11 research outputs found
Data-Driven Robust Backward Reachable Sets for Set-Theoretic Model Predictive Control
In this paper, we propose a novel approach for computing robust backward
reachable sets from noisy data for unknown constrained linear systems subject
to bounded disturbances. In particular, we develop an algorithm for obtaining
zonotopic inner approximations that can be used for control purposes. It is
shown that such sets, if built on an extended space including states and
inputs, can be used to embed the system's one-step evolution in the computed
extended regions. Such a result is then exploited to build a set-theoretic
model predictive controller that, offline, builds a recursive family of robust
data-driven reachable sets, and online, computes recursively admissible control
actions without explicitly resorting to either a model of the system or the
available data.The validity of the proposed data-driven solution is verified by
means of a numerical simulation and its performance is contrasted with the
model-based counterpart.Comment: Preprint jointly submitted to IEEE Control Systems Letters (L-CSS)
and IEEE Conference on Decision and Control (CDC
Algorithmic Verification of Continuous and Hybrid Systems
We provide a tutorial introduction to reachability computation, a class of
computational techniques that exports verification technology toward continuous
and hybrid systems. For open under-determined systems, this technique can
sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
Functional sets with typed symbols: Framework and mixed Polynotopes for hybrid nonlinear reachability and filtering
Verification and synthesis of Cyber-Physical Systems (CPS) are challenging
and still raise numerous issues so far. In this paper, an original framework
with mixed sets defined as function images of symbol type domains is first
proposed. Syntax and semantics are explicitly distinguished. Then, both
continuous (interval) and discrete (signed, boolean) symbol types are used to
model dependencies through linear and polynomial functions, so leading to mixed
zonotopic and polynotopic sets. Polynotopes extend sparse polynomial zonotopes
with typed symbols. Polynotopes can both propagate a mixed encoding of
intervals and describe the behavior of logic gates. A functional completeness
result is given, as well as an inclusion method for elementary nonlinear and
switching functions. A Polynotopic Kalman Filter (PKF) is then proposed as a
hybrid nonlinear extension of Zonotopic Kalman Filters (ZKF). Bridges with a
stochastic uncertainty paradigm are outlined. Finally, several discrete,
continuous and hybrid numerical examples including comparisons illustrate the
effectiveness of the theoretical results.Comment: 21 pages, 8 figure
Reachability computation for polynomial dynamical systems
This paper is concerned with the problem of computing the bounded time reachable set of a polynomial discrete-time dynamical system. The problem is well-known for being difficult when nonlinear systems are considered. In this regard, we propose three reachability methods that differ in the set representation. The proposed algorithms adopt boxes, parallelotopes, and parallelotope bundles to construct flowpipes that contain the actual reachable sets. The latter is a new data structure for the symbolic representation of polytopes. Our methods exploit the Bernstein expansion of polynomials to bound the images of sets. The scalability and precision of the presented methods are analyzed on a number of dynamical systems, in comparison with other existing approaches
Computer Aided Verification
This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book
Computer Aided Verification
This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications
Computer Aided Verification
This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications
Computer Aided Verification
This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications