The multi-disciplinary research field of hybrid systems has emerged over the last decade and lies at the boundary of computer science, control engineering and applied mathematics. The behaviors and interactions of components are governed by models of computation.

Hybrid phenomena captured by such mathematical models are manifested in a great diversity of complex engineering applications such as real-time systems, embedded software, robotics, mechatronics, aeronautics, and process control. The high-profile and safety-critical nature of such applications has fostered a large and growing body of work on formal methods for hybrid systems: mathematical logic, computational models and methods and automated reasoning tools supporting the formal specification and verification of performance requirements for hybrid systems, and the design and synthesis of control programs for hybrid systems that are provably correct with respect to formal specifications.

This course investigates modeling, analysis and verification of various classes of hybrid systems. Applications ranging from networked sensors, power electronics, avionics, autonomous vehicles will be covered. The course consists of lectures, a handful of homework assignments, and a final project. Students should understand basic concepts in differential equations, dynamical systems and logic. They should know how to program in some language: for example, Matlab, Mathematica, Java or C.

Lygeros, C. Tomlin and S. VaanDrager and J. LNCS,pp. Luca Carloni, Maria D. Lafferiere, G. Pappas and S. Mitchell, A, M. Bayen, C. Hernandez, M.

Page, T. Sari, J. Belta, P. Finin, L. Habets, A. Halasz, M. Imielinski, V. Kumar, and H. Lincoln, P. Joshi, K.Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few. In many of these applications, one requires to compute a reachable set starting within a previously computed reachable set.

While it was previously required to re-compute the entire reachable set, we demonstrate that one can leverage the dependencies of states within the previously computed set. As a result, we almost instantly obtain an over-approximative subset of a previously computed reachable set by evaluating analytical maps.

The advantages of our novel method are demonstrated for falsification of systems, optimization over reachable sets, and synthesizing safe maneuver automata. In all of these applications, the computation time is reduced significantly. Reachability analysis is one of the most important methods for formal verification of hybrid systems.

The main difficulty for hybrid system reachability analysis is to calculate the intersection between reachable set and guard sets. While there exist several approaches for guard sets defined by hyperplanes or polytopes, only few methods are able to handle nonlinear guard sets. In this work we present a novel approach to tightly enclose the intersections of reachable sets with nonlinear guard sets.

How to avoid scraping bottom of car on drivewayOne major advantage of our method is its polynomial complexity with respect to the system dimension, which makes it applicable for high-dimensional systems. Furthermore, our approach can be combined with different reachability algorithms for continuous systems due to its modular design. We demonstrate the advantages of our novel approach compared to existing methods with numerical examples.

Hybrid automata are an emerging formalism used to model sampled-data control Cyber-Physical Systems CPSand analyze their behavior using reachability analysis. This is because hybrid automata provide a richer and more flexible modeling framework, compared to traditional approaches.

However, modern state-of-the-art tools struggle to analyze such systems, due to the computational complexity of the reachability algorithm, and due to the introduced overapproximation error.

These shortcomings are largely attributed but not limited to the aggregation of sets. In this paper we propose a subspace identification approach for decomposed aggregation in the reachability analysis of hybrid automata with linear dynamics. Our key contribution is the observation that the choice of a good subspace basis does not only depend on the sets being aggregated, but also on the continuous-time dynamics of an automaton.

With this observation in mind, we present a dynamics-aware sub-space identification algorithm that we use to construct tight decomposed convex hulls for the aggregated sets. Our approach is evaluated on two practically relevant hybrid automata models of sampled-data CPS that have been shown to be difficult to analyze by modern state-of-the-art tools. Specifically, we show that for these models our approach can improve the accuracy of the reachable set by up-to 10 times when compared to standard Principal Component Analysis PCAfor which finding a fixed point is not guaranteed.

We also show that while the computational complexity is increased, a fixed-point is found earlier. We introduce and study the concept of worst-case topological entropy of switched linear systems under arbitrary switching.

It is shown that this quantity is equal to the minimal data rate number of bits per second required for the state observation of the switched linear system with any switching signal. A computable closed-form expression is presented for the worst-case topological entropy of switched linear systems. Finally, a practical coder-decoder, operating at a data rate arbitrarily close to the worst-case topological entropy, is described. Our problem is to compute trajectories of a hybrid system that switches between stable affine ODEs, with switching triggered by hyperplane crossings.

Instead of integrating over relatively short time steps, we propose to analytically calculate the affine ODE trajectories between switching times. Our algorithm computes the switching times themselves by Chebyshev interpolation of the analytic trajectory pieces, and polynomial root finding.

We shrink the interpolation time intervals using bounds on the times needed by the affine ODE trajectories to enter certain Lyapunov sub-level sets. We find that this implementation simulates Relay feedback systems as accurately and sometimes faster than conventional algorithms.

AReN thus offers new insight into the design of ReLU NN architectures for the control of LTI systems: instead of training a heuristically chosen NN architecture on data - or iterating over many architectures until a suitable one is found - AReN can suggest an adequate NN architecture before training begins.

AReN achieves this using two novel features. Second, we show that we can efficiently over-approximate the number of affine regions in the optimal MPC controller without solving the MPC problem exactly. Runtime monitoring is commonly used to detect the violation of desired properties in safety critical cyber-physical systems by observing its executions.

Bauer et al. However, a wide range of formulas are not monitorable under this approach, meaning that they have a prefix for which satisfaction and violation will always remain undetermined no matter how it is extended. In particular, Bauer et al. Recently, a robust semantics for LTL was introduced to capture different degrees by wich a property can be violated.PreciadoMichael M. ZavlanosAli JadbabaieGeorge J. Agung JuliusGeorge J. Agung JuliusM. Selman SakarEdward SteagerU. Pappas: Harnessing bacterial power in microscale actuation.

Pappas: Multi-vehicle path planning in dynamically changing environments.

Best automation gamesJohanssonGeorge J. Pappas: Temporal logic motion planning for dynamic robots. Pappas: Hierarchical control system design using approximate simulation. FainekosGeorge J. Pappas: Robustness of temporal logic specifications for continuous-time signals. ZavlanosLeonid SpesivtsevGeorge J. Pappas: A distributed auction algorithm for the assignment problem. Pappas: Probabilistic testing for stochastic hybrid systems.

Pappas: Metabolic networks analysis using convex optimization. ZavlanosVijay KumarGeorge J.

Pappas: Distributed multi-robot task assignment and formation control. VolkowPanayotis K.

Mockk verifyThanosDimitris N. Metaxas : A novel learning based segmentation method for rodent brain structures using MRI. ZavlanosGeorge J.

Pappas: A dynamical systems approach to weighted graph matching. Pappas: Introduction. FainekosAntoine GirardGeorge J. Agung JuliusGeorgios E. Pappas: Where's Waldo? Pappas: From structured english to robot motion. RizziGeorge J. Pappas: Valet parking without a valet. Pappas: Approximate bisimulation relations for constrained linear systems. Pappas: Robustness of Temporal Logic Specifications. Pappas: Verification Using Simulation.

KellerGeorge J. Pappas: Corrigendum to "Hierarchical trajectory refinement for a class of nonlinear systems" [Automatica 41 4 ]. KellerVijay KumarGeorge J. Pappas: Hierarchical trajectory refinement for a class of nonlinear systems.

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Pappas: Bisimulation relations for dynamical, control, and hybrid systems.However, progress on continuous and thus hybrid systems has been limited to systems of small continuous dimension, motivating research on model reduction [27], and projection based methods [28] fo Even though these approaches can handle low-dimensional hybrid systems, for the class of uncertain linear systems, promising scalable results have been obta Compute or obtain a lower bound on 3. Among them, there a An existence of a barrier certificate demonstrates that the unsafe region is not reachable from the initial states.

Several of the functions proposed by us to be included in the set P satisfy condit Documents: Advanced Search Include Citations. Safety verification of hybrid systems using barrier certificates. Add To MetaCart. Approximation metrics for discrete and continuous systems by Antoine Girard, George J. Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust.

In thi Abstract - Cited by 16 self - Add to MetaCart Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical.

In this paper, we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion, approximate simulation, and approximate bisimulation relations. We define a hierarchy of approximation pseudo-metrics between two systems that quantify the quality of the approximation, and capture the established exact relationships as zero sections.

Our approximation framework is compositional for a synchronous composition operator. Algorithms are developed for computing the proposed pseudo-metrics, both exactly and approximately. The exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations, or dually, the solution of a static game whose cost is the so-called branching distance between the systems.

Approximations for the pseudo-metrics can be obtained by considering Lyapunov-like functions called simulation and bisimulation functions.

We illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems. Citation Context ClarkeSecure multi-party computation for cloud-based control.

Andreea Alexandru and George J. In: Farokhi F. Verification of hybrid systems. Pappas, and Andre Platzer. In: Clarke E. Victor M. Cambridge University Press. Sakar, E. Steager, George J. Pappas, Vijay Kumar.

Microrobotics, Trajectory based verification using local finite-time invariance. Agung Julius, and George J. Maintaining Connectivity in Mobile Robot Networks.

How to put back fuse cover for honda crv fullNathan Michael, Michael M. Zavlanos, Vijay Kumar and George J. Robust sampling for MITL specifications. Georgios Fainekos and George J. Robust test generation and coverage for hybrid systems. Agung Julius, Georgios E. Hierarchical synthesis of hybrid controllers from temporal logic specifications. Temporal logic verification using simulation. Robustness of temporal logic specifications. Verification using simulation. Antoine Girard and George J. R- Charon : A modeling language for reconfigurable hybrid systems.

Pappas, and Insup Lee. Observability of switched linear systems in continuous time. Mohamed Babaali, and George J. Model checking LTL over controllable linear systems is decidable. Paulo Tabuada and George J. Composing abstractions of hybrid systems. Paulo Tabuada, George J. Pappas, and Pedro Lima. Hierarchical hybrid modeling of embedded systems. Alur, T.

Life after death stories youtubeDang, J.Pappas, and Ali Jadbabaie. Latency-Reliability Tradeoffs for State Estimation. In press. Network Design for Controllability Metrics. Pappas, Victor M.

List of behavioral objectives examplesApproximate submodularity of Kalman Filter Sensor Selection. Pappas, and Alejandro Ribeiro. Bowman, J. Pappas, Daniel E. Consensus of multi-agent systems via asynchronous cloud communication.

Fernando de Oliveira Chamon, George J.

May Finite-dimensional control of linear discrete-time fractional order systems. Pappas, A. Pedro Aguiar. Automatica, May Minimal Edge Addition for Network Controllability.

Pappas and Alejandro Ribeiro. Minimal reachability is hard to approximate. Pappas, and Vassilis Tzoumas.Event-Based Information-Theoretic Privacy.

In Proceedings of the American Control Conference. Boston, MA, July Multi-agent coordination with asynchronous cloud access. Cameron Nowzari and George J. Pappas, Dragoslav D. Siljak, Danielle Bassett, Brian Litt. Diffusing Private Data over Networks. Fragkiskos Koufogiannis, George J.

Control-aware Random Access Communication. Ivanov, N. Atanasov, J. Weimer, M. Pajic, A. Simpao, M. Rehman, G. Pappas, I. Pappas, Sanjit A.

Distributed leader selection. Minimal reachability problems. Taxi Dispatch under Model Uncertainties. Control with Random Access Wireless Sensors. A general class of spreading processes with non-Markovian dynamics. Preciado, George J.

Joao Carvalho, Sergio Pequito, A. Self-triggered Pursuit and Evasion. Saad A. Aleem, Cameron Nowzari, George J. Automatic Verification of Linear Controller Software. Pequito, James Svacha, George J.

Pappas, Vijay Kumar. Pappas, Ali Jadbabaie. Team-triggered coordination of robotic networks for optimal deployment. Value of forecasts in planning under uncertainty.

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