Exhaustive coverage of all possible behaviours is important when we model safety-critical or mission-critical systems, either embedded or cyber-physical, since uncertain inputs, disturbances or noise can have an adverse effect in performance and reliability. In this talk we survey methods that have emerged recently to soundly verify properties of systems using sum-of-squares optimisation methods. The study is conducted with our software tool JuliaReach that gives a unified user interface implementing different reachability approaches while not sacrificing features or performance.
joint work with Paulo Tabuada, Raphaël Jungers
We develop a method for computing controlled invariant sets of discrete-time affine systems using Sum-of-Squares programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets but our work also improves the state of the art for the particular case of LTI systems. The task is reduced to a Sum-of-Squares programming problem by enforcing an invariance relation in the dual space of the geometric problem.
joint work with Juan Pablo Vielma, Lea Kapelevich
Hypatia is an open-source optimization solver in Julia for primal-dual conic problems involving general convex cones. Hypatia makes it easy to define and model with any closed convex conic set for which an appropriate primal or dual barrier function is known. Using novel nonsymmetric cones, we model control applications with smaller, more natural formulations, and demonstrate Hypatia's superior performance (relative to other state-of-the-art conic interior point solvers) on several large problems.