Target control for hybrid systems with linear continuous dynamics

We consider the target control problem for hybrid systems with linear continuous dynamics. The system is modelled as a hybrid automaton. Control action is applied on the discrete level, while the continuous dynamics is subject to constant or set valued disturbance. The proposed controller ensures that the system can be transferred from any point of an initial set to a target set of the hybrid state space. A control design algorithm based on reachability analysis is proposed. For the implementation of the algorithm, approximate reachability analysis is employed. This involves under-approximation of reachable sets under linear continuous dynamics. The algorithm is applied to a batch control proble

Formal Verification of Full-Wave Rectifier: A Case Study

We present a case study of formal verification of full-wave rectifier for analog and mixed signal designs. We have used the Checkmate tool from CMU [1], which is a public domain formal verification tool for hybrid systems. Due to the restriction imposed by Checkmate it necessitates to make the changes in the Checkmate implementation to implement the complex and non-linear system. Full-wave rectifier has been implemented by using the Checkmate custom blocks and the Simulink blocks from MATLAB from Math works. After establishing the required changes in the Checkmate implementation we are able to efficiently verify the safety properties of the full-wave rectifier.Comment: The IEEE 8th International Conference on ASIC (IEEE ASICON 2009), October 20-23 2009, Changsha, Chin

Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

Weak Singular Hybrid Automata

The framework of Hybrid automata, introduced by Alur, Courcourbetis, Henzinger, and Ho, provides a formal modeling and analysis environment to analyze the interaction between the discrete and the continuous parts of cyber-physical systems. Hybrid automata can be considered as generalizations of finite state automata augmented with a finite set of real-valued variables whose dynamics in each state is governed by a system of ordinary differential equations. Moreover, the discrete transitions of hybrid automata are guarded by constraints over the values of these real-valued variables, and enable discontinuous jumps in the evolution of these variables. Singular hybrid automata are a subclass of hybrid automata where dynamics is specified by state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed that for even very restricted subclasses of singular hybrid automata, the fundamental verification questions, like reachability and schedulability, are undecidable. In this paper we present \emph{weak singular hybrid automata} (WSHA), a previously unexplored subclass of singular hybrid automata, and show the decidability (and the exact complexity) of various verification questions for this class including reachability (NP-Complete) and LTL model-checking (PSPACE-Complete). We further show that extending WSHA with a single unrestricted clock or extending WSHA with unrestricted variable updates lead to undecidability of reachability problem

IST Austria Thesis

Hybrid automata combine finite automata and dynamical systems, and model the interaction of digital with physical systems. Formal analysis that can guarantee the safety of all behaviors or rigorously witness failures, while unsolvable in general, has been tackled algorithmically using, e.g., abstraction, bounded model-checking, assisted theorem proving. Nevertheless, very few methods have addressed the time-unbounded reachability analysis of hybrid automata and, for current sound and automatic tools, scalability remains critical. We develop methods for the polyhedral abstraction of hybrid automata, which construct coarse overapproximations and tightens them incrementally, in a CEGAR fashion. We use template polyhedra, i.e., polyhedra whose facets are normal to a given set of directions. While, previously, directions were given by the user, we introduce (1) the first method for computing template directions from spurious counterexamples, so as to generalize and eliminate them. The method applies naturally to convex hybrid automata, i.e., hybrid automata with (possibly non-linear) convex constraints on derivatives only, while for linear ODE requires further abstraction. Specifically, we introduce (2) the conic abstractions, which, partitioning the state space into appropriate (possibly non-uniform) cones, divide curvy trajectories into relatively straight sections, suitable for polyhedral abstractions. Finally, we introduce (3) space-time interpolation, which, combining interval arithmetic and template refinement, computes appropriate (possibly non-uniform) time partitioning and template directions along spurious trajectories, so as to eliminate them. We obtain sound and automatic methods for the reachability analysis over dense and unbounded time of convex hybrid automata and hybrid automata with linear ODE. We build prototype tools and compare—favorably—our methods against the respective state-of-the-art tools, on several benchmarks

On the Trade-off Between Efficiency and Precision of Neural Abstraction

Neural abstractions have been recently introduced as formal approximations of complex, nonlinear dynamical models. They comprise a neural ODE and a certified upper bound on the error between the abstract neural network and the concrete dynamical model. So far neural abstractions have exclusively been obtained as neural networks consisting entirely of $ReLU$ activation functions, resulting in neural ODE models that have piecewise affine dynamics, and which can be equivalently interpreted as linear hybrid automata. In this work, we observe that the utility of an abstraction depends on its use: some scenarios might require coarse abstractions that are easier to analyse, whereas others might require more complex, refined abstractions. We therefore consider neural abstractions of alternative shapes, namely either piecewise constant or nonlinear non-polynomial (specifically, obtained via sigmoidal activations). We employ formal inductive synthesis procedures to generate neural abstractions that result in dynamical models with these semantics. Empirically, we demonstrate the trade-off that these different neural abstraction templates have vis-a-vis their precision and synthesis time, as well as the time required for their safety verification (done via reachability computation). We improve existing synthesis techniques to enable abstraction of higher-dimensional models, and additionally discuss the abstraction of complex neural ODEs to improve the efficiency of reachability analysis for these models.Comment: To appear at QEST 202

LNCS

Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions. They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata. While previously, the choice of directions has been left to the user or a heuristic, we present a method for the automatic discovery of directions that generalize and eliminate spurious counterexamples. We show that for the class of convex hybrid automata, i.e., hybrid automata with (possibly nonlinear) convex constraints on derivatives, such directions always exist and can be found using convex optimization. We embed our method inside a CEGAR loop, thus enabling the time-unbounded reachability analysis of an important and richer class of hybrid automata than was previously possible. We evaluate our method on several benchmarks, demonstrating also its superior efficiency for the special case of linear hybrid automata