Realizability of embedded controllers: from hybrid models to correct implementations

Un controller embedded \ue8 un dispositivo (ovvero, un'opportuna combinazione di componenti hardware e software) che, immerso in un ambiente dinamico, deve reagire alle variazioni ambientali in tempo reale. I controller embedded sono largamente adottati in molti contesti della vita moderna, dall'automotive all'avionica, dall'elettronica di consumo alle attrezzature mediche. La correttezza di tali controller \ue8 indubbiamente cruciale. Per la progettazione e per la verifica di un controller embedded, spesso sorge la necessit\ue0 di modellare un intero sistema che includa sia il controller, sia il suo ambiente circostante. La natura di tale sistema \ue8 ibrido. Esso, infatti, \ue8 ottenuto integrando processi ad eventi discreti (i.e., il controller) e processi a tempo continuo (i.e., l'ambiente). Sistemi di questo tipo sono chiamati cyber-physical (CPS) o sistemi ibridi. Le dinamiche di tali sistemi non possono essere rappresentati efficacemente utilizzando o solo un modello (i.e., rappresentazione) discreto o solo un modello continuo. Diversi tipi di modelli possono sono stati proposti per descrivere i sistemi ibridi. Questi si concentrano su obiettivi diversi: modelli dettagliati sono eccellenti per la simulazione del sistema, ma non sono adatti per la sua verifica; modelli meno dettagliati sono eccellenti per la verifica, ma non sono convenienti per i successivi passi di raffinamento richiesti per la progettazione del sistema, e cos\uec via. Tra tutti questi modelli, gli Automi Ibridi (HA) [8, 77] rappresentano il formalismo pi\uf9 efficace per la simulazione e la verifica di sistemi ibridi. In particolare, un automa ibrido rappresenta i processi ad eventi discreti per mezzo di macchine a stati finiti (FSM), mentre i processi a tempo continuo sono rappresentati mediante variabili "continue" la cui dinamica \ue8 specificata da equazioni differenziali ordinarie (ODE) o loro generalizzazioni (e.g., inclusioni differenziali). Sfortunatamente, a causa della loro particolare semantica, esistono diverse difficolt\ue0 nel raffinare un modello basato su automi ibridi in un modello realizzabile e, di conseguenza, esistono difficolt\ue0 nell'automatizzare il flusso di progettazione di sistemi ibridi a partire da automi ibridi. Gli automi ibridi, infatti, sono considerati dispositivi "perfetti e istantanei". Essi adottano una nozione di tempo e di variabili basata su insiemi "densi" (i.e., l'insieme dei numeri reali). Pertanto, gli automi ibridi possono valutare lo stato (i.e., i valori delle variabili) del sistema in ogni istante, ovvero in ogni infinitesimo di tempo, e con la massima precisione. Inoltre, sono in grado di eseguire computazioni o reagire ad eventi di sincronizzazione in modo istantaneo, andando a cambiare la modalit\ue0 di funzionamento del sistema senza alcun ritardo. Questi aspetti sono convenienti a livello di modellazione, ma nessun dispositivo hardware/software potrebbe implementare correttamente tali comportamenti, indipendentemente dalle sue prestazioni. In altre parole, il controller modellato potrebbe non essere implementabile, ovvero, esso potrebbe non essere realizzabile affatto. Questa tesi affronta questo problema proponendo una metodologia completa e gli strumenti necessari per derivare da modelli basati su automi ibridi, modelli realizzabili e le corrispondenti implementazioni corrette. In un modello realizzabile, il controller analizza lo stato del sistema ad istanti temporali discreti, tipicamente fissati dalla frequenza di clock del processore installato sul dispositivo che implementa il controller. Lo stato del sistema \ue8 dato dai valori delle variabili rilevati dai sensori. Questi valori vengono digitalizzati con precisione finita e propagati al controller che li elabora per decidere se cambiare la modalit\ue0 di funzionamento del sistema. In tal caso, il controller genera segnali che, una volta trasmessi agli attuatori, determineranno il cambiamento della modalit\ue0 di funzionamento del sistema. \uc8 necessario tener presente che i sensori e gli attuatori introducono ritardi che seppur limitati, non possono essere trascurati.An embedded controller is a reactive device (e.g., a suitable combination of hardware and software components) that is embedded in a dynamical environment and has to react to environment changes in real time. Embedded controllers are widely adopted in many contexts of modern life, from automotive to avionics, from consumer electronics to medical equipment. Noticeably, the correctness of such controllers is crucial. When designing and verifying an embedded controller, often the need arises to model the controller and also its surrounding environment. The nature of the obtained system is hybrid because of the inclusion of both discrete-event (i.e., controller) and continuous-time (i.e., environment) processes whose dynamics cannot be characterized faithfully using either a discrete or continuous model only. Systems of this kind are named cyber-physical (CPS) or hybrid systems. Different types of models may be used to describe hybrid systems and they focus on different objectives: detailed models are excellent for simulation but not suitable for verification, high-level models are excellent for verification but not convenient for refinement, and so forth. Among all these models, hybrid automata (HA) [8, 77] have been proposed as a powerful formalism for the design, simulation and verification of hybrid systems. In particular, a hybrid automaton represents discrete-event processes by means of finite state machines (FSM), whereas continuous-time processes are represented by using real-numbered variables whose dynamics is specified by (ordinary) differential equation (ODE) or their generalizations (e.g., differential inclusions). Unfortunately, when the high-level model of the hybrid system is a hybrid automaton, several difficulties should be solved in order to automate the refinement phase in the design flow, because of the classical semantics of hybrid automata. In fact, hybrid automata can be considered perfect and instantaneous devices. They adopt a notion of time and evaluation of continuous variables based on dense sets of values (usually R, i.e., Reals). Thus, they can sample the state (i.e., value assignments on variables) of the hybrid system at any instant in such a dense set R 650. Further, they are capable of instantaneously evaluating guard constraints or reacting to incoming events by performing changes in the operating mode of the hybrid system without any delay. While these aspects are convenient at the modeling level, any model of an embedded controller that relies for its correctness on such precision and instantaneity cannot be implemented by any hardware/software device, no matter how fast it is. In other words, the controller is un-realizable, i.e., un-implementable. This thesis proposes a complete methodology and a framework that allows to derive from hybrid automata proved correct in the hybrid domain, correct realizable models of embedded controllers and the related discrete implementations. In a realizable model, the controller samples the state of the environment at periodic discrete time instants which, typically, are fixed by the clock frequency of the processor implementing the controller. The state of the environment consists of the current values of the relevant variables as observed by the sensors. These values are digitized with finite precision and reported to the controller that may decide to switch the operating mode of the environment. In such a case, the controller generates suitable output signals that, once transmitted to the actuators, will effect the desired change in the operating mode. It is worth noting that the sensors will report the current values of the variables and the actuators will effect changes in the rates of evolution of the variables with bounded delays

First Annual Workshop on Space Operations Automation and Robotics (SOAR 87)

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Design and integrity of deterministic system architectures.

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Radio Communications

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