A symbolic simulator for hybrid equations.

In this paper, the symbolic simulation of hybrid dynamical systems is studied and an algorithm to compute symbolic solutions for such systems is presented. The tasks to perform such simulations are introduced and an algorithm to symbolically calculate a solution to a hybrid system is presented. The symbolic representation allows the proposed simulator to calculate the actual solution to the system. Benefits and drawbacks of symbolic simulation with respect to the numerical approach are presented. These statements are supported and illustrated in several examples throughout the paper

Discrete Simulation of Behavioural Hybrid Process Calculus

Hybrid systems combine continuous-time and discrete behaviours. Simulation is one of the tools to obtain insight in dynamical systems behaviour. Simulation results provide information on performance of system and are helpful in detecting potential weaknesses and errors. Moreover, the results are handy in choosing adequate control strategies and parameters. In our contribution we report a work in progress, a technique for simulation of Behavioural Hybrid Process Calculus, an extension of process algebra that is suitable for the modelling and analysis of hybrid systems

Synthesizing SystemC Code from Delay Hybrid CSP

Delay is omnipresent in modern control systems, which can prompt oscillations and may cause deterioration of control performance, invalidate both stability and safety properties. This implies that safety or stability certificates obtained on idealized, delay-free models of systems prone to delayed coupling may be erratic, and further the incorrectness of the executable code generated from these models. However, automated methods for system verification and code generation that ought to address models of system dynamics reflecting delays have not been paid enough attention yet in the computer science community. In our previous work, on one hand, we investigated the verification of delay dynamical and hybrid systems; on the other hand, we also addressed how to synthesize SystemC code from a verified hybrid system modelled by Hybrid CSP (HCSP) without delay. In this paper, we give a first attempt to synthesize SystemC code from a verified delay hybrid system modelled by Delay HCSP (dHCSP), which is an extension of HCSP by replacing ordinary differential equations (ODEs) with delay differential equations (DDEs). We implement a tool to support the automatic translation from dHCSP to SystemC

SBML models and MathSBML

MathSBML is an open-source, freely-downloadable Mathematica package that facilitates working with Systems Biology Markup Language (SBML) models. SBML is a toolneutral,computer-readable format for representing models of biochemical reaction networks, applicable to metabolic networks, cell-signaling pathways, genomic regulatory networks, and other modeling problems in systems biology that is widely supported by the systems biology community. SBML is based on XML, a standard medium for representing and transporting data that is widely supported on the internet as well as in computational biology and bioinformatics. Because SBML is tool-independent, it enables model transportability, reuse, publication and survival. In addition to MathSBML, a number of other tools that support SBML model examination and manipulation are provided on the sbml.org website, including libSBML, a C/C++ library for reading SBML models; an SBML Toolbox for MatLab; file conversion programs; an SBML model validator and visualizer; and SBML specifications and schemas. MathSBML enables SBML file import to and export from Mathematica as well as providing an API for model manipulation and simulation

ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics

Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and therefore they are significantly more computationally expensive to simulate. Computing gradients with respect to physical design or controller parameters is typically even more computationally challenging. In this paper, we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical simulator for deformable objects, ChainQueen, based on the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects including contact and can be seamlessly incorporated into inference, control and co-design systems. We demonstrate that our simulator achieves high precision in both forward simulation and backward gradient computation. We have successfully employed it in a diverse set of control tasks for soft robots, including problems with nearly 3,000 decision variables.Comment: In submission to ICRA 2019. Supplemental Video: https://www.youtube.com/watch?v=4IWD4iGIsB4 Project Page: https://github.com/yuanming-hu/ChainQuee

StocHy: automated verification and synthesis of stochastic processes

StocHy is a software tool for the quantitative analysis of discrete-time stochastic hybrid systems (SHS). StocHy accepts a high-level description of stochastic models and constructs an equivalent SHS model. The tool allows to (i) simulate the SHS evolution over a given time horizon; and to automatically construct formal abstractions of the SHS. Abstractions are then employed for (ii) formal verification or (iii) control (policy, strategy) synthesis. StocHy allows for modular modelling, and has separate simulation, verification and synthesis engines, which are implemented as independent libraries. This allows for libraries to be easily used and for extensions to be easily built. The tool is implemented in C++ and employs manipulations based on vector calculus, the use of sparse matrices, the symbolic construction of probabilistic kernels, and multi-threading. Experiments show StocHy's markedly improved performance when compared to existing abstraction-based approaches: in particular, StocHy beats state-of-the-art tools in terms of precision (abstraction error) and computational effort, and finally attains scalability to large-sized models (12 continuous dimensions). StocHy is available at www.gitlab.com/natchi92/StocHy

Investigation of Air Transportation Technology at Princeton University, 1989-1990

The Air Transportation Technology Program at Princeton University proceeded along six avenues during the past year: microburst hazards to aircraft; machine-intelligent, fault tolerant flight control; computer aided heuristics for piloted flight; stochastic robustness for flight control systems; neural networks for flight control; and computer aided control system design. These topics are briefly discussed, and an annotated bibliography of publications that appeared between January 1989 and June 1990 is given

Minimally Constrained Stable Switched Systems and Application to Co-simulation

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation, where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.Comment: Technical report complementing the following conference publication: Gomes, Cl\'audio, Beno\^it Legat, Rapha\"el Jungers, and Hans Vangheluwe. "Minimally Constrained Stable Switched Systems and Application to Co-Simulation." In IEEE Conference on Decision and Control. Miami Beach, FL, USA, 201