Robust Simulation for Hybrid Systems: Chattering Path Avoidance

The sliding mode approach is recognized as an efficient tool for treating the chattering behavior in hybrid systems. However, the amplitude of chattering, by its nature, is proportional to magnitude of discontinuous control. A possible scenario is that the solution trajectories may successively enter and exit as well as slide on switching mani-folds of different dimensions. Naturally, this arises in dynamical systems and control applications whenever there are multiple discontinuous control variables. The main contribution of this paper is to provide a robust computational framework for the most general way to extend a flow map on the intersection of p intersected (n--1)-dimensional switching manifolds in at least p dimensions. We explore a new formulation to which we can define unique solutions for such particular behavior in hybrid systems and investigate its efficient computation/simulation. We illustrate the concepts with examples throughout the paper.Comment: The 56th Conference on Simulation and Modelling (SIMS 56), Oct 2015, Link\"oping, Sweden. 2015, Link\"oping University Pres

Hybrid Behaviour of Markov Population Models

We investigate the behaviour of population models written in Stochastic Concurrent Constraint Programming (sCCP), a stochastic extension of Concurrent Constraint Programming. In particular, we focus on models from which we can define a semantics of sCCP both in terms of Continuous Time Markov Chains (CTMC) and in terms of Stochastic Hybrid Systems, in which some populations are approximated continuously, while others are kept discrete. We will prove the correctness of the hybrid semantics from the point of view of the limiting behaviour of a sequence of models for increasing population size. More specifically, we prove that, under suitable regularity conditions, the sequence of CTMC constructed from sCCP programs for increasing population size converges to the hybrid system constructed by means of the hybrid semantics. We investigate in particular what happens for sCCP models in which some transitions are guarded by boolean predicates or in the presence of instantaneous transitions

Forward Invariant Cuts to Simplify Proofs of Safety

The use of deductive techniques, such as theorem provers, has several advantages in safety verification of hybrid sys- tems; however, state-of-the-art theorem provers require ex- tensive manual intervention. Furthermore, there is often a gap between the type of assistance that a theorem prover requires to make progress on a proof task and the assis- tance that a system designer is able to provide. This paper presents an extension to KeYmaera, a deductive verification tool for differential dynamic logic; the new technique allows local reasoning using system designer intuition about per- formance within particular modes as part of a proof task. Our approach allows the theorem prover to leverage for- ward invariants, discovered using numerical techniques, as part of a proof of safety. We introduce a new inference rule into the proof calculus of KeYmaera, the forward invariant cut rule, and we present a methodology to discover useful forward invariants, which are then used with the new cut rule to complete verification tasks. We demonstrate how our new approach can be used to complete verification tasks that lie out of the reach of existing deductive approaches us- ing several examples, including one involving an automotive powertrain control system.Comment: Extended version of EMSOFT pape

Reduction of dynamical biochemical reaction networks in computational biology

Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multi-scaleness is another property of these networks, that can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler networks, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state and quasi-equilibrium approximations, and provide practical recipes for model reduction of linear and nonlinear networks. We also discuss the application of model reduction to backward pruning machine learning techniques

Analysis and synthesis of systems with discrete and continuous control

Two different lines of research are presented in the study of an industrially relevant problem of impact control. One is focused on actual control of the process, while the other is focused on the development of a general language for modeling hybrid systems, of which the case study is an appropriate example

Detection and emotional evaluation of an electric vehicle’s exterior sound in a simulated environment

Electric vehicles are quiet at low speeds and thus potentially pose a threat to pedestrians’ safety. Laws are formulating worldwide that mandate these vehicles emit sounds to alert the pedestrians of the vehicles’ approach. It is necessary that these sounds promote a positive perception of the vehicle brand, and understanding their impact on soundscapes is also important. Detection time of the vehicle sounds is an important measure to assess pedestrians’ safety. Emotional evaluation of these sounds influences assessment of the vehicle brand. Laboratory simulation is a new approach for evaluating exterior automotive sounds. This study describes the implementation of laboratory simulation to compare the detection time and emotional evaluation of artificial sounds for an electric vehicle. An Exterior Sound Simulator simulated audio-visual stimuli of an electric car passing a crossroad of a virtual town at 4.47 ms-1 (10 mph), from the perspective of a pedestrian standing at the crossroad. In this environment, 15 sounds were tested using experiments where participants detected the car and evaluated its sound using perceptual dimensions. Results show that these sounds vary significantly in their detection times and emotional evaluations, but crucially that traditional metrics like dB(A) do not always relate to the detection of these sounds. Detection time and emotional evaluation do not have significant correlation. Hence, sounds of a vehicle could be detected quickly, but may portray negative perceptions of the vehicle. Simulation provides a means to more fully evaluate potential electric vehicle sounds against the competing criteria