Survey of modeling, analysis, and control of hybrid systems

Schutter, de B Bart; Heemels, Wpmh Maurice; Lunze, Jan; Prieur, Christophe

doi:10.1017/cbo9780511807930.003

Cited by 28 publications

(26 citation statements)

References 95 publications

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“…The first class of methods manipulates directly sets of states, finitely represented, for instance, as polytopes [25], ellipsoids [26], or zonotopes [27], or by relying on interval arithmetic [28] combined with constraint solving [29], [30], exploiting satisfaction modulo solvers over reals [31], [32]. The dynamics of the system is lifted at the set level, so that one computes the evolution of the reachable set under the action of the dynamics.…”

Section: A Related Work On Numerical Methodsmentioning

confidence: 99%

Mean Field Approximation of Uncertain Stochastic Models

Bortolussi

Gast

2016

2016 46th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN)

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Abstract-We consider stochastic models in presence of uncertainty, originating from lack of knowledge of parameters or by unpredictable effects of the environment. We focus on population processes, encompassing a large class of systems, from queueing networks to epidemic spreading. We set up a formal framework for imprecise stochastic processes, where some parameters are allowed to vary in time within a given domain, but with no further constraint. We then consider the limit behaviour of these systems as the population size goes to infinity. We prove that this limit is given by a differential inclusion that can be constructed from the (imprecise) drift. We provide results both for the transient and the steady state behaviour. Finally, we discuss different approaches to compute bounds of the soobtained differential inclusions, proposing an effective controltheoretic method based on Pontryagin principle for transient bounds. This provides an efficient approach for the analysis and design of large-scale uncertain and imprecise stochastic models. The theoretical results are accompanied by an in-depth analysis of an epidemic model and a queueing network. These examples demonstrate the applicability of the numerical methods and the tightness of the approximation.

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Section: A Related Work On Numerical Methodsmentioning

confidence: 99%

Mean Field Approximation of Uncertain Stochastic Models

Bortolussi

Gast

2016

2016 46th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN)

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“…Since the system under study involves a combination of discrete-event dynamics and continuous-time dynamics, we propose to represent the dynamics using a hybrid automaton (Henzinger, 1996;Schutter & Heemels, 2001). A general hybrid automaton H can be defined as H = (S, X, U, f, Init, Inv, E, G, R) (Schutter & Heemels, 2001), where • S is a finite set of discrete modes; • X is a finite set of continuous state variables;…”

Section: Hybrid Automatonmentioning

confidence: 99%

Energy-efficient container handling using hybrid model predictive control

Xin

Negenborn

Lodewijks

2015

International Journal of Control

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The performance of container terminals needs to be improved to adapt the growth of containers while maintaining sustainability. This paper provides a methodology for determining the trajectory of three key interacting machines for carrying out the so-called bay handling task, involving transporting containers between a vessel and the stacking area in an automated container terminal. The behaviours of the interacting machines are modelled as a collection of interconnected hybrid systems. Hybrid model predictive control (MPC) is proposed to achieve optimal performance, balancing the handling capacity and energy consumption. The underlying control problem is hereby formulated as a mixed-integer linear programming problem. Simulation studies illustrate that a higher penalty on energy consumption indeed leads to improved sustainability using less energy. Moreover, simulations illustrate how the proposed energy-efficient hybrid MPC controller performs under different types of uncertainties.

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“…Another aspect that arises in numerous industrial applications is switching or hybrid behavior of the system model, e.g., mechanical systems with dry friction [10] or impact phenomena, electrical circuits with switching elements like diodes or switches [46], or control systems where the value of a control switches [59]. For such systems, the framework of DAEs provides essential information for a robust numerical treatment.…”

Section: Introductionmentioning

confidence: 99%

DAEs in Applications

Scholz

Steinbrecher

2015

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

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Differential-algebraic equations (DAEs) arise naturally in many technical and industrial applications. By incorporating the special structure of the DAE systems arising in certain physical domains, the general approach for the regularization of DAEs can be efficiently adapted to the system structure. We will present the analysis and regularization approaches for DAEs arising in mechanical multibody systems, electrical circuit equations, and flow problems. In each of these cases the DAEs exhibit a certain structure that can be used for an efficient analysis and regularization. Moreover, we discuss the numerical treatment of hybrid DAE systems, that also occur frequently in industrial applications. For such systems, the framework of DAEs provides essential information for a robust numerical treatment. IntroductionIn the simulation and control of constrained dynamical systems differential-algebraic equations (DAEs) are widely used, since they naturally arise in the modeling process. In particular, the automatic modeling using coupling of modularized subcomponents is frequently used in industrial applications yielding large-scale (but often sparse) DAE systems. An important aspect in the simulation of these systems is that conservation laws (e.g. conservation of mass or momentum, mass or population balances, etc.) included in the model equations should be preserved during the numerical integration. These algebraic relations pose constraints on the solution and may lead to so-called hidden constraints (for higher index DAEs). Also path-following constraints can be considered as additional algebraic constraints. The occurrence of hidden constraints leads to difficulties in the numerical solution as

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Survey of modeling, analysis, and control of hybrid systems

Cited by 28 publications

References 95 publications

Mean Field Approximation of Uncertain Stochastic Models

Mean Field Approximation of Uncertain Stochastic Models

Energy-efficient container handling using hybrid model predictive control

DAEs in Applications

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