Ernesto Kofman

Level Crossing Sampling in Feedback Stabilization under Data-Rate Constraints

This paper introduces a novel event-driven sampled-data feedback scheme where the plant output samples are triggered by the crossings - with hysteresis - of the signal through its quantization levels. The plant and controller communicate over binary channels that operate asynchronously and are assumed to be error and delay-free. The paper proposes two systematic output feedback control design strategies. The first strategy consists in the digital emulation of a previously designed analog controller. The second strategy is a simple direct design that drives the plant state to the origin in finite time after a total transmission of 2n + 2 bits, where n is the order of the plant

A systematic method to obtain ultimate bounds for perturbed systems

In this paper, we develop a systematic method to obtain ultimate bounds for both continuous- and discrete-time perturbed systems. The method is based on a componentwise analysis of the system in modal coordinates and thus exploits the system geometry as well as the perturbation structure without requiring calculation of a Lyapunov function for the system. The method is introduced for linear systems having constant componentwise perturbation bounds and is then extended to the case of state-dependent perturbation bounds. This extension enables the method to be applied to non-linear systems by treating the perturbed non-linear system as a linear system with a perturbation bounded by a non-linear function of the state. Examples are provided where the proposed systematic method yields bounds that are tighter or at least not worse than those obtained via standard Lyapunov analysis. We also show how our method can be combined with Lyapunov analysis to improve on the bounds provided by either approach.

Discrete Event Simulation of Hybrid Systems

This paper describes the quantization-based integration methods and extends their use to the simulation of hybrid systems. Using the fact that these methods approximate ordinary differential equations (ODEs) and differential algebraic equations (DAEs) by discrete event systems, it is shown how hybrid systems can be approximated by pure discrete event simulation models (within the DEVS formalism framework). In this way, the treatment and detection of events representing discontinuities---which constitute an important problem for classic ODE solvers---is notably simplified. It can be also seen that the main advantages of quantization-based methods (error control, reduction of computational costs, possibilities of parallelization, sparsity exploitation, etc.) are still verified in the presence of discontinuities. Finally, some examples which illustrate the use and the advantages of the methodology in hybrid systems are discussed.

PowerDEVS: a tool for hybrid system modeling and real-time simulation

In this paper we introduce a general-purpose software tool for discrete event system specification (DEVS) modeling and simulation oriented to the simulation of hybrid systems. The environment, called PowerDEVS, allows atomic DEVS models to be defined in C++ language that can then be coupled graphically in hierarchical block diagrams to create more complex systems. The environment automatically translates the graphically coupled models into a C++ code which executes the simulation. A remarkable feature of PowerDEVS is the possibility to perform simulations under a real-time operating system (RTAI) synchronizing with a real-time clock, which permits the design and automatic implementation of synchronous and asynchronous digital controllers. Combined with its continuous system simulation library, PowerDEVS is also an efficient tool for real-time simulation of physical systems. Another feature is the interconnection between PowerDEVS and the numerical package Scilab. PowerDEVS simulations can make use of Scilab workspace variables and functions, and the results can be sent back to Scilab for further processing and data analysis. In addition to describing the main features of the software tool, the article also illustrates its use with some examples which show its simplicity and efficiency.

A Second-Order Approximation for DEVS Simulation of Continuous Systems

In this article, based on the methodology of discrete event simulation of continuous systems via quantized state systems (QSS), a new second-order approximation, called second-order quantized state systems (QSS2), is proposed. This new approximation, which satisfies the same stability and convergence properties that were deduced for QSS in previous works, also allows reducing the number of calculations with respect to the former method. It is shown that in the particular case of linear time-invariant (LTI) systems, the QSS2 can be exactly represented by a DEVS model, and in nonlinear systems, an approximated DEVS model can be also obtained. For the LTI case, a closed formula giving the necessary quantization that allows achieving a bound in the error during the whole simulation is deduced. This formula, which stands for both QSS and QSS2 approaches, also proves that for any quantization, the error is always bounded.

MUESTREO, CONTROL Y COMUNICACIÓN BASADOS EN EVENTOS

Los sistemas de control periodicos o activados por tiempo han dominado casi de manera exclusiva la investigacion en ingenieria de control. El control basado en eventos es una alternativa muy prometedora particularmente cuando se consideran sistemas con capacidades reducidas de computacion y de comunicacion. En un sistema de control basado en eventos es la ocurrencia de un evento, en lugar del paso del tiempo lo que decide cuando se debe efectuar el muestreo. En este trabajo se presenta una revision panoramica de la situacion actual del campo de los sistemas de muestreo basados en eventos. Se presentan los principales esquemas de muestreo basados en eventos y se analizan las diferentes estrategias de diseno de controladores que funcionan con este tipo de muestreo. Finalmente se analiza la implicacion que tendra su aplicacion en el campo de los nuevos sistemas de control en red.

Technical communique: Non-conservative ultimate bound estimation in LTI perturbed systems

A closed formula for ultimate bound estimation in LTI systems with non-vanishing perturbations is presented. The formula, based on geometrical properties of the system, provides an alternative to Lyapunovs second method based study. Although it is not proven that the bound obtained is always less conservative than the Lyapunovs bound, some examples are introduced where the estimations are significantly improved. An extension of the idea for nonlinear systems is also sketched.

Quantization-based simulation of differential algebraic equation systems

The author studies the use of first-and second-order quantized state systems methods (QSS and QSS2) in the simulation of differential algebraic equation (DAE) systems. A general methodology to obtain the QSS and the QSS2 approximations of a generic DAE of index 1 is provided, and their corresponding discrete event system (DEVS) implementations are developed. Furthermore, an alternative method is given based on the block-by-block translation from block diagrams containing algebraic loops into coupled DEVS representations of the corresponding QSS and QSS2 approximations. The author shows that the main advantages provided by the quantization-based methods in the simulation of ordinary differential equations—stability properties, reduction of computational costs, sparsity exploitation, and so on—are still verified in DAEs. These advantages are illustrated and discussed in the simulation of two examples that show the main features of the methodology.

Linearly Implicit Quantization-Based Integration Methods for Stiff Ordinary Differential Equations

Abstract In this paper, new integration methods for stiff ordinary differential equations (ODEs) are developed. Following the idea of quantization-based integration (QBI), i.e., replacing the time discretization by state quantization, the proposed algorithms generalize the idea of linearly implicit algorithms. Also, the implementation of the new algorithms in a DEVS simulation tool is discussed. The efficiency of these new methods is verified by comparing their performance in the simulation of two benchmark problems with that of other numerical stiff ODE solvers. In particular, the advantages of these new algorithms for the simulation of electronic circuits are demonstrated.

Brief paper: Control design with guaranteed ultimate bound for perturbed systems

We present a new control design method for perturbed multiple-input systems, which guarantees any desired componentwise ultimate bound on the system state. The method involves eigenvalue/eigenvector assignment by state feedback and utilises a componentwise bound computation procedure. This procedure directly takes into account both the system and perturbation structures by performing componentwise analysis, thus avoiding the need for bounds on the norm of the perturbation. The perturbation description adopted can accommodate numerous types of uncertainties, including uncertain time-delays in the feedback loop. We apply the method to an example taken from the literature to illustrate its simplicity and generality.