Authors: Frehse, Goran; Ray, Rajarshi

Abstract: The verification of continuous and hybrid systems is known to be hard, and today tools are limited to relatively small problems. Several novel approaches are currently under investigation that exploit various kinds of set representations (polyhedra, zonotopes), improved algorithms (avoiding the wrapping effect) and strategies (such as abstraction refinement). We outline a tool framework that is able to integrate and combine different elements from these approaches. The framework includes implementations for common functionality (hybrid automata, graphical output, basic set operations, etc.) and interfaces that allow us to plug in different implementations, such as a particular kind of set representation or a particular optimization algorithm. This allows us to experimentally evaluate competing ideas, combine promising elements and explore new approaches with relatively little development effort.

Keywords: hybrid automata,support functions,reachability

Identifier: 10.3182/20090916-3-ES-3003.00043

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Melin, Julie; Jungers, Marc; Daafouz, Jamal; Iung, Claude

Abstract: The presence of a bounded time-varying delay in discrete-time controlled system implies a deterioration of the performance (stability and guaranteed cost). This paper studies controllers design for such a system, leading to a stabilized controlled system and to an upper bound of guaranteed cost as small as possible. The two contexts of state or only output availability are considered. These controllers are obtained via optimization algorithms using Linear Matrix Inequalities and Lyapunov-Krasovskii functions approach. An example illustrates the main results.

Keywords: delay systems,switched systems,LMI,observer based state feedback,performances

Identifier: 10.3182/20090916-3-ES-3003.00034

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Angulo, Marco Tulio; Levant, Arie

Abstract: Finite-Time stability of Linear Time Invariant systems with matched perturbations using dynamic output feedback is achieved under the assumptions of well-defined relative degree and a known bound of the perturbations. The approach is based on high order sliding modes, using global controllers and differentiator. A separation criteria that allows to detect the convergence of the differentiator and posterior gain adaptation is presented. Analysis of the performance under noise and sampling is presented.

Keywords: dynamic output feedback,sliding-mode control

Identifier: 10.3182/20090916-3-ES-3003.00039

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Petreczky, M.; Collins, P.; Van Beek, D. A.; Van Schuppen, J. J. H.; Rooda, J. E.

Abstract: We address the control synthesis of hybrid systems with discrete inputs, disturbances and outputs. The control objective is to ensure that the events of the closed-loop system belong to the language of the control requirements. The controller is sampling-based and it is representable by a finitestate machine. We formalize the control problem and provide a theoretically sound solution. The solution is based on solving a discrete-event control problem for a finite-state abstraction of the plant. We propose a specific construction for the finite-state abstraction. This construction is not based on discretizing the state-space, but rather on converting the continuous-time hybrid system to a discrete-time one based on sampling. The construction works only for a specific class of hybrid systems. We describe this class of systems and we provide an example of such a system, inspired by an industrial use-case.

Keywords: hybrid systems,discrete-event systems,symbolic control

Identifier: 10.3182/20090916-3-ES-3003.00058

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Floquet, Thierry; Hetel, Laurentiu; Perruquetti, Wilfrid

Abstract: In this paper, the existence of stabilizing sliding motions in the context of switched linear systems is investigated. We consider the case of switched systems with two subsystems and we propose conditions for the existence of stable sliding hyper-planes. For particular cases of switched systems (planar systems, integrator chains), we provide constructive analytical methods for deriving a stabilizing switching sequence.

Keywords:

Identifier: 10.3182/20090916-3-ES-3003.00063

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Dotoli, Mariagrazia; Fanti, Maria Pia; Mangini, Agostino M.; Ukovich, Walter

Abstract: The efficient management of the Emergency Department (ED) has become an important issue in the past decade. Indeed, the increased demand for emergency services has saturated the capacity of EDs that require suitable tools for the efficient flow of work and people. The paper proposes a model to describe in a concise and effective way the structure and dynamics of a critical ED of the general hospital of Bari (Italy): the Emergency Cardiology Department (ECD). The model describes in a continuous Petri net framework the complete workflow and management of patients starting from their arrival to the ED until either their discharge from the hospital or their admission in a suitable hospital department. The fluid approximation allows defining suitable optimization problems to optimize the system performances and determine the optimal resource dimension guaranteeing the efficient management of the ECD. A simulation study shows that the optimized parameters lead to an effective workflow organization while maximizing the patient flow.

Keywords: modeling,continuous Petri nets,simulation,performance evaluation,healthcare systems

Identifier: 10.3182/20090916-3-ES-3003.00010

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Castro, Rodrigo; Kofman, Ernesto; Wainer, Gabriel

Abstract: We present a formal Modeling and Simulation (M&S) methodology for hybrid control of networking systems. The method is used for analysis, design and implementation of Quality of Service (QoS) control systems in Network Processor (NP)-based applications. We apply continuous Control Systems Theory to enforce Admission Control strategies into discrete-event network traffic. This represents a hybrid system modeling problem, that has to be treated formally to guarantee the applicability of the continuous control theoretical results into discrete-event systems. We show that using DEVS (Discrete Event System Specification), in combination with Quantized State Systems (QSS) numerical methods for the approximation of continuous systems, offers numerous advantages: these frameworks provide the means to accurately analyze and design hybrid models for Admission Control and they can be seamlessly integrated into a unified formal framework. It also enables the transition between the DEVS-based simulation and the deployment of the obtained hybrid models into the target networking platform.

Keywords: DEVS,hybrid systems,embedded networking,admission control

Identifier: 10.3182/20090916-3-ES-3003.00014

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Mojica-Nava, Eduardo; Quijano, Nicanor; Rakoto-Ravalontsalama, Naly

Abstract: A generalization of a polynomial approach to solve the optimal control problem of nonlinear switched systems is presented. We present a technique to deal with the more general non-polynomial switched systems, using the polynomial approach previously presented, combined with a recasting process. It is shown that the representation of the original switched problem into a continuous polynomial system allows us to use the generalized Maximum Principle. With this method and from a theoretical point of view, we provide necessary and sufficient conditions for the existence of minimizer by using particular features of its relaxed, convex formulation using the theory of moments.

Keywords: optimal control,polynomial systems,switched systems

Identifier: 10.3182/20090916-3-ES-3003.00022

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Mazaeda, Rogelio; De Prada, César; Merino, Alejandro; Acebes, Felipe

Abstract: The final department of any sugar factory is in charge of producing commercial sugar grains out of an impure sucrose in water solution by means of crystallization. Quality requirements demand a fed-batch mode of operation from most of the process units of the section and in particular from the industrial crystallizers. A library of reusable simulation models of the Sugar House have been developed taking advantage of object oriented modeling concepts. The dynamic simulation of batch equipment usually demands the use of hybrid type models.

Keywords: numerical simulation,simulation languages,dynamic modeling,process models,object modeling techniques

Identifier: 10.3182/20090916-3-ES-3003.00017

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Haque, Musad; Rahmani, Amir; Egerstedt, Magnus

Abstract: Social behavior of animals can offer solution models for missions involving a large number of heterogeneous vehicles, such as light combat ships, unmanned aerial vehicles, and unmanned underwater vehicles. We draw inspiration from the foraging techniques of bottlenose dolphins to address the problem of heterogeneous multi-agent herding. We produce a hybrid automaton model of the entire foraging method - search, detect, and capture - where agents are modeled as first-order systems in which interactions are defined through spatial proximity. Finally, simulations are provided to illustrate that our model is expressive enough to capture this complex biological phenomenon.

Keywords: biologically-inspired methods,hybrid systems,decentralized control,multi-agent herding,networked control systems

Identifier: 10.3182/20090916-3-ES-3003.00046

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Summers, Sean; Lygeros, John

Abstract: In this paper we present a dynamic programming based solution to a probabilistic reachavoid problem for a controlled discrete time stochastic hybrid system. Similar to recent results related to the problem of probabilistic safety and stochastic target hitting, we introduce a summultiplicative cost function and a dynamic recursion that quantifies the probability of hitting a target set while avoiding an unsafe set. Optimal and worst-case reach while avoid control policies are introduced as the solution to an optimal control problem via dynamic programming. A computational example is provided.

Keywords: hybrid systems,stochastic systems,reachability,safety,target hitting,optimal control,dynamic programming

Identifier: 10.3182/20090916-3-ES-3003.00027

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Tian, Yang; Floquet, Thierry; Belkoura, Lotfi; Perruquetti, Wilfrid

Abstract: In this paper, a method for the finite time estimation of the switching times in linear switched systems is proposed. The approach is based on distribution theory. Switching time estimates are given by explicit algebraic formulae that can be implemented in a straightforward manner using standard tools from computational mathematics. Simulations illustrate the proposed techniques.

Keywords: linear systems,switched systems,switching time estimation,distribution theory

Identifier: 10.3182/20090916-3-ES-3003.00069

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Apaydin-Ozkan, Hanife; Júlvez, Jorge; Mahulea, Cristian; Silva, Manuel

Abstract: This paper considers the problem of controlling timed continuous Petri nets under infinite server semantics. The proposed control strategy assigns piecewise constant flows to transitions in order to reach the target state. First, by using linear programming, a method driving the system from the initial to the target state through a linear trajectory is developed. Then, in order to improve the time of the trajectory, intermediate states are added by means of bilinear programming.

Keywords: timed continuous Petri nets,minimum time control,piecewise linear trajectory

Identifier: 10.3182/20090916-3-ES-3003.00009

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Giua, Alessandro; Seatzu, Carla; Wardi, Yorai

Abstract: Infinitesimal Perturbation Analysis (IPA) recently has been extensively investigated in the setting of fluid queues, where it was shown to yield simple algorithms for computing the gradients of several performance functions. More lately, efforts have been made to extend its application domain from fluid queueing networks to other kinds of stochastic hybrid systems. In this vein, the present paper inaugurates a study of the application of IPA to a class of hybrid Petri nets. The main point of concern is the modeling element of the fluid transition with multiple input places, representing concurrency and synchronization in Petri nets, and not yet studied in the context of IPA. We first derive the IPA gradient of the throughput with respect to fluid flow parameters at the input places, and then consider an example of optimizing throughput in a fork-join system. Simulation experiments are presented in support of the theoretical results. We point out that the main purpose of the paper is to initiate a study of IPA in the setting of hybrid Petri nets, and not to consider application examples.

Keywords: infinitesimal perturbation analysis,hybrid Petri nets,stochastic hybrid systems

Identifier: 10.3182/20090916-3-ES-3003.00047

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Lefebvre, D.; Leclercq, E.; Khalij, L.; De Cursi, E. Souza; El Akchioui, N.

Abstract: Reliability analysis is often based on stochastic discrete event models like Markov models or stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. The contribution of this paper is to approximate the steady state of mono T-semiflow stochastic nets by mean of continuous Petri nets according to a modification of the maximal firing speed vector definition. This result is then used to accelerate convergence of stochastic simulations.

Keywords: stochastic Petri nets,continuous Petri nets,steady state,reliability analysis

Identifier: 10.3182/20090916-3-ES-3003.00012

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Hultgren, Anders; Melin, Jan; Ranstad, Per

Abstract: An industrially applied LCC power converter is modelled as a hybrid system. It is found that the hybrid system given a parameter set up and different initial conditions has three different limit cycles, one unstable and two asymmetric stable limit cycles. Effects of the asymmetric limit cycles are considered.

Keywords: modelling,analysis,simulation,control,hybrid,limit cycles,resonant power converters

Identifier: 10.3182/20090916-3-ES-3003.00008

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Kerber, Florian; Van Der Schaft, Arjan J.

Abstract: Modular modeling techniques play an important role in the analysis of engineering processes as well as in control applications. While individual components of aggregated models can be relatively simple, complexity increases significantly when interconnections are considered. To address the problem of complexity explosion, simulation relations can be employed to abstract system behaviors by lower order models. As an application to formal verification, simulation relations allow to check system properties such as safety requirements. In a compositional framework, they can be used to approximate interconnections of systems based on approximations of the individual components. While results with regard to compositional analysis have been presented for discrete and recently also for continuous-time systems, it is our aim to develop compositional and assume-guarantee reasoning for a specific class of hybrid systems, namely switching linear systems.

Keywords: switching linear systems,simulation relations,compositional reasoning,assume-guarantee reasoning

Identifier: 10.3182/20090916-3-ES-3003.00057

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Ramdani, Nacim; Nedialkov, Nedialko S.

Abstract: We investigate solution techniques for numerical constraint satisfaction problems and validated numerical set integration methods for computing reachable sets of nonlinear hybrid dynamical systems in presence of uncertainty. To use interval simulation tools with higher dimensional hybrid systems, while assuming large domains for either initial continuous state or model parameter vectors, we need to solve the problem of flow/sets intersection in an effective and reliable way. The main idea developed in this paper is first to derive an analytical expression for the boundaries of continuous flows, using interval Taylor methods and techniques for controlling the wrapping effect. Then, the event detection and localization problems underlying flow/sets intersection are expressed as numerical constraint satisfaction problems, which are solved using global search methods based on branch-and-prune algorithms, interval analysis and consistency techniques. The method is illustrated with a hybrid system with uncertain nonlinear continuous dynamics and nonlinear invariants and guards.

Keywords: continuous-time systems,hybrid systems,interval analysis,non-linear systems reachability,uncertain systems

Identifier: 10.3182/20090916-3-ES-3003.00028

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Kara, R.; Ahmane, M.; Loiseau, J-J.; Djennoune, S.

Abstract: This paper deals with constrained state feedback control of piecewise affine systems, an important class of hybrid systems. Our objective is to design stabilizing feedback gains that guarantees, for any arbitrary switching rule, the respect of the control and state constraints. The existence of a solution is first expressed geometrically, in terms of two polyhedral sets inclusion. The geometric conditions is then reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem.

Keywords: hybrid systems,piecewise affine systems,constrained control,positive invariance,linear matrix inequalities (LMI)

Identifier: 10.3182/20090916-3-ES-3003.00035

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Teige, Tino; Fränzle, Martin

Abstract: Aiming at fully symbolic methods for the analysis of probabilistic hybrid systems, we recently introduced the notion of stochastic satisfiability modulo theories (SSMT) problems and the corresponding SiSAT solving algorithm. The notion of SSMT extends SMT with randomized (aka. stochastic) as well as existential and universal quantification as known from stochastic propositional satisfiability. In this paper, we describe the symbolic encoding of scheduled-event probabilistic hybrid automata by means of a case study from the networked automation system domain. We furthermore report on the SSMT solver SiSAT including recent enhancements in terms of solver performance, expressiveness of the input language, and handling of numerical issues. The significance of the performance enhancements is demonstrated by empirical results.

Keywords: probabilistic hybrid systems,probabilistic logic,constraint satisfaction problems,problem solvers,automatic verification

Identifier: 10.3182/20090916-3-ES-3003.00029

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Azhmyakov, V.; Egerstedt, M.; Fridman, L.; Poznyak, A.

Abstract: This paper focuses on the continuity and approximability properties for nonlinear affine control systems. We consider dynamical systems governed by ordinary differential equations and establish the continuity properties of the given and relaxed (in the sense of Filippov) systems with respect to controls and initial state variables. The approach based on the set-valued analysis makes it possible to study discontinuous models in the abstract setting and to obtain general theoretical results. The latter can be effectively applied to wide classes of variable structure control systems. In particular, this paper deals with applications of the above-mentioned continuity and approximability to some hybrid control systems and to the classical sliding mode control processes.

Keywords: nonlinear affine control systems,differential inclusions,hybrid systems,sliding mode control,robustness

Identifier: 10.3182/20090916-3-ES-3003.00036

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Collins, Pieter J.; Habets, Luc C. G. J. M.; Petreczky, Mihály; Van Schuppen, Jan H.

Abstract: The character of this paper is an extended Abstracact of the approach developed by the authors for control of piecewise-affine hybrid systems. Control of hybrid systems is a wide ranging research topic with many theoretical problems. The authors have therefore decided early on to restrict attention to piecewise-affine hybrid systems on polytopes. The approach developed includes for affine systems on polytopes sufficient conditions for the problems (1) leaving the polytope in finite time through a prespecified set of facets; (2) remaining inside a particular polytope forever; and (3) converging to a fixed state inside a particular polytope. For piecewise-affine hybrid system on polytopes a procedure for reachability and control synthesis is proposed consisting of (1) for each discrete state the computation of all possible exit facets and exit events; (2) abstraction of the continuous dynamics to an automaton; and (3) the search of a path in the automaton from an initial discrete state to a target discrete state. Open research issues for control of hybrid systems are stated.

Keywords: piecewise-affine hybrid system,control system synthesis,control-to-facet

Identifier: 10.3182/20090916-3-ES-3003.00041

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Tran, Thanh-Ha; Engell, Sebastian

Abstract: This contribution presents an approach to synthesize logic feedback controllers for Discretely Controlled Continuous Systems such that given specifications are fulfilled. This class of systems consists of a continuous plant with nonlinear dynamics which is controlled by a logic controller that processes discrete measurements. The control problem is to optimally steer the system from a set of initial states to a set of target states without reaching unsafe states. For given thresholds, the algorithm first computes the optimal discrete inputs for each boundary section to obtain optimal trajectories from each boundary section to the target by a dynamic programming approach. The controller then has to be verified to guarantee that the unsafe states are not reached for arbitrary trajectories. The approach is demonstrated for a two-tank benchmark.

Keywords: dynamic programming,logic controllers design,hybrid systems,optimal control,quantized systems,switched dynamics

Identifier: 10.3182/20090916-3-ES-3003.00023

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Yang, Hao; Cocquempot, Vincent; Jiang, Bin

Abstract: This paper develops the dissipativity theory for switched systems and proposes a "global dissipativity" concept which means that the total energy stored by the system is less than the total energy supplied from the outside. This result is applied to the design of a novel supervisory fault tolerant control scheme for non-switched systems, which relies on a simple dissipativity-based switching among a family of pre-computed candidate controllers without any additional model or filter. The states are ensured to be bounded during the switching delay. A RLC circuit example illustrates the efficiency of the proposed method.

Keywords:

Identifier: 10.3182/20090916-3-ES-3003.00059

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009

Authors: Bejarano, Francisco J.; Fridman, Leonid

Abstract: This paper discusses the problem of observability synthesis of switching systems. Based only on the continuous output information, an observer is proposed ensuring the reconstruction of the entire state (continuous and discrete) in finite time. For the observer design a exact sliding mode differentiator is used, which allows the finite time convergence of the observer trajectories to the original trajectories. The observer design includes both cases zero control input and nonzero control input. Simulations illustrate the effectiveness of the proposed observation scheme.

Keywords: high order sliding mode,switching systems,observer design

Identifier: 10.3182/20090916-3-ES-3003.00064

Conference: 3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009)

Location: University of Zaragoza, Spain

Start Date: Wed Sep 16 2009 - End Date: Fri Sep 18 2009