On Optimal Design of Highly Dependable Hybrid Dynamical Systems

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On the design of highly dependable hybrid dynamical systems (EDS), we aim to incorporate various techniques on formal approaches with problems on optimal control, and have obtained the following results.(1) We have developed a computer tool, called KCLP-HS, as a basis of dealing with various kinds of computations on HDS. KCLP-HS is equipped with linear and quadratic solver, manipulation of convex polyhedra, and interval arithmetic.(2) We have applied quantifier elimination, which is a symbolic computation technique to remove quantifiers from first-order formula, to solving optimal control problem for piecewise affine systems. We have verified effectiveness of the approach through computer experiments.(3) As a framework for dealing with logical constraints, given by temporal logic formula, in model predictive control of HDS, we have proposed notion of bounded bisimilation. We have also developed a pre-computation method for obtaining approximated solutions.(4) We have proposed a new representation of logical dynamics in MLD system. We have verified advantages of the proposed representation against the previous one through computer experiments.(5) We have applied the above results on HDS to the fluidification technique, a technique for approximating discrete state transition by continuous flows. We have developed a scalable method to evaluate performance of large information systems.