The Experts below are selected from a list of 17319 Experts worldwide ranked by ideXlab platform
Z. Retchkiman - One of the best experts on this subject based on the ideXlab platform.
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From stability to the stabilization problem of discrete event systems modeled by Petri nets using Lyapunov Methods
Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251), 1999Co-Authors: Z. RetchkimanAbstract:Presents some preliminary results in the stabilization problem of discrete event systems modeled by Petri nets using Lyapunov theory. After recalling some known stability information about discrete event systems modeled by Petri nets, the stabilization problem is addressed. A new promising methodology based on vector Lyapunov functions shows that it is possible to restrict the systems state space in such a way that boundedness is guaranteed.
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practical stability of discrete event systems using Lyapunov Methods
American Control Conference, 1998Co-Authors: Z. RetchkimanAbstract:This paper deals with the practical stability problem of discrete event systems using Lyapunov Methods. A new analysis methodology based on Lyapunov functions and comparison principles is presented. This approach allows to get immediate information about the system's stability in a very easy and convenient way. By proving practical stability one is allowed to preassign the bound on the system's dynamics performance. An example where the methodology presented is applied is given.
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stability analysis of singularly perturbed systems via vector Lyapunov Methods
Conference on Decision and Control, 1996Co-Authors: Z. Retchkiman, G SilvaAbstract:The aim of this paper consists of providing a more general and flexible methodology for the stability analysis of nonlinear singularly perturbed systems. Starting from slow and fast comparison principles, for each subsystem, a two-time scale comparison principle is constructed for the full-order singularly perturbed system to conclude its stability. The technique results natural and appropriate for studying stability for this class of systems and obtaining an upper bound for the singular perturbation parameter. To illustrate the procedure an example for the position control of a dc-motor with unmodelled dynamics is worked out.
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The load balancing problem
IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems Man and Cybernetics (Cat. No.99CH37028), 2024Co-Authors: Z. Retchkiman, F.s. SurianoAbstract:This paper studies the load balancing problem for distributed computer systems. A load balancing algorithm is proposed to solve the problem. The algorithm is modeled with Petri nets and using Lyapunov Methods a formal proof of stability and convergence is presented. The formulation is shown to be simple and straightforward.
Juntao Fei - One of the best experts on this subject based on the ideXlab platform.
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robust adaptive sliding mode control of mems gyroscope using t s fuzzy model
Nonlinear Dynamics, 2014Co-Authors: Shitao Wang, Juntao FeiAbstract:In this paper, a multi-input multi-output Takagi–Sugeno (T–S) fuzzy model is proposed to represent the nonlinear model of micro-electro mechanical systems (MEMS) gyroscope and improve the tracking and compensation performance. A robust adaptive sliding mode control with on-line identification for the upper bounds of external disturbances and an adaptive estimator for the model uncertainty parameters are proposed in the Lyapunov framework. The adaptive algorithm of model uncertainty parameters could compensate the error between the optimal T–S model and the designed T–S model, and decrease the chattering of the sliding surface. Based on Lyapunov Methods, these adaptive laws can guarantee that the system is asymptotically stable. For the purpose of comparison, the designed controller is also implemented on the nonlinear model of MEMS gyroscope. Numerical simulations are investigated to verify the effectiveness of the proposed control scheme on the T–S model and the nonlinear model.
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An adaptive fuzzy sliding mode controller for MEMS triaxial gyroscope with angular velocity estimation
Nonlinear Dynamics, 2012Co-Authors: Juntao Fei, Ming Yuan XinAbstract:In this paper, an adaptive fuzzy sliding mode control (AFSMC) for Micro-Electro-Mechanical Systems (MEMS) triaxial gyroscope is proposed. First, a novel adaptive identification approach with sliding mode controller which can identify angular velocity and other system parameters is developed. And in order to reduce the chattering, an AFSMC is designed to approximate the upper bound of the uncertainties and external disturbances. Based on Lyapunov Methods, these adaptive laws can guarantee that the system is asymptotically stable. Numerical simulations are investigated to verify the effectiveness of the proposed AFSMC scheme.
W E Dixon - One of the best experts on this subject based on the ideXlab platform.
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automatic control of cycling induced by functional electrical stimulation with electric motor assistance
IEEE Transactions on Automation Science and Engineering, 2017Co-Authors: Matthew J. Bellman, Anup Parikh, Ryan J Downey, W E DixonAbstract:Cycling induced by automatic control of functional electrical stimulation provides a means of therapeutic exercise and functional restoration for people affected by paralysis. During cycling induced by functional electrical stimulation, various muscle groups are stimulated according to the cycle crank angle; however, because of kinematic constraints on the cycle-rider system, stimulation is typically only applied in a subsection of the crank cycle. Therefore, these systems can be considered as switched control systems with autonomous, state-dependent switching with potentially unstable modes. Previous studies have included an electric motor in the system to provide additional control authority, but no studies have considered the effects of switched control in the stability analysis of the motorized functional electrical stimulation cycling system. In this paper, a model of the motorized cycle-rider system with functional electrical stimulation is developed that includes the effects of a switched control input. A novel switching strategy for the electric motor is designed to only provide assistance in the regions of the crank cycle where the kinematic effectiveness of the rider's muscles is low. A switched sliding-mode controller is designed, and global, exponentially stable tracking of a desired crank trajectory is guaranteed via Lyapunov Methods for switched systems, despite parametric uncertainty in the nonlinear model and unknown, time-varying disturbances. Experimental results from five able-bodied, passive riders are presented to validate the control design, and the developed control system achieves an average cadence tracking error of $0.00\pm 2.91$ revolutions per minute for a desired trajectory of 50 revolutions per minute.
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stationary cycling induced by switched functional electrical stimulation control
Advances in Computing and Communications, 2014Co-Authors: Matthew J. Bellman, Ryan J Downey, Tenghu Cheng, W E DixonAbstract:Functional electrical stimulation (FES) is used to activate the dysfunctional lower limb muscles of individuals with neuromuscular disorders to produce cycling as a means of exercise and rehabilitation. In this paper, a stimulation pattern for quadriceps femoris-only FES-cycling is derived based on the effectiveness of knee joint torque in producing forward pedaling. In addition, a switched sliding-mode controller is designed for the uncertain, nonlinear cycle-rider system with autonomous state-dependent switching. The switched controller yields ultimately bounded tracking of a desired trajectory in the presence of an unknown, time-varying, bounded disturbance, provided a reverse dwell-time condition is satisfied by appropriate choice of the control gains and a sufficient desired cadence. Stability is derived through Lyapunov Methods for switched systems, and experimental results demonstrate the performance of the switched control system under typical cycling conditions.
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stationary cycling induced by switched functional electrical stimulation control
arXiv: Systems and Control, 2013Co-Authors: Matthew J. Bellman, Ryan J Downey, Tenghu Cheng, W E DixonAbstract:Functional electrical stimulation (FES) is used to activate the dysfunctional lower limb muscles of individuals with neuromuscular disorders to produce cycling as a means of exercise and rehabilitation. However, FES-cycling is still metabolically inefficient and yields low power output at the cycle crank compared to able-bodied cycling. Previous literature suggests that these problems are symptomatic of poor muscle control and non-physiological muscle fiber recruitment. The latter is a known problem with FES in general, and the former motivates investigation of better control Methods for FES-cycling.In this paper, a stimulation pattern for quadriceps femoris-only FES-cycling is derived based on the effectiveness of knee joint torque in producing forward pedaling. In addition, a switched sliding-mode controller is designed for the uncertain, nonlinear cycle-rider system with autonomous state-dependent switching. The switched controller yields ultimately bounded tracking of a desired trajectory in the presence of an unknown, time-varying, bounded disturbance, provided a reverse dwell-time condition is satisfied by appropriate choice of the control gains and a sufficient desired cadence. Stability is derived through Lyapunov Methods for switched systems, and experimental results demonstrate the performance of the switched control system under typical cycling conditions.
Dennis S Bernstein - One of the best experts on this subject based on the ideXlab platform.
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modeling and analysis of mass action kinetics
IEEE Control Systems Magazine, 2009Co-Authors: Vijaysekhar Chellaboina, S Bhat, Wassim M Haddad, Dennis S BernsteinAbstract:Mass-action kinetics are used in chemistry and chemical engineering to describe the dynamics of systems of chemical reactions, that is, reaction networks. These models are a special form of compartmental systems, which involve mass- and energy-balance relations. Aside from their role in chemical engineering applications, mass-action kinetics have numerous analytical properties that are of inherent interest from a dynamical systems perspective. Because of physical considerations, however, mass- action kinetics have special properties, such as nonnegative solutions, that are useful for analyzing their behavior. With this motivation in mind, this article has several objectives. First, a general construction of the kinetic equations based on the reaction laws is provided in a state-space form. Next, the nonnegativity of solutions to the kinetic equations is considered. The realizability problem, which is concerned with the inverse problem of constructing a reaction network having specified essentially nonnegative dynamics, is also considered. In particular, an explicit construction of a reaction network for essentially nonnegative polynomial dynamics involving a scalar state is provided. Next, the reducibility of the kinetic equations is considered as well as the stability of the equilibria of the kinetic equations. Lyapunov Methods are applied to the kinetic equations, and semistability is guaranteed through the convergence to a Lyapunov- stable equilibrium that depends on the initial concentrations. Semistability is the appropriate notion of stability for compartmental systems in general, and reaction networks in particular, where the limiting concentration maybe nonzero and may depend on the initial concentrations. Finally, the zero deficiency result for mass-action kinetics in standard matrix terminology is presented and semistability is proven.
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nonnegativity reducibility and semistability of mass action kinetics
Conference on Decision and Control, 1999Co-Authors: Dennis S Bernstein, Sanjay P BhatAbstract:Mass action kinetics have numerous analytical properties that are of inherent interest from a dynamical systems perspective. We provide a general construction of the kinetic equation from reaction laws based upon the formulation given by Erdi et al. (1988). We consider the nonnegativity of the solutions to the kinetic equation, the reducibility of the mass action kinetics, and the stability of the equilibria of the kinetic equation. To do this, we apply Lyapunov Methods to the kinetic equation and obtain results that guarantee semistability, that is, convergence to an equilibrium that depends upon initial concentrations. This notion was previously developed by the authors (1995, 1999), which extends the linear semistability theory to nonlinear systems. Finally, we revisit the "zero deficiency" result given by Feinberg (1995), which provides rate-independent conditions guaranteeing stability.
Lars Naujok - One of the best experts on this subject based on the ideXlab platform.
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stability of interconnected impulsive systems with and without time delays using Lyapunov Methods
Nonlinear Analysis: Hybrid Systems, 2012Co-Authors: Sergey Dashkovskiy, Michael Kosmykov, Andrii Mironchenko, Lars NaujokAbstract:Abstract In this paper, we consider the input-to-state stability (ISS) of impulsive control systems with and without time delays. We prove that, if the time-delay system possesses an exponential Lyapunov–Razumikhin function or an exponential Lyapunov–Krasovskii functional, then the system is uniformly ISS provided that the average dwell-time condition is satisfied. Then, we consider large-scale networks of impulsive systems with and without time delays and prove that the whole network is uniformly ISS under the small-gain and the average dwell-time condition. Moreover, these theorems provide us with tools to construct a Lyapunov function (for time-delay systems, a Lyapunov–Krasovskii functional or a Lyapunov–Razumikhin function) and the corresponding gains of the whole system, using the Lyapunov functions of the subsystems and the internal gains, which are linear and satisfy the small-gain condition. We illustrate the application of the main results on examples.
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stability of interconnected impulsive systems with and without time delays using Lyapunov Methods
arXiv: Dynamical Systems, 2010Co-Authors: Sergey Dashkovskiy, Michael Kosmykov, Andrii Mironchenko, Lars NaujokAbstract:In this paper we consider input-to-state stability (ISS) of impulsive control systems with and without time-delays. We prove that if the time-delay system possesses an exponential Lyapunov-Razumikhin function or an exponential Lyapunov-Krasovskii functional, then the system is uniformly ISS provided that the average dwell-time condition is satisfied. Then, we consider large-scale networks of impulsive systems with and without time-delays and we prove that the whole network is uniformly ISS under a small-gain and a dwell-time condition. Moreover, these theorems provide us with tools to construct a Lyapunov function (for time-delay systems - a Lyapunov-Krasovskii functional or a Lyapunov-Razumikhin function) and the corresponding gains of the whole system, using the Lyapunov functions of the subsystems and the internal gains, which are linear and satisfy the small-gain condition. We illustrate the application of the main results on examples.
