system. Necessary and sufficient conditions are obtained and the analysis illustrated with graphs from numerical solutions.

Event-based switching control for production inventory systems with time-varying delays

2019 ◽  
Vol 42 (9) ◽  
pp. 1585-1593
Author(s):  
Chen-Yu Wu
Keyword(s):  
Raw Materials ◽  
Sufficient Conditions ◽  
Switching Control ◽  
Inventory Systems ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Varying ◽  
Production Inventory ◽  
Disturbance Attenuation Level ◽  
Event Based

This paper investigates event-based switching control for production inventory systems with time-varying delays. The different subsystems are established to describe the fact that the different production rates are adjusted to meet the different customer needs, and the conditions of average dwelling time are used to constrain the switchings. The event-triggered scheme, where the event generates when the relative error between the current review-data and the last transmission review-data exceeds a certain threshold, depicts the transmission of raw materials (or finished products) in practice. Then, the sufficient conditions of exponentially stable with a prescribed disturbance attenuation level [Formula: see text] and controller synthesis are formulated as linear matrix inequalitiess for the production inventory switching systems. A numerical example is presented to illustrate the effectiveness of the proposed method.

scholarly journals Multicriteria Adaptive Observers for Singular Systems with Unknown Time-Varying Parameters

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Wookyong Kwon ◽  
Jaepil Ban ◽  
Soohee Han ◽  
Chong Soo Lee ◽  
Sangchul Won
Keyword(s):  
Singular Systems ◽  
Disturbance Attenuation ◽  
Estimation Accuracy ◽  
Time Varying ◽  
Varying Parameters ◽  
Integral Action ◽  
Attenuation Level ◽  
Adaptive Observers ◽  
Time Varying Parameters ◽  
Disturbance Attenuation Level

This paper proposes multicriteria adaptive observers for a class of singular systems with unknown time-varying parameters. Two criteria for theH∞disturbance attenuation level and the upper bound of an ultimate invariant set are scalarized into a single cost function and then it is minimized by varying the weight parameter, which creates the optimal trade-off curve or Pareto optimal points. The proposed multicriteria adaptive observers are shown to be able to easily include integral action for better robust performance. It is demonstrated with numerical simulations that the proposed multicriteria adaptive observers provide the good estimation accuracy and allow effective and compromising design by considering two different cost functions simultaneously.

Sign in / Sign up

Export Citation Format

Share Document