Sound Code Generation from Communicating Hybrid Models

Abstract

Precise translation from hybrid models to code is difficult because models are defined in the continuous-time domain whereas code executes on digital computers in a discrete fashion. Traditional approach is to associate the model with a sampling rate before code generation, and rely on an approximate algorithm that computes the next state numerically. Depending on the choice of the sampling rate and the algorithm, the behavior of the code may vary significantly due to numerical errors, but the discrepancy has been addressed informally, making the analysis results at the model level less meaningful for implementation. Formal relationship between the model and the code becomes even more unclear when components of the code execute concurrently. In this paper, we propose a formal framework that addresses the issue of soundness of concurrent programs generated from communicating hybrid models. The motivation is that concurrent programs executing in different rates may cause an erroneous transition when transition conditions are evaluated using values from different time instances. The essence of our technique is to refine the model by tightening transition conditions according to the maximum errors due to different sampling rates. We claim that the generated code has a trace of discrete transitions that is equivalent to one of the traces observable from the model, and that the values of variables are bounded. Our framework demonstrates how hybrid models defined in the continuous time domain are translated into discretized models with or without consideration of errors due to asynchronous sampling, and finally into executable code with real-time scheduling.

Distributed-code generation from hybrid systems models for time-delayed multirate systems

“…This was extended to multithreaded models accounting for faulty transitions in [14] and unirate distributed systems with no delays in [4]. To guarantee value and time determinism in the discretized code, we use an E machine approach [13] with the concept of logical execution time in our on-going prototype.…”

“…The guarantees for faithful implementation are given with respect to this model. In [14], the authors provide a rigorous definition of system of communicating agents and their semantics.…”

“…In [14], we have proposed a scheme to prevent faulty transitions by shrinking the guard set to account for the errors due to mixed sampling times. However, introducing such a margin into the guard in turn increases the chances of a missed transition, since it reduces the time interval during which a transition must be taken.…”

Computing Schedules for Time-Triggered Control using Genetic Algorithms

“…The problem of generating code from hybrid automata has been considered in Alur et al (2003) and Hur et al (2004), but the focus has been on choosing the sampling period so as to avoid errors due to switching and communication. Automaton-based scheduling of control systems was introduced in Alur and Weiss (2008).…”

Time-triggered implementations of dynamic controllers

“…Recently, the problem of generating code from timed and hybrid automata has been considered in [2, 11,18], but the focus has been on choosing the sampling period so as to avoid errors due to switching and communication. The work on mapping Simulink blocks to Lustre focuses on signal dependencies [6].…”