Showing papers by "Wpmh Maurice Heemels published in 2003"

Switched networks and complementarity

Abstract: A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also cover switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone-complementarity problem. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we show that within our framework, energy cannot increase as a result of a jump, and we derive a stability result from this.

Two approaches to state estimation for a class of piecewise affine systems

Abstract: In this paper we present two approaches to state estimation for a class of discrete time bi-modal piece-wise affine systems. The proposed approaches have the characteristic feature that they do not require information on the currently active dynamics of the piecewise affine system. We propose a Luenberger-type observer, and derive sufficient conditions for the observation error to be globally asymptotically stable, in the case when the system dynamics is continuous over the switching plane. When the dynamics is discontinuous, we derive conditions that guarantee that the estimation error will be bounded with respect to the state bound. Second, we propose to apply particle filtering algorithm, which aims at approximating the a posteriori probability density of the state. The presented approaches are compared and illustrated with examples.

Stability and controllability of planar bimodal linear complementarity systems

Abstract: The object of study of this paper is the class of hybrid systems consisting of so-called linear complementarity (LC) systems, that received a lot of attention recently and has strong connections to piecewise affine (PWA) systems. In addition to PWA systems, some of the linear or affine submodels of the LC systems can 'live' at lower-dimensional subspaces and re-initializations of the state variable at mode changes is possible. For LC systems we study the stability and controllability problem. Although these problems received for various classes of hybrid systems ample attention, necessary and sufficient conditions, which are explicit and easily verifiable, are hardly found in the literature. For LC systems with two modes and a state dimension of two such conditions are presented.

Modelling, well-posedness, and stability of switched electrical networks

Abstract: A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we derive a stability result. Hence, for a subclass of hybrid dynamical systems, the issues of well-posedness, regularity of trajectories, jump rules, consistent states and stability are resolved.

Advanced energy management strategies for vehicle power nets

Abstract: In the near future a significant increase in electric power consumption in vehicles is to be expected. To limit the associated increase in fuel consumption (and CO2 emission), smart strategies for the generation, storage/retrieval, distribution and consumption of the electric power can be used. This paper presents a preliminary case study based on a Model Predictive Control-based strategy that uses a prediction of the future driving pattern and load request in order to minimize fuel use by generating only at the most efficient moments. The strategy is tested in a simulation environment, showing a decrease in fuel consumption compared to a baseline strategy.

A Multi Target Track Before Detect Application

Abstract: This paper deals with a radar track before detect application in a multi target setting. Track before detect is a method to track weak objects (targets) on the basis raw radar measurements, e.g. the reflected target power. In classical target tracking, the tracking process is performed on the basis of pre-processed measurements, that are constructed from the original measurement data every time step. In this way no integration over time takes place and information is lost. In this paper we will give a modelling setup and a particle filter based algorithm to deal with a multiple target track before detect situation. In simulations we show that, using this method, it is possible to track multiple, closely spaced, (weak) targets.

Modelling, well-posedness, and stability of switched electrical networks

Abstract: A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we derive a stability result. Hence, for a subclass of hybrid dynamical systems, the issues of well-posedness, regularity of trajectories, jump rules, consistent states and stability are resolved.

Control of quantized linear systems: an l/sub 1/-optimal control approach

Abstract: In many practical situations, the outputs of a plant are not measured exactly, but are corrupted by quantization errors. Often the effect of the quantization error is neglected in the control design phase, which can lead to undesirable effects like limit cycles and even chaotic behavior once the controller has been implemented. In this paper we present a method based on l/sub 1/ optimal control that minimizes the amplitude of the oscillations in the to-be-controlled variables. Analytical and numerical examples illustrate the elegance of the l/sub 1/-theory in this setting.

On the existence and uniqueness of solution trajectories to hybrid dynamical systems

Abstract: In this paper, we study the fundamental system-theoretic property of wellposedness for several classes of hybrid dynamical systems. Hybrid systems are characterized by the presence and interaction of continu-ous dynamics and discrete actions. Many different description formats have been proposed in recent years for such systems; some proposed forms are quite direct, others lead to rather indirect descriptions. The more indirect a description form is, the harder it becomes to show that solutions are well-defined. This paper intends to provide a survey on the available results on existence and uniqueness of solutions for given initial conditions in the context of various description formats for hybrid systems.

Switched networks and complementarity

Abstract: A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also cover switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone-complementarity problem.We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we show that within our framework, energy cannot increase as a result of a jump, and we derive a stability result from this.

Control of quantized systems based on discrete event models

Abstract: This paper presents controller design methods for dynamical systems that are observed by discrete sensors. These sensors induce a partitioning of the state space and only this quantized information is available for the controller. The so-called 'quantized system' is modelled by a discrete-event model that serves as a basis for the controller design methods. However, instead of using solely the classical control methodologies for discrete-event systems as found in the literature, improvements are proposed by including additional information provided by the fact that the underlying plant is continuous by nature, such as continuity of the state trajectories and information on derivatives that holds for parts of the state space. The concept of discretely controlled invariant sets will play a crucial role in the development of control strategies and necessary and sufficient conditions for controlled invariance are presented. Also algorithms are included to compute the smallest and largest discretely controlled...

A semi-explicit MPC set-up for constrained piecewise affine systems

Abstract: Recently quite some effort has been dedicated towards the use of Model Predictive Control (MPC) for regulating discrete-time piecewise affine systems. One of the obstructions for implementation is the high on-line computational load. In this paper we present an approach to reduce the on-line computations by using an algorithm that solves off-line a controllability problem with respect to an invariant target set. The algorithm generates a tree containing minimal discrete events controllable paths to the target set. For an initial state (or a measured state), a controllable path to the target set with a minimal number of discrete events is easily obtained and a resulting ordered sequence of state space regions (sets) is pre-computed; each region corresponds to a single sub-model, part of the piecewise affine system. It is then shown how, under certain assumptions, this controllable path can be used to design a computationally more friendly semi-explicit MPC algorithm for constrained piecewise affine systems. Finally, an example is given for illustration purposes.

State estimation for systems with varying sampling rate

Abstract: We investigate problems that occur in state estimation when the outputs of a continuous time system are sampled at non-equidistant time instants. The time interval between the samples is assumed to be known, and to belong to a prescribed set. An observer synthesis procedure is proposed which guarantees the stability of the estimation error and in addition minimizes the covariance of the observation error.