We present HySIA: a reliable runtime verification tool for nonlinear hybrid automata (HA) and signal temporal logic (STL) properties. HySIA simulates an HA with interval analysis techniques so that a trajectory is enclosed sharply within a set of intervals. Then, HySIA computes whether the simulated trajectory satisfies a given STL property; the computation is performed again with interval analysis to achieve reliability. Simulation and verification using HySIA are demonstrated through several example HA and STL formulas.
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of hybrid systems. In this paper, we propose an interval method for verifying the properties described by a bounded linear temporal logic. We relax the problem to allow outputting an inconclusive result when verification process cannot succeed with a prescribed precision, and present an efficient and rigorous monitoring algorithm that demonstrates that the problem is decidable. This algorithm performs a forward simulation of a hybrid automaton, detects a set of time intervals in which the atomic propositions hold, and validates the property by propagating the time intervals. A continuous state at a certain time computed in each step is enclosed by an interval vector that is proven to contain a unique solution. In the experiments, we show that the proposed method provides a useful tool for formal analysis of nonlinear and complex hybrid systems.  dReach is a bounded reachability analysis tool for nonlinear hybrid systems. It encodes reachability problems of hybrid systems to first-order formulas over real numbers, which are solved by delta-decision procedures in the SMT solver dReach. In this way, dReach is able to handle a wide range of highly nonlinear hybrid systems. It has scaled well on various realistic models from biomedical and robotics applications. The tool Flow* performs Taylor model-based flowpipe construction for non-linear (polynomial) hybrid systems. Flow* combines well-known Taylor model arithmetic techniques for guaranteed approximations of the continuous dynamics in each mode with a combination of approaches for handling mode invariants and discrete transitions. Flow* supports a wide variety of optimizations including adaptive step sizes, adaptive selection of approximation orders and the heuristic selection of template directions for aggregating flowpipes. This paper describes Flow* and demonstrates its performance on a series of non-linear continuous and hybrid system benchmarks. Our comparisons show that Flow* is competitive with other tools. Hybrid systems are a widely used model to represent and reason about control-command systems. In an industrial context, these are often implemented in Simulink and their validity is checked by performing many numerical simulations in order to test their behavior with various possible inputs. In this article, we present a tool named HySon which performs set-based simulation of hybrid systems with uncertain parameters, expressed in Simulink. Our tool handles advanced features such as non-linear operations, zero-crossing events or discrete sampling. It is based on well-known efficient numerical algorithms that were adapted to handle set-based domains. We demonstrate the performance of our method on various examples. Aiming at automatic verification and analysis techniques for hybrid discrete-continuous systems, we present a novel combination of enclosure methods for ordinary differential equations (ODEs) with the iSAT solver for large Boolean combinations of arithmetic constraints. Improving on our previous work, the contribution of this paper lies in combining iSAT with VNODE-LP, as a state-of-the-art interval solver for ODEs, and with bracketing systems, which exploit monotonicity properties allowing to find enclosures for problems that VNODE-LP alone cannot enclose tightly. We apply the combined iSAT-ODE solver to the analysis of a variety of non-linear hybrid systems by solving predicative encodings of reachability properties and of an inductive stability argument, and evaluate the impact of the different enclosure methods, decision heuristics and their combination. Our experiments include classic benchmarks from the literature, as well as a newly-designed conveyor belt system that combines hybrid behavior of parallel components, a slip-stick friction model with non-linear dynamics and flow invariants and several dimensions of parameterization. In the paper, we also present and evaluate an extension of VNODE-LP tailored to its use as a deduction mechanism within iSAT-ODE, to allow fast re-evaluations of enclosures over arbitrary subranges of the analyzed time span. The development of Cyber-Physical Systems benefits from better methods and tools to support the simulation and verification of hybrid (continuous discrete) models. Acumen is an open source testbed for exploring the design space of what rigorous-but-practical next-generation tools can deliver to developers. Central to Acumen is the notion of rigorous simulation. Like verification tools, rigorous simulation is intended to provide guarantees about the behavior of the system. Like traditional simulation tools, it is intended to be intuitive, practical, and scalable. Whether these two goals can be achieved simultaneously is an important, long-term challenge. This paper proposes a design principle that can play an important role in meeting this challenge. The principle addresses the criticism that accumulating numerical errors is a serious impediment to practical rigorous simulation. It is inspired by a twofold insight: one relating to the nature of systems engineered in the real world, and the other relating to how numerical errors in the simulation of a model can be recast as errors in the state or parameters of the model in the simulation. We present a suite of small, concrete benchmarks that can be used to assess the extent to which a rigorous simulator upholds the proposed principle. We also report on which benchmarks Acumen's current rigorous simulator already succeeds and which ones remain challenging.