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433
A control engineer’s guide to sliding mode control
 IEEE Transactions on Control Systems Technology
, 1999
"... Abstract—This paper presents a guide to sliding mode control for practicing control engineers. It offers an accurate assessment of the socalled chattering phenomenon, catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding mode control rese ..."
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Cited by 159 (0 self)
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Abstract—This paper presents a guide to sliding mode control for practicing control engineers. It offers an accurate assessment of the socalled chattering phenomenon, catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding mode control research. Index Terms — Discretetime systems, multivariable systems, nonlinear systems, robustness, sampled data systems, singularly perturbed systems, uncertain systems, variable structure systems. I.
Dynamical Properties of Hybrid Automata
 IEEE Transactions on Automatic Control
, 2003
"... Hybrid automata provide a language for modeling and analyzing digital and analogue computations in realtime systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid ..."
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Cited by 147 (17 self)
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Hybrid automata provide a language for modeling and analyzing digital and analogue computations in realtime systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized. The results on existence, uniqueness, and continuity serve as a starting point for stability analysis. Lyapunov's theorem on stability via linearization and LaSalle's invariance principle are generalized to hybrid automated
High performance adaptive robust control of nonlinear systems: A general framework and new schemes
 Proceedings of the 36th Conference on Decision and Control
, 1997
"... A general framework is proposed for the design of a new class of highperformance robust controllers. The framework is based on the recently proposed adaptive robust control (ARC), which effectively combines deterministic robust control with adaptive control. The approach intends to use all availabl ..."
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Cited by 96 (49 self)
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A general framework is proposed for the design of a new class of highperformance robust controllers. The framework is based on the recently proposed adaptive robust control (ARC), which effectively combines deterministic robust control with adaptive control. The approach intends to use all available means in achieving high performance; robust filter structures are used to attenuate the effect of model uncertainties as much as possible while learning mechanisms such as parameter adaptation are used to reduce the model uncertainties. Under the proposed general framework, a simple new ARC controller is also constructed for a class of nonlinear systems transformable to a semistrict feedback form. The new design utilizes the popular discontinuous projection method in solving the conflicts between the deterministic robust control design and the adaptive control design, which is much simpler than the smooth projection or the smooth modifications of adaptation law used in the previously proposed ARC controllers. The controller achieves a guaranteed transient performance and a prescribed final tracking accuracy in the presence of both parametric uncertainties and uncertain nonlinearities while achieving asymptotic stability in the presence of parametric uncertainties without using a discontinuous control law or infinitegain feedback. 1
Control Using LogicBased Switching
 Trends in Control: A European Perspective
, 1998
"... this paper is to give a brief tutorial review of four different classes of hybrid systems of this type  each consists of a continuoustime process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic. Three of the logics, called prerouted switching, ..."
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Cited by 84 (19 self)
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this paper is to give a brief tutorial review of four different classes of hybrid systems of this type  each consists of a continuoustime process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic. Three of the logics, called prerouted switching, hysteresis switching and dwelltime switching respectively, are simple strategies capable of determining in real time which candidate controller should be put in feedback with a process in order to achieve desired closedloop performance. The fourth, called cyclic switching, has been devised to solve the longstanding stabilizability problem which arises in the synthesis of identifierbased adaptive controllers because of the existence of points in parameter space where the estimated model upon which certainty equivalence synthesis is based, loses stabilizability
Syntax and consistent equation semantics of hybrid Chi
 Journal of Logic and Algebraic Programming
, 2006
"... † This work was partially supported by the EU project HyCon (FP6IST511368) ii The hybrid χ (Chi) formalism integrates concepts from dynamics and control theory with concepts from computer science, in particular from process algebra and hybrid automata. It integrates ease of modeling with a straigh ..."
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Cited by 60 (24 self)
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† This work was partially supported by the EU project HyCon (FP6IST511368) ii The hybrid χ (Chi) formalism integrates concepts from dynamics and control theory with concepts from computer science, in particular from process algebra and hybrid automata. It integrates ease of modeling with a straightforward, structured operational semantics. Its ‘consistent equation semantics ’ enforces state changes to be consistent with invariants as in most hybrid automata. Ease of modeling is ensured by means of the following concepts: 1) different classes of variables: discrete and continuous, of subclass jumping or nonjumping, and algebraic; 2) strong time determinism of alternative composition in combination with delayable guards; 3) integration of urgent and nonurgent actions; 4) differential algebraic equations as a process term as in mathematics; 5) steadystate initialization; and 6) several userfriendly modeling extensions. Furthermore, the Chi language incorporates several concepts for complex system specification: 1) process terms for scoping that integrate abstraction, local variables, local channels and recursion definitions; 2) process definition and instantiation that enable process reuse,
Optimal flow control and routing in multipath networks
, 2003
"... We propose two flow control algorithms for networks with multiple paths between each source–destination pair. Both are distributed algorithms over the network to maximize aggregate source utility. Algorithm 1 is a first order Lagrangian method applied to a modified objective function that has the sa ..."
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Cited by 51 (0 self)
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We propose two flow control algorithms for networks with multiple paths between each source–destination pair. Both are distributed algorithms over the network to maximize aggregate source utility. Algorithm 1 is a first order Lagrangian method applied to a modified objective function that has the same optimal solution as the original objective function but has a better convergence property. Algorithm 2 is based on the idea that, at optimality, only paths with the minimum price carry positive flows, and naturally decomposes the overall decision into flow control (determines total transmission rate based on minimum path price) and routing (determines how to split the flow among available paths). Both algorithms can be implemented as simply a sourcebased mechanism in which no link algorithm nor feedback is needed. We present numerical examples to illustrate their behavior.
Piecewiselinear models of genetic regulatory networks: equilibria and . . .
 J. MATH. BIOL.
, 2005
"... A formalism based on piecewiselinear (PL) differential equations, originally due to Glass and Kauffman, has been shown to be wellsuited to modelling genetic regulatory networks. However, the discontinuous vector field inherent in the PL models raises some mathematical problems in defining solutio ..."
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Cited by 46 (20 self)
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A formalism based on piecewiselinear (PL) differential equations, originally due to Glass and Kauffman, has been shown to be wellsuited to modelling genetic regulatory networks. However, the discontinuous vector field inherent in the PL models raises some mathematical problems in defining solutions on the surfaces of discontinuity. To overcome these difficulties we use the approach of Filippov, which extends the vector field to a differential inclusion. We study the stability of equilibria (called singular equilibrium sets) that lie on the surfaces of discontinuity. We prove several theorems that characterize the stability of these singular equilibria directly from the state transition graph, which is a qualitative representation of the dynamics of the system. We also formulate a stronger conjecture on the stability of these singular equilibrium sets.
Image Segmentation and Edge Enhancement with Stabilized Inverse Diffusion Equations.
 IEEE Transactions on Image Processing
, 1999
"... We introduce a family of firstorder multidimensional ordinary differential equations (ODEs) with discontinuous righthand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabil ..."
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Cited by 40 (10 self)
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We introduce a family of firstorder multidimensional ordinary differential equations (ODEs) with discontinuous righthand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations "stabilized inverse diffusion equations" ("SIDEs"). Existence and uniqueness of solutions, as well as stability, are proven for SIDEs. A SIDE in one spatial dimension may be interpreted as a limiting case of a semidiscretized PeronaMalik equation [14], [15]. In an experimental section, SIDEs are shown to suppress noise while sharpening edges present in the input signal. Their application to image segmentation is also demonstrated.
High performance robust motion control of machine tools: An adaptive robust control approach and comparative experiments,’’
 IEEE/ASME Trans. Mechatron.,
, 1997
"... ..."