Sergiy Bogomolov

Hui Kong, Sergiy Bogomolov, Christian Schilling et al.

In this paper, we propose an approach to automatically compute invariant clusters for semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u,x)=0, parametric in u, which can yield an infinite number of concrete invariants by assigning different values to u so that every trajectory of the system can be overapproximated precisely by a union of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial vector flow, invariant clusters can be obtained by first computing the remainder of the Lie derivative of a template multivariate polynomial w.r.t. its Groebner basis and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is effective and efficient.

Alessandro Abate, Sergiy Bogomolov, Alec Edwards et al.

We present a novel technique for online safety verification of autonomous systems, which performs reachability analysis efficiently for both bounded and unbounded horizons by employing neural barrier certificates. Our approach uses barrier certificates given by parameterized neural networks that depend on a given initial set, unsafe sets, and time horizon. Such networks are trained efficiently offline using system simulations sampled from regions of the state space. We then employ a meta-neural network to generalize the barrier certificates to state space regions that are outside the training set. These certificates are generated and validated online as sound over-approximations of the reachable states, thus either ensuring system safety or activating appropriate alternative actions in unsafe scenarios. We demonstrate our technique on case studies from linear models to nonlinear control-dependent models for online autonomous driving scenarios.

Daniel Bryce, Sergiy Bogomolov, Alexander Heinz et al.

PDDL+ planning has its semantics rooted in hybrid automata (HA) and recent work has shown that it can be modeled as a network of HAs. Addressing the complexity of nonlinear PDDL+ planning as HAs requires both space and time efficient reasoning. Unfortunately, existing solvers either do not address nonlinear dynamics or do not natively support networks of automata. We present a new algorithm, called HNSolve, which guides the variable selection of the dReal Satisfiability Modulo Theories (SMT) solver while reasoning about network encodings of nonlinear PDDL+ planning as HAs. HNSolve tightly integrates with dReal by solving a discrete abstraction of the HA network. HNSolve finds composite runs on the HA network that ignore continuous variables, but respect mode jumps and synchronization labels. HNSolve admissibly detects dead-ends in the discrete abstraction, and posts conflict clauses that prune the SMT solver's search. We evaluate the benefits of our HNSolve algorithm on PDDL+ benchmark problems and demonstrate its performance with respect to prior work.

Amit Gurung, Arup Deka, Ezio Bartocci et al.

We propose two parallel state-space exploration algorithms for hybrid systems with the goal of enhancing performance on multi-core shared memory systems. The first is an adaption of the parallel breadth first search in the SPIN model checker. We show that the adapted algorithm does not provide the desired load balancing for many hybrid systems benchmarks. The second is a task parallel algorithm based on cheaply precomputing cost of post (continuous and discrete) operations for effective load balancing. We illustrate the task parallel algorithm and the cost precomputation of post operators on a support-function-based algorithm for state-space exploration. The performance comparison of the two algorithms displays a better CPU utilization/load-balancing of the second over the first, except for certain cases. The algorithms are implemented in the model checker XSpeed and our experiments show a maximum speed-up of $900\times$ on a navigation benchmark with respect to SpaceEx LGG scenario, comparing on the basis of equal number of post operations evaluated.