"Nonlinear Algorithms for Verification, Control, Design and Analysis of Nonlinear Continuous and Hybrid Systems"

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I propose to develop numerical algorithms and implementations for the verification, control and design of systems whose dynamics are best described by nonlinear continuous or hybrid (a mixture of continuous and discrete) models. Such systems arise whenever a digital computer interacts with the external world, and they are hence becoming ever more widespread as computers are embedded into devices throughout our environment. The foundation of this research program will be the study of a variety of reachability algorithms for continuous systems, including both grid and trajectory based with both parametric and nonparametric reach set representations. Application of these techniques can reduce the likelihood of undesirable behaviours, but for nonlinear continuous and hybrid systems it has rarely been possible or it has required the intervention of reachability experts. With the long-term goal of bringing these formal analysis methods into industrial practice, two distinct application domains will inform this program of research: safe collaborative control of robots, and design of robust analog and mixed-signal integrated circuits. In order to solve real problems without the intervention of experts in formal methods, this program will also address two other key needs: construction of the mathematical model of the system and problem to be solved based on descriptions typically used by domain experts, and conversion of the verification results into a form which addresses those experts' concerns. For the domain specific toolchains and, where necessary, for the core reachability algorithms I will create and release flexible, efficient, robust and well-documented implementations that will do for these techniques what the Toolbox of Level Set Methods has done for time-dependent Hamilton-Jacobi equations: permit other researchers in industry and academia to reproduce, utilize and extend published results. Trainees will gain experience in numerical algorithms, robust software development practices, integrated circuits and/or robotics, all areas with positive job prospects. Finally, the choice of distinct application areas will guide the extension of automated formal analysis into other domains exhibiting continuous and hybrid dynamics.