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Abstraction-based control design is a promising approach for ensuring safety-critical control of complex cyber-physical systems. A key aspect of this methodology is the relation between the original and abstract systems, which ensures that the abstract controller can be transformed into a valid controller for the original system through a concretization procedure. In this paper, we provide a comprehensive and systematic framework that characterizes various simulation relations, through their associated concretization procedures. We introduce the concept of augmented system, which universally enables a feedback refinement relation with the abstract system. This augmented system encapsulates the specific characteristics of each simulation relation within an interface, enabling a plug-and-play control architecture. Our results demonstrate that the existence of a particular simulation relation between the concrete and abstract systems is equivalent to the implementability of a specific control architecture, which depends on the considered simulation relation. This allows us to introduce new types of relations, and to establish the advantages and drawbacks of different relations, which we exhibit through detailed examples., Comment: 14 pages, 6 figures

We have investigated the Raman spectrum and excitonic effects of the novel two-dimensional Ta$_2$Ni$_3$Te$_5$ structure. The monolayer is an indirect band gap semiconductor with an electronic band gap value of 0.09 eV and 0.38 eV, determined using GGA-PBE and HSE06 exchange-correlation functionals, respectively. Since this structure is energetically, dynamically, and mechanically stable, it could be synthesized as a free-standing material. We identify ten Raman and ten infrared active modes for various laser energies, including those commonly used in Raman spectroscopy experiments. It was also observed that the contribution of Ni atoms is minimal in most Raman vibrational modes. In contrast, most infrared vibrational modes do not involve the vibration of the Ta atoms. As far as the optical properties are concerned, this monolayer shows a robust linear anisotropy, an exciton binding energy of 287 meV, and also presents a high reflectivity in the ultraviolet region, which is more intense for linear light polarization along the x-direction.

We extend the notion of Cantor-Kantorovich distance between Markov chains introduced by (Banse et al., 2023) in the context of Markov Decision Processes (MDPs). The proposed metric is well-defined and can be efficiently approximated given a finite horizon. Then, we provide numerical evidences that the latter metric can lead to interesting applications in the field of reinforcement learning. In particular, we show that it could be used for forecasting the performance of transfer learning algorithms., Comment: Presented at the 26th International Symposium on Mathematical Theory of Networks and Systems (Cambridge, UK)

Recently, a new 2D carbon allotrope called Irida-Graphene (Irida-G) was proposed. Irida-G consists of a flat sheet topologically arranged into 3-6-8 carbon rings exhibiting metallic and non-magnetic properties. In this study, we investigated the thermal transport properties of Irida-G using classical reactive molecular dynamics simulations. The findings indicate that Irida-G has an intrinsic thermal conductivity of approximately 215 W/mK at room temperature, significantly lower than that of pristine graphene. This decrease is due to characteristic phonon scattering within Irida-G's porous structure. Additionally, the phonon group velocities and vibrational density of states for Irida-G were analyzed, revealing reduced average phonon group velocities compared to graphene. The thermal conductivity of Irida-G is isotropic and shows significant size effects, transitioning from ballistic to diffusive heat transport regimes as the system length increases. These results suggest that while Irida-G has lower thermal conductivity than graphene, it still holds potential for specific thermal management applications, sharing characteristics with other two-dimensional materials., Comment: 09 pages, 06 figures

The boron nitride (BN) analogue of 8-16-4 graphyne, termed SBNyne, is proposed for the first time. Its physical properties were explored using first-principles calculations and classical molecular dynamics (MD) simulations. Thermal stability assessments reveal that SBNyne maintains structural integrity up to 1000 K. We found that SBNyne exhibits a wide indirect bandgap of 4.58 eV using HSE06 and 3.20 eV using PBE. It displays strong optical absorption in the ultraviolet region while remaining transparent in the infrared and visible regions. Additionally, SBNyne exhibits significantly lower thermal conductivity compared to h-BN. Phonon spectrum analysis indicates that out-of-plane phonons predominantly contribute to the vibrational density of states only at very low frequencies, explaining its low thermal conductivity. These findings expand the knowledge of BN-based 2D materials and open new avenues for their design and advanced technological applications., Comment: We have reviewed the thermal stability calculation and found that the SBNyne structure is metastable and undergoes a transition to a new phase. We are currently investigating this new phase, and to avoid misunderstandings, we need to remove the preprint

A recent breakthrough has been achieved by synthesizing monolayer amorphous carbon (MAC), which introduces a material with unique optoelectronic properties. Here, we used ab initio (DFT) molecular dynamics simulations to study silicon and germanium MAC analogs. Typical unit cells contain more than 600 atoms. We also considered their corresponding nanotube structures. The cohesion energy values for MASi and MAGe range from -8.41 to -7.49 eV/atom and follow the energy ordering of silicene and germanene. Their electronic behavior varies from metallic to small band gap semiconductors. Since silicene, germanene, and MAC have already been experimentally realized, the corresponding MAC-like versions we propose are within our present synthetic capabilities., Comment: 5 pages

In the present work, we have carried out DFT simulations to investigate the electronic and optical properties of a porphyrin-based 2D crystal named 2D Diboron-Porphyrin (2DDP). We showed that it is possible to use strain to tune the 2DDP electronic properties (from semiconductor to metal) depending on the direction of the applied strain. 2DDP exhibits optical activity from the infrared to the ultraviolet region. Similarly to electronic bands, strain can also modulate the optical activity response. 2DDP can be a promising candidate for some electro-opto-mechanical applications.

Abstractions of dynamical systems enable their verification and the design of feedback controllers using simpler, usually discrete, models. In this paper, we propose a data-driven abstraction mechanism based on a novel metric between Markov models. Our approach is based purely on observing output labels of the underlying dynamics, thus opening the road for a fully data-driven approach to construct abstractions. Another feature of the proposed approach is the use of memory to better represent the dynamics in a given region of the state space. We show through numerical examples the usefulness of the proposed methodology., Comment: Submitted to IEEE Transactions on Automatic Control

This paper studies the controller synthesis problem for nonlinear control systems under linear temporal logic (LTL) specifications using zonotope techniques. A local-to-global control strategy is proposed for the desired specification expressed as an LTL formula. First, a novel approach is developed to divide the state space into finite zonotopes and constrained zonotopes, which are called cells and allowed to intersect with the neighbor cells. Second, from the intersection relation, a graph among all cells is generated to verify the realization of the accepting path for the LTL formula. The realization verification determines if there is a need for the control design, and also results in finite local LTL formulas. Third, once the accepting path is realized, a novel abstraction-based method is derived for the controller design. In particular, we only focus on the cells from the realization verification and approximate each cell thanks to properties of zonotopes. Based on local symbolic models and local LTL formulas, an iterative synthesis algorithm is proposed to design all local abstract controllers, whose existence and combination establish the global controller for the LTL formula. Finally, the proposed framework is illustrated via a path planning problem of mobile robots., Comment: 16 pages, 11 figures

We introduce Dionysos.jl, a modular package for solving optimal control problems for complex dynamical systems using state-of-the-art and experimental techniques from symbolic control, optimization, and learning. More often than not with Cyber-Physical systems, the only sensible way of developing a controller is by discretizing the different variables, thus transforming the control task into a purely combinatorial problem on a finite-state mathematical object, called an abstraction of this system. Although this approach offers a safety-critical framework, the available techniques suffer important scalability issues. In order to render these techniques practical, it is necessary to construct smarter abstractions that differ from classical techniques by partitioning the state-space in a non trivial way., Comment: Submitted to the Proceedings of the JuliaCon Conferences

We introduce the concept of memoryless concretization relation (MCR) to describe abstraction within the context of controller synthesis. This relation is a specific instance of alternating simulation relation (ASR), where it is possible to simplify the controller architecture. In the case of ASR, the concretized controller needs to simulate the concurrent evolution of two systems, the original and abstract systems, while for MCR, the designed controllers only need knowledge of the current concrete state. We demonstrate that the distinction between ASR and MCR becomes significant only when a non-deterministic quantizer is involved, such as in cases where the state space discretization consists of overlapping cells. We also show that any abstraction of a system that alternatingly simulates a system can be completed to satisfy MCR at the expense of increasing the non-determinism in the abstraction. We clarify the difference between the MCR and the feedback refinement relation (FRR), showing in particular that the former allows for non-constant controllers within cells. This provides greater flexibility in constructing a practical abstraction, for instance, by reducing non-determinism in the abstraction. Finally, we prove that this relation is not only sufficient, but also necessary, for ensuring the above properties., Comment: to appear in proc. of HSCC 2024

We propose a multi-scale approach for computing abstractions of dynamical systems, that incorporates both local and global optimal control to construct a goal-specific abstraction. For a local optimal control problem, we not only design the controller ensuring the transition between every two subsets (cells) of the state space but also incorporate the volume and shape of these cells into the optimization process. This integrated approach enables the design of non-uniform cells, effectively reducing the complexity of the abstraction. These local optimal controllers are then combined into a digraph, which is globally optimized to obtain the entire trajectory. The global optimizer attempts to lazily build the abstraction along the optimal trajectory, which is less affected by an increase in the number of dimensions. Since the optimal trajectory is generally unknown in practice, we propose a methodology based on the RRT* algorithm to determine it incrementally. Finally, we provide a tractable implementation of this algorithm for the optimal control of L-smooth nonlinear dynamical systems., Comment: 9 pages, 8 figures

Two-dimensional carbon allotropes have attracted much attention due to their extraordinary optoelectronic and mechanical properties, which can be exploited for energy conversion and storage applications. In this work, we use density functional theory simulations and semi-empirical methods to investigate the mechanical, thermoelectric, and excitonic properties of Tetrahexcarbon (also known as Tetragraphene). This quasi-2D carbon allotrope exhibits a combination of squared and hexagonal rings in a buckled shape. Our findings reveal that tetragraphene is a semiconductor material with a direct electronic bandgap of 2.66 eV. Despite the direct nature of the electronic band structure, this material has an indirect exciton ground state of 2.30 eV, which results in an exciton binding energy of 0.36 eV. At ambient temperature, we obtain that the lattice thermal conductivity for tetragraphene is approximately 118 W/mK. Young's modulus and the shear modulus of tetragraphene are almost isotropic, with maximum values of 286.0 N/m and 133.7 N/m, respectively, while exhibiting a very low anisotropic Poisson ratio value of 0.09.

Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely model-free, data-driven approach, but also for handling arbitrary complex functions via their power of representation (as opposed to, e.g. algebraic optimization techniques that are restricted to polynomial functions). Whilst classical Lyapunov techniques allow to provide a formal and robust guarantee of stability of a switched dynamical system, very little is yet known about correctness guarantees for Neural Lyapunov functions, nor about their performance (amount of data needed for a certain accuracy). We thus formally introduce neural Lyapunov functions for the stability analysis of switched linear systems: we benchmark them on this paradigmatic problem, which is notoriously difficult (and in general Turing-undecidable), but which admits recently-developed technologies and theoretical results. Inspired by switched systems theory, we provide theoretical guarantees on the representative power of neural networks, leveraging recent results from the ML community. We additionally experimentally display how neural Lyapunov functions compete with state-of-the-art results and techniques, while admitting a wide range of improvement, both in theory and in practice. This study intends to improve our understanding of the opportunities and current limitations of neural-based data-driven analysis and control of complex dynamical systems., Comment: 13 pages, 8 figures

Modern applications commonly need to manage dataset types composed of heterogeneous data and schemas, making it difficult to access them in an integrated way. A single data store to manage heterogeneous data using a common data model is not effective in such a scenario, which results in the domain data being fragmented in the data stores that best fit their storage and access requirements (e.g., NoSQL, relational DBMS, or HDFS). Besides, organization workflows independently consume these fragments, and usually, there is no explicit link among the fragments that would be useful to support an integrated view. The research challenge tackled by this work is to provide the means to query heterogeneous data residing on distinct data repositories that are not explicitly connected. We propose a federated database architecture by providing a single abstract global conceptual schema to users, allowing them to write their queries, encapsulating data heterogeneity, location, and linkage by employing: (i) meta-models to represent the global conceptual schema, the remote data local conceptual schemas, and mappings among them; (ii) provenance to create explicit links among the consumed and generated data residing in separate datasets. We evaluated the architecture through its implementation as a polystore service, following a microservice architecture approach, in a scenario that simulates a real case in Oil \& Gas industry. Also, we compared the proposed architecture to a relational multidatabase system based on foreign data wrappers, measuring the user's cognitive load to write a query (or query complexity) and the query processing time. The results demonstrated that the proposed architecture allows query writing two times less complex than the one written for the relational multidatabase system, adding an excess of no more than 30% in query processing time., Comment: Reference the paper as L. G. Azevedo, R. Souza, E. F. de S. Soares, R. M. Thiago, J. C. D. Tesolin, A. C. Oliveira, M. F. Moreno, A Polystore Architecture Using Knowledge Graphs to Support Queries on Heterogeneous Data Stores. Proceedings of 20th Brazilian Symposium in Information Systems, 2024 (to be published)

Cell-free massive MIMO systems are currently being considered as potential enablers of future (6G) technologies for wireless communications. By combining distributed processing and massive MIMO, they are expected to deliver improved user coverage and efficiency. A possible source of performance degradation in such systems is pilot contamination, which contributes to causing interference during uplink training and affects channel estimation negatively. Contamination occurs when the same pilot sequence is assigned to more than one user. This is in general inevitable, as the number of mutually orthogonal pilot sequences corresponds to only a fraction of the coherence interval. We introduce a new algorithm for pilot assignment and analyze its performance both from a theoretical perspective and in computational experiments. We show that it has an approximation ratio close to 1 for a plausibly large number of orthogonal pilot sequences, as well as low computational complexity under massive parallelism. We also show that, on average, it outperforms other methods in terms of per-user SINR and throughput on the uplink., Comment: This version updates metadata and expands content

We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to leverage language theory tools in order to provide a universal characterization of Lyapunov stability for this class of systems. We establish, in particular, a formal connection between multiple Lyapunov functions and techniques based on memorization and/or prediction of the discrete part of the state. This allows us to provide an equivalent (single) Lyapunov function, for any given multiple-Lyapunov criterion. By leveraging our language-theoretic formalism, a new class of stability conditions is then obtained when considering both memory and future values of the state in a joint fashion, providing new numerical schemes that outperform existing technique. Our techniques are then illustrated on numerical examples., Comment: To appear in SICON

This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: i) the \emph{robust} case, in which the active mode is completely unknown and unobservable, and ii) the \emph{mode-dependent} case, in which the controller depends on the current active switching mode. The technical developments are based on graph-theory tools, relying in particular on the path-complete Lyapunov functions framework. The main idea is to use directed and labeled graphs to encode Lyapunov inequalities to design robust and mode-dependent piecewise linear state-feedback controllers. This results in novel and flexible conditions, with the particular feature of being in the form of linear matrix inequalities (LMIs). Our technique thus provides a first controller-design strategy allowing piecewise linear feedback maps and piecewise quadratic (control) Lyapunov functions by means of semidefinite programming. Numerical examples illustrate the application of the proposed techniques, the relations between the graph order, the robustness, and the performance of the closed loop.

We introduce an adaptive refinement procedure for smart, and scalable abstraction of dynamical systems. Our technique relies on partitioning the state space depending on the observation of future outputs. However, this knowledge is dynamically constructed in an adaptive, asymmetric way. In order to learn the optimal structure, we define a Kantorovich-inspired metric between Markov chains, and we use it as a loss function. Our technique is prone to data-driven frameworks, but not restricted to. We also study properties of the above mentioned metric between Markov chains, which we believe could be of application for wider purpose. We propose an algorithm to approximate it, and we show that our method yields a much better computational complexity than using classical linear programming techniques., Comment: This paper is an extended version of a CDC2023 submission

Due to the success achieved by graphene, several 2D carbon-based allotropes were theoretically predicted and experimentally synthesized. We used density functional theory and reactive molecular dynamics simulations to investigate the mechanical, structural, electronic, and optical properties of 8-16-4 Graphyne. The results showed that this material exhibits good dynamical and thermal stabilities. Its formation energy and elastic moduli are -8.57 eV/atom and 262.37 GPa, respectively. This graphyne analogue is a semi-metal and presents two Dirac cones in its band structure. Moreover, it is transparent, and its intense optical activity is limited to the infrared region. Remarkably, the band structure of 8-16-4 Graphyne remains practically unchanged at even moderate strain regimes. As far as we know, this is the first 2D carbon allotrope to exhibit this behavior., Comment: 09 pages, and 11 figures

We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is constrained by labeled graphs, namely constrained switching linear systems. In order to do so, we provide chance-constrained bounds on stability guarantees, that can be obtained from a finite number of noisy observations. We first present a method providing stability guarantees from sampled trajectories in the hybrid state-space of the system. We then study the harder situation where one only observes the continuous part of the hybrid states. We show that in this case, one may still obtain formal chance-constrained stability guarantees. For this latter result we provide a new upper bound of general interest, also for model-based stability analysis, Comment: Submitted to Nonlinear Analysis: Hybrid Systems

In this work, we propose a new methodology for obtaining 3D carbon allotrope structures from 2D ones through topological mapping. The idea is to select a 3D target structure and 'slice' it along different structural directions, creating a series of 2D structures. As a proof of concept, we chose the Tubulane structure 12-hexa(3,3) as a target. Tubulanes are 3D carbon allotropes based on cross-linked carbon nanotubes. One of obtained 2D 'sliced' structures was mapped into the biphenylene carbon (BPC). We showed that compressing BPC along different directions can generate not only the target Tubulane 12-hexa(3,3) but at least two other structures, bcc-C6 and an unreported member of the Tubulane family, which we called Tubulane X. The methodology proposed here is completely general, it can be used coupled with any quantum method. Considering that new 2D carbon allotropes, such as the biphenylene carbon network, which is closely related to BPC, have been recently synthesized, the approach proposed here opens new perspectives to obtain new 3D carbon allotropes from 2D structures.

Hydrogen is a promising element for applications in new energy sources like fuel cells. One key issue for such applications is storing hydrogen. And, to improve storage capacity, understanding the interaction mechanism between hydrogen and possible storage materials is critical. This work uses DFT simulations to comprehensively investigate the adsorption mechanism of H/H$_2$ on the 2D metallic porphyrins with one transition metal in its center. Our results suggest that the mechanism for adsorption of H (H$_2$) is chemisorption (physisorption). The maximum adsorption energy for atomic hydrogen was $-3.7$ eV for 2D porphyrins embedded with vanadium or chromium atoms. Our results also revealed charge transfer of up $-0.43$ e to chemisorbed H atoms. In contrast, the maximum adsorption energy calculated for molecular hydrogen was $-122.5$ meV for 2D porphyrins embedded with scandium atoms. Furthermore, charge transfer was minimal for physisorption. Finally, we also determined that uniaxial strain has a minimal effect on the adsorption properties of 2D metallic porphyrins.

This paper deals with learning stability of partially observed switched linear systems under arbitrary switching. Such systems are widely used to describe cyber-physical systems which arise by combining physical systems with digital components. In many real-world applications, the internal states cannot be observed directly. It is thus more realistic to conduct system analysis using the outputs of the system. Stability is one of the most frequent requirement for safety and robustness of cyber-physical systems. Existing methods for analyzing stability of switched linear systems often require the knowledge of the parameters and/or all the states of the underlying system. In this paper, we propose an algorithm for deciding stability of switched linear systems under arbitrary switching based purely on observed output data. The proposed algorithm essentially relies on an output-based Lyapunov stability framework and returns an estimate of the joint spectral radius (JSR). We also prove a probably approximately correct error bound on the quality of the estimate of the JSR from the perspective of statistical learning theory.

We propose a sample-based, sequential method to abstract a (potentially black-box) dynamical system with a sequence of memory-dependent Markov chains of increasing size. We show that this approximation allows to alleviating a correlation bias that has been observed in sample-based abstractions. We further propose a methodology to detect on the fly the memory length resulting in an abstraction with sufficient accuracy. We prove that under reasonable assumptions, the method converges to a sound abstraction in some precise sense, and we showcase it on two case studies.

We present a novel method for deciding whether a given n-dimensional ellipsoid contains another one (possibly with a different center). This method consists in constructing a particular concave function and deciding whether it has any value greater than -1 in a compact interval that is a subset of [0,1]. This can be done efficiently by a bisection algorithm method that is guaranteed to stop in a finite number of iterations. The initialization of the method requires O(n^3) floating-point operations and evaluating this function and its derivatives requires O(n). This can be also generalized to compute the smallest level set of a convex quadratic function containing a finite number of n-ellipsoids. In our benchmark with randomly generated ellipsoids, when compared with a classic method based on semidefinite programming, our algorithm performs 27 times faster for ellipsoids of dimension n=3 and 2294 times faster for dimension n=100. We illustrate the usefulness of this method with a problem in the control theory field., Comment: 8 Pages, 3 Figures, submitted to international conference

We study path-complete Lyapunov functions, which are stability criteria for switched systems, described by a combinatorial component (namely, an automaton), and a functional component (a set of candidate Lyapunov functions, called the template). We introduce a class of criteria based on what we call memory-based Lyapunov functions, which generalize several techniques in the literature. Our main result is an equivalence result: any path-complete Lyapunov function is equivalent to a memory-based Lyapunov function, however defined on another template. We show the usefulness of our result in terms of numerical efficiency via an academic example., Comment: Preprint, Submitted to ACC23

We present an algorithmic framework for the identification of candidate invariant subspaces for switched linear systems. Namely, the framework allows to compute an orthonormal basis in which the matrices of the system are close to block-triangular matrices, based on a finite set of observed one-step trajectories and with a priori confidence level. The link between the existence of an invariant subspace and a common block-triangularization of the system matrices is well known. Under some assumptions on the system, one can also infer the existence of an invariant subspace when the matrices are close to be block-triangular. Our approach relies on quadratic Lyapunov analysis and recent tools in scenario optimization. We present two applications of our results for problems of consensus and opinion dynamics; the first one allows to identify the disconnected components in a switching hidden network, while the second one identifies the stationary opinion vector of a switching gossip process with antagonistic interactions.

In this paper, we develop tools to establish almost sure stability of stochastic switched systems whose switching signal is constrained by an automaton. After having provided the necessary generalizations of existing results in the setting of stochastic graphs, we provide a characterization of almost sure stability in terms of multiple Lyapunov functions. We introduce the concept of lifts, providing formal expansions of stochastic graphs, together with the guarantee of conserving the underlying probability framework. We show how these techniques, firstly introduced in the deterministic setting, provide hierarchical methods in order to compute tight upper bounds for the almost sure decay rate. The theoretical developments are finally illustrated via a numerical example., Comment: Extended version of conference submission

Schwarzites are porous structures that present negative Gaussian curvatures. Although initially proposed for carbon, in principle, schwarzites of other elements are possible. In this work, we have carried out a detailed investigation of the effect of element composition (C, Ge, Si, SiC, and BN) on the structural, electronic and optical properties of a gyroid schwarzite structure, the so-called G688. The DFT simulations were carried out using the well-known SIESTA code. Our results showed that formation energy values are in similar range of other related allotrope structures and are thermally stable (up to 1000~K). From the electronic analyses, our results indicate that all structures, except the carbon one, present semiconductor characteristics. From the optical properties, except for the infrared region where only silicon and germanium show some absorption, the other structures exhibit optical activity only in the visible and ultra-violet regions, and all of them have large refractive index values. For reflectivity, except for Si and Ge schwarzites that reflect almost 40\% of light, the other schwarzites exhibit low reflectivity. These characteristics make them good candidates for optoelectronic applications, such as infrared/ultraviolet absorbers, and ultraviolet blockers.

Closely packed quasi-hexagonal and quasi-tetragonal crystalline phase of C$_{60}$ molecules (named qHPC$_{60}$) was recently synthesized. Here, we used DFT simulations to investigate the electronic, optical, and mechanical properties of qHPC$_{60}$ monolayers. qHPC$_{60}$ has a moderate direct electronic bandgap, with anisotropic mechanical properties. Their elastic modulus ranges between 50 and 62 GPa. The results for optical properties suggest that qHPC$_{60}$ can act as UV collectors for photon energies until 5.5 eV since they present low reflectivity and refractive index greater than one. The estimated optical bandgap (1.5-1.6 eV) is in very good agreement with the experimental one (1.6 eV)., Comment: 13 pages

We present a framework based on multiple Lyapunov functions to find probabilistic data-driven guarantees on the stability of unknown constrained switching linear systems (CSLS), which are switching linear systems whose switching signal is constrained by an automaton. The stability of a CSLS is characterized by its constrained joint spectral radius (CJSR). Inspired by the scenario approach and previous work on unconstrained switching systems, we characterize the number of observations needed to find sufficient conditions on the (in-)stability of a CSLS using the notion of CJSR. More precisely, our contribution is the following: we derive a probabilistic upper bound on the CJSR of an unknown CSLS from a finite number of observations. We also derive a deterministic lower bound on the CJSR. From this we obtain a probabilistic method to characterize the stability of an unknown CSLS., Comment: CDC2022 pre-print, 6 pages

We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic stability guarantees based on data harvested from observations of the system. By generalizing previous results on arbitrary switching linear systems, we show that, by sampling a finite number of observations, we are able to construct an approximate Lyapunov function for the underlying system. Moreover, we show that the entropy of the language accepted by the automaton allows to bound the number of samples needed in order to reach some pre-specified accuracy., Comment: Extended abstract (4 pages), accepted final version

This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel control barrier functions/functionals for the safety problem. The proposed control Lyapunov and barrier functions/functionals extend the existing ones from the delay-free case to the time-delay case, and allow for designing the stabilizing and safety controllers in closed-form. Since analytical solutions to time-delay optimal control problems are hard to be achieved, a sliding mode control based approach is developed to merge the proposed control Lyapunov and barrier functions/functionals. Based on the sliding surface functional, a feedback control law is established to investigate the stabilization and safety objectives simultaneously. In particular, the properties of the sliding surface functional are analyzed, and further how to construct the sliding surface functional is discussed. Finally, the proposed approaches are illustrated via two numerical examples from the connected cruise control problem of automotive systems and the synchronization problem of multi-agent systems., Comment: 15 pages, 12 figures, accepted as Regular Paper by Automatica

This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number of samples. This method relies on a max-min reformulation and the concept of complexity of robust optimization problems. With additional continuity and regularity conditions, via sensitivity analysis, we also provide explicit bounds which outperform an existing result in the literature. To illustrate the improvements of our results, we also provide a numerical example.

This paper treats the global stabilization problem of continuous-time switched affine systems that have rank-deficient convex combinations of their dynamic matrices. For these systems, the already known set of attainable equilibrium points has higher dimensionality than in the full-rank case due to the existence of what we define as singular equilibrium points. Our main goal is to design a state-dependent switching function to ensure global asymptotic stability of a chosen point inside this set with conditions expressed in terms of linear matrix inequalities. For this class of systems, global exponential stability is generally impossible to be guaranteed. Hence, the proposed switching function is shown to ensure global asymptotic and local exponential stability of the desired equilibrium point. The position control and the velocity control with integral action of a dc motor driven by an h-bridge fed via a boost converter are used for validation. This practical application example is composed of eight subsystems, and all possible convex combinations of the dynamic matrices are singular., Comment: 16 pages, 5 figures, forwarded to be published in Automatica