Bader Alouffi
The growing use of computers in modern control systems has led to the develop- ment of complex dynamic systems known as hybrid systems, which integrates both discrete and continuous systems. Given that hybrid systems are systems that operates in real time allowing for changes in continuous state over time periods, and discrete state changes across zero time, their modelling, analysis and verification becomes very difficult. The formal verifications of such systems based on specifications that can guar- antee their behaviour is very important especially as it pertains to safety critical applications. Accordingly, addressing such verifications issues are important and is the focus of this thesis. In this thesis, in order to actualise the specification and verification of hybrid systems, Interval Temporal Logic(ITL) was adopted as the underlying formalism given its inherent characteristics of providing methods that are flexible for both propositional and first-order reasoning regarding periods found in hardware and software systemâs descriptions. Given that an interval specifies the behaviour of a system, specifications of such systems are therefore represented as a set of intervals that can be used to gain an understanding of the possible behaviour of the system in terms of its composition whether in sequential or parallel form. ITL is a powerful tool that can handle both forms of composition given that it offers very strong and extensive proof and specifi- cation techniques to decipher essential system properties including safety, liveliness and time projections.However, a limitation of ITL is that the intervals within its framework are considered to be a sequence of discrete states. Against this back- drop, the current research provides an extension to ITL with the view to deal with verification and other related issues that centres around hybrid systems. The novelty within this new proposition is new logic termed SPLINE Interval Temporal Logic (SPITL) in which not only a discrete behaviour can be expressed, but also a continuous behaviour can be represented in the form of a spline i.e. the interval is considered to be a sequence of continuous phases instead of a sequence of discrete states. The syntax and semantics of the newly developed SPITL are provided in this thesis and the new extension of the interval temporal logic using a hybrid system as a case study. The overall framework adopted for the overall struc- ture of SPITL is based on three fundamental steps namely the formal specification of hybrid systems is expressed in SPLINE Interval Temporal Logic, followed by the executable subset of ITL, called Tempura, which is used to develop and test a hybrid system specification that is written in SPITL and finally a runtime verification tool for ITL called AnaTempura which is linked with Matlab in order to use them as an integrated tool for the verification of hybrid systems specification. Overall, the current work contributes to the growing body of knowledge in hybrid systems based on the following three major milestones namely: i. the proposition of a new logic termed SPITL; ii. executable subset, Tempura, integrated with SPITL specification for hybrid systems; and iii. the development of a tool termed Ana Tempura which is integrated with Matlab to ensure accurate runtime verification of results.