Dissipative systems and complementarity conditions

Heemels, W.P.M.H.; Schumacher, J.M.; Weiland, S.

doi:10.1109/cdc.1998.761949

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…The circuit analysis is at steady state. The theory of Linear Complimentary system [15] can be used to study the dynamic circuit behavior. This is a subject of ongoing research.…”

Section: Discussionmentioning

confidence: 99%

Solving linear and quadratic programs with an analog circuit

Vichik

Borrelli

2014

Computers & Chemical Engineering

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We present the design of an analog circuit which solves linear programming (LP) problems. In particular, the steady-state circuit voltages are the components of the LP optimal solution. The paper shows how to construct the circuit and provides a proof of equivalence between the circuit and the LP problem. The proposed method is used to implement a LPbased Model Predictive Controller by using an analog circuit. Simulative and experimental results show the effectiveness of the proposed approach.

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“…The circuit analysis is at steady state. The theory of Linear Complimentary system [15] can be used to study the dynamic circuit behavior. This is a subject of ongoing research.…”

Section: Discussionmentioning

confidence: 99%

Solving linear and quadratic programs with an analog circuit

Vichik

Borrelli

2014

Computers & Chemical Engineering

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“…In the specific context of mechanical systems the use of complementarity conditions, which in this case relates to the presence of unilateral constraints, goes back much further and can in fact be traced to work by Fourier and by Farkas for the static (equilibrium) case and papers by Moreau and by Lotstedt for the dynamic case; see [35] for a brief review. The theory of complementarity systems has been further developed and considerably expanded in a number of recent papers, see for instance [36,21,20,29,7,16,18,19,17]. It is the purpose of the present chapter to give a survey of results obtained in these papers.…”

Section: ±(T) = F(x(t) U(t)) Y(t) = H(x(t) U(t)) (113)mentioning

confidence: 97%

Between Mathematical Programming and Systems Theory: Linear Complementarity Systems

Schumacher¹

2001

Systems &Amp; Control: Foundations &Amp; Applications

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Complementarity systems arise from the interconnection of an input-output system (of the type well known in mathematical systems theory) with a set of complementarity conditions (of the type well known in mathematical programming IntroductionInequalities have played a rather minor role in the powerful development of systems theory that has taken place since about 1960. In contrast to this, they are central to the field of mathematical programming that has likewise seen major advances in the past decades. Of course, systems theory is concerned with differential equations; mixing these with inequalities means giving up the smoothness properties that form the basis of much of the theory of dynamical systems. Technological innovation, however, pushes toward the consideration of systems of a mixed continuous/discrete nature, which are likely to be described by systems of differential equations as well as algebraic equations and inequalities. In fact there are many situations in which there are good reasons to consider dynamics in conjunction with inequalities; think for instance of saturation effects in control systems, unilateral constraints in robotics, piecewise linear dynamics, and so on.Among the many systems of equations and inequalities that one may imagine, the ones that are in so-called complementarity form enjoy particular attention in mathematical programming. More specifically the linear complementarity problem (LCP) has been the subject of extensive study because of its wide range of applications; see the book by Cottle et al. [5] for a comprehensive treatment. The LCP may be formulated as follows:given a vector q E JRk and a matrix M of size k x k, find vectors y and u

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“…El par de variables complementarias z y ω son las que le confieren el carácter híbrido a esta clase de sistemas, pues la violación de la no-negatividad implica un cambio de modo, como consecuencia la evolución del sistema está caracterizado por una serie de dinámicas consecutivas, en las que puede ser necesario actualizar el vector de estados [29]. Algunos de los trabajos en los que se ha obtenido el modelo de convertidores utilizando este formalismo son [42,43,44,45].…”

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Modelado, simulación y control de un convertidor boost acoplado magnéticamente

Carrero Candelas

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This thesis covered the modeling, simulation as well as the design of a control law for a coupled inductor Boost converter. In particular, from the point of view of modeling, we focused on the use of averaged modeling and linear complementarity systems (LCS), in order to obtain the dynamic of a coupled inductor Boost converter, which works in discontinuous conduction mode (DCM). The analysis of the converter was performed assuming ideal voltage-current characteristics in the switch and the diodes. In addition, those models were validated through simulation with the model of the converter obtained from the simulation tool for electrical circuits Psim. The interest in researching this converter topology was mainly due to its high efficiency and high conversion rate without extreme duty cycle values. Moreover, from the point of view of control we have proposed a cascade control architecture. The inner loop is a sliding mode current control loop, while the outer one is a PI controller that tunes the current reference to regulate the output voltage to a reference value. The performance and the effectiveness of the feedback control was validated under the presence of load disturbances and input voltage variations through computer simulations by using the linear complementarity model as well as experimentally. Additionally from the linear complementarity model of the converter, it was performed an analysis of the ideal dynamic that takes place when occurs sliding motions in the converter and numerical stability analysis was also carried out. La presente tesis abarca el modelado, simulación y diseño de una ley de control para un convertidor Boost de inductancias acopladas. En particular, desde el punto de vista de modelado, nos enfocamos en las teoíıas de modelos promediados y sistemas lineales complementarios (LCS), para obtener la dinámica del convertidor Boost de inductancias acopladas, el cual trabaja en modo discontinuo de conducción (DCM). El análisis del convertidor se lleva a cabo asumiendo características ideales de tensión-corriente en el interruptor y los diodos. Además, los modelos obtenidos son validados mediante simulación con el modelo del convertidor proporcionado por la herramienta de simulación para circuitos eléctricos Psim. El interés en la topología de este convertidor se debe principalmente a su alta eficiencia y su elevada tasa de conversión sin necesidad de ciclos de trabajos extremos. Por otra parte, desde el punto de vista de control se propone una arquitectura de control en cascada. El lazo interno del control se compone de una estrategia de control no lineal, similar a la teoría de control en modo de deslizamiento, mientras que para el lazo externo se diseña un control de tipo PI. El principal objetivo del control diseñado es regular el voltaje de salida del convertidor a el valor de referencia deseado. La efectividad y desempeño del controlador diseñado es validada tanto en simulación como experimentalmente ante diferentes escenarios que incluyen perturbaciones en la carga y el voltaje de entrada. Adicionalmente a partir del modelo lineal complementario del convertidor, se lleva a cabo un análisis de la dinámica ideal de deslizamiento y un análisis numérico de la estabilidad cuando se tiene modo de deslizamiento.

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Dissipative systems and complementarity conditions

Cited by 5 publications

References 9 publications

Solving linear and quadratic programs with an analog circuit

Solving linear and quadratic programs with an analog circuit

Between Mathematical Programming and Systems Theory: Linear Complementarity Systems

Modelado, simulación y control de un convertidor boost acoplado magnéticamente

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