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system modeling for inverse problems
 IEEE Trans. Circuits Syst. I: Reg. Papers
, 2004
"... Abstract—Large disturbances in power systems often initiate complex interactions between continuous dynamics and discrete events. The paper develops a hybrid automaton that describes such behavior. Hybrid systems can be modeled in a systematic way by a set of differentialalgebraic equations, modifi ..."
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Abstract—Large disturbances in power systems often initiate complex interactions between continuous dynamics and discrete events. The paper develops a hybrid automaton that describes such behavior. Hybrid systems can be modeled in a systematic way by a set of differentialalgebraic equations, modified to incorporate impulse (state reset) action and constraint switching. This differentialalgebraic impulsiveswitched (DAIS) model is a realization of the hybrid automaton. The paper presents a practical objectoriented approach to implementing the DAIS model. Each component of a system is modeled autonomously. Connections between components are established by simple algebraic equations. The systematic nature of the DAIS model enables efficient computation of trajectory sensitivities, which in turn facilitate algorithms for solving inverse problems. The paper outlines a number of inverse problems, including parameter uncertainty, parameter estimation, grazing bifurcations, boundary value problems, and dynamic embedded optimization. Index Terms—Boundary value problems, dynamic embedded optimization, dynamic modeling, hybrid systems, inverse problems, power system dynamics. I.
Stability analysis of the continuousconductionmode buck converter via Filippov’s method
 IEEE Transactions on Circuits and Systems–I: Regular Papers
, 2008
"... Abstract—To study the stability of a nominal cyclic steady state in power electronic converters, it is necessary to obtain a linearization around the periodic orbit. In many past studies, this was achieved by explicitly deriving the Poincaré map that describes the evolution of the state from one cl ..."
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Cited by 11 (4 self)
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Abstract—To study the stability of a nominal cyclic steady state in power electronic converters, it is necessary to obtain a linearization around the periodic orbit. In many past studies, this was achieved by explicitly deriving the Poincaré map that describes the evolution of the state from one clock instant to the next and then locally linearizing the map at the fixed point. However, in many converters, the map cannot be derived in closed form, and therefore this approach cannot directly be applied. Alternatively, the orbital stability can be worked out by studying the evolution of perturbations about a nominal periodic orbit, and some studies along this line have also been reported. In this paper, we show that Filippov’s method—which has commonly been applied to mechanical switching systems—can be used fruitfully in power electronic circuits to achieve the same end by describing the behavior of the system during the switchings. By combining this and the Floquet theory, it is possible to describe the stability of power electronic converters. We demonstrate the method using the example of a voltagemodecontrolled buck converter operating in continuous conduction mode. We find that the stability of a converter is strongly dependent upon the socalled saltation matrix—the state transition matrix relating the state just after the switching to that just before. We show that the Filippov approach, especially the structure of the saltation matrix, offers some additional insights on issues related to the stability of the orbit, like the recent observation that coupling with spurious signals coming from the environment causes intermittent subharmonic windows. Based on this approach, we also propose a new controller that can significantly extend the parameter range for nominal period1 operation. Index Terms—Bifurcation, buck converter, differential inclusions, discontinuous systems, Filippov systems, power electronics. I.
A COMPUTATIONAL TOOL FOR THE REDUCTION OF NONLINEAR ODE SYSTEMS POSSESSING MULTIPLE SCALES ∗
"... Abstract. Near an orbit of interest in a dynamical system, it is typical to ask which variables dominate its structure at what times. What are its principal local degrees of freedom? What local bifurcation structure is most appropriate? We introduce a combined numerical and analytical technique that ..."
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Cited by 8 (3 self)
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Abstract. Near an orbit of interest in a dynamical system, it is typical to ask which variables dominate its structure at what times. What are its principal local degrees of freedom? What local bifurcation structure is most appropriate? We introduce a combined numerical and analytical technique that aids the identification of structure in a class of systems of nonlinear ordinary differential equations (ODEs) that are commonly applied in dynamical models of physical processes. This “dominant scale ” technique prioritizes consideration of the influence that distinguished “inputs ” to an ODE have on its dynamics. On this basis a sequence of reduced models is derived, where each model is valid for a duration that is determined selfconsistently as the system’s state variables evolve. The characteristic time scales of all sufficiently dominant variables are also taken into account to further reduce the model. The result is a hybrid dynamical system of reduced differentialalgebraic models that are switched at discrete event times. The technique does not rely on explicit small parameters in the ODEs and automatically detects changing scale separation both in time and in “dominance strength ” (a quantity we derive to measure an input’s influence). Reduced regimes describing the full system have quantified domains of validity in time and with respect to variation in state variables. This enables the qualitative analysis of the system near known orbits (e.g., to study bifurcations) without sole reliance on numerical shooting methods. These methods have been incorporated into a new software tool named Dssrt, which we demonstrate on a limit cycle of a synaptically driven Hodgkin–Huxley neuron model.
Finite Controlled Invariants for Sampled Switched Systems
, 2013
"... We consider in this paper switched systems, a class of hybrid systems recently used with success in various domains such as automotive industry and power electonics. We propose a statedependent control strategy which makes the trajectories of the analyzed system converge to finite cyclic sequences ..."
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Cited by 4 (3 self)
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We consider in this paper switched systems, a class of hybrid systems recently used with success in various domains such as automotive industry and power electonics. We propose a statedependent control strategy which makes the trajectories of the analyzed system converge to finite cyclic sequences of points. Our method relies on a technique of decomposition of the state space into local regions where the control is uniform. We have implemented the procedure using zonotopes, and applied it successfully to several examples of the literature and industrial case studies in power electronics.
Locomotion Studies for a 5DoF Gymnastic Robot
, 2005
"... Legged locomotion with its variable contact situations between feet and ground is of interest in todays research on humanoid locomotion. This paper uses a hybrid modeling framework to account for different possible ground contact situations of a simple biped gymnast experimental platform with five j ..."
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Legged locomotion with its variable contact situations between feet and ground is of interest in todays research on humanoid locomotion. This paper uses a hybrid modeling framework to account for different possible ground contact situations of a simple biped gymnast experimental platform with five joints. For the considered biped unactuated rotation around foot edges as well as plane foot contact is considered in modeling and trajectory planning. Presented is a planning algorithm for periodic walking trajectories. The stability of the resulting hybrid periodic orbits is investigated in numerical experiments.
Modelling, Analysis and Design of Discretely Controlled Switched Positive Systems
, 2004
"... Abstract: Discretely controlled switched positive systems are characterized by interacting continuous and discrete dynamics. Switching must take place not only to move the continuous state from the initial state to a goal state, but also to make the system remain in the surroundings of the goal sta ..."
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Abstract: Discretely controlled switched positive systems are characterized by interacting continuous and discrete dynamics. Switching must take place not only to move the continuous state from the initial state to a goal state, but also to make the system remain in the surroundings of the goal state. The continuous dynamics are positive. This paper shows that if the continuous positive systems making up the switched system have a certain structure, it is possible to design stabilizing statefeedback controllers which ensure that the trajectories of the switched system cannot diverge to infinity regardless of the way the switching thresholds are selected. The trajectories of the discretely controlled switched positive systems can be restricted to invariant sets (called Hinvariant sets) away from the equilibrium points of the continuous system parts. For a planar system, the trajectories within an Hinvariant set converge to a stable and unique limit cycle regardless of the initial state. It is shown how this idea can be applied to design controllers which restrict the steadystate values of the continuous states to desired sets. Experimental results concern a manufacturing cell with hybrid dynamics. Copyright c©2005 IFAC
Stability Controllers for Sampled Switched Systems
"... We consider in this paper switched systems, a class of hybrid systems recently used with success in various domains such as automotive industry and power electonics. We propose a statedependent control strategy which makes the trajectories of the analyzed system converge to finite cyclic sequences ..."
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Cited by 1 (1 self)
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We consider in this paper switched systems, a class of hybrid systems recently used with success in various domains such as automotive industry and power electonics. We propose a statedependent control strategy which makes the trajectories of the analyzed system converge to finite cyclic sequences of points. Our method relies on a technique of decomposition of the state space into local regions where the control is uniform. We have implemented the procedure using zonotopes, and applied it successfully to several examples of the literature.
CasingHeading Phenomenon In
, 2005
"... Oil well instabilities cause production losses. One of these instabilities, referred to as the "casingheading" is an oscillatory phenomenon occurring on gaslift artificially lifted well. This behavior is well represented by a 2D model with a vector field that is not continuously di#ere ..."
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Cited by 1 (0 self)
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Oil well instabilities cause production losses. One of these instabilities, referred to as the "casingheading" is an oscillatory phenomenon occurring on gaslift artificially lifted well. This behavior is well represented by a 2D model with a vector field that is not continuously di#erentiable across several switching curves.
Switching Surface Design for Periodically Operated Discretely Controlled Continuous Systems
"... Abstract. Discretely controlled continuous systems (DCCS) represent an important class of hybrid systems, in which a continuous process is regulated by a discrete controller. The paper introduces a novel modelbased design procedure for periodically operated DCCS with the objective to produce a per ..."
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Abstract. Discretely controlled continuous systems (DCCS) represent an important class of hybrid systems, in which a continuous process is regulated by a discrete controller. The paper introduces a novel modelbased design procedure for periodically operated DCCS with the objective to produce a periodic stationary operation. The method exploits an equivalence to periodic control systems to obtain an eventdriven switching strategy that locally stabilizes a predetermined limit cycle and enforces a desired transient behavior. In contrast to earlier results, the controller responds to deviations without a dead time. 1