Formalization of Complex Vectors in Higher-Order Logic

Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting this analysis within the sound core of a theorem prover: HOL Light. Our definition of complex vector builds upon the definitions of complex numbers and real vectors. This extension allows us to extensively benefit from the already verified theorems based on complex analysis and real vector analysis. To show the practical usefulness of our library we adopt it to formalize electromagnetic fields and to prove the law of reflection for the planar waves.Comment: 15 pages, 1 figur

Reference Modelling in Support of M&S—Foundations and Applications

Whether by design or by practice, systems engineering (SE) processes are used more and more often in Modeling and Simulation (M&S). While the two disciplines are very close, there are some differences that must be taken into account in order to successfully reuse practices from one community to another. In this paper, we introduce the M&S System Development Framework (MS-SDF) that unifies SE and M&S processes. The MS-SDF comprises the SE processes of requirements capture, conceptual modelling, and verification and validation (V&V), and extends them to M&S. We use model theory as a deductive apparatus in order to develop the MS-SDF. We discuss the benefits of the MS-SDF especially in the selection between federation development and multi-model approaches and the design of composable models and simulations. Lastly, a real life application example of the framework is provided

Scalable Verification of Linear Controller Software

We consider the problem of verifying software implementations of linear time-invariant controllers against mathematical specifications. Given a controller specification, multiple correct implementations may exist, each of which uses a different representation of controller state (e.g., due to optimizations in a third-party code generator). To accommodate this variation, we first extract a controller\u27s mathematical model from the implementation via symbolic execution, and then check input-output equivalence between the extracted model and the specification by similarity checking. We show how to automatically verify the correctness of C code controller implementation using the combination of techniques such as symbolic execution, satisfiability solving and convex optimization. Through evaluation using randomly generated controller specifications of realistic size, we demonstrate that the scalability of this approach has significantly improved compared to our own earlier work based on the invariant checking method

A Formal Proof in Coq of LaSalle's Invariance Principle

International audienceStability analysis of dynamical systems plays an important role in the study of control techniques. LaSalle's invariance principle is a result about the asymptotic stability of the solutions to a nonlinear system of differential equations and several extensions of this principle have been designed to fit different particular kinds of system. In this paper we present a formalization, in the Coq proof assistant, of a slightly improved version of the original principle. This is a step towards a formal verification of dynamical systems