# differential equations

- attack defense differential equation
- Communication networks
- computer network security
- Control Theory
- defense differential game theory
- defensive differential game
- differential equations
- Differential game
- Differential Games
- Games
- Information systems
- Mathematical model
- network active security threat process
- network attack and defense
- network security target
- network security threat
- offensive differential game
- process control
- pubcrawl
- Safety
- security
- traditional network active security threat model

- AD 2015 to 2016
- candidate C
- cell memory
- cellular automata
- complex social systems
- composability
- control group behavior
- delay time intervals
- description models
- differential equations
- differential kinetic equations
- electoral campaign
- electoral processes
- events prediction
- interaction process
- Kinetic theory
- memory steps
- Metrics
- node types
- numeric parameter
- oscillating behaviors
- possible transitions
- preferences in social and economic systems
- privacy
- probability
- pubcrawl
- random link network
- random processes
- resilience
- Resiliency
- social sciences
- sociological data
- stochastic cellular automata
- Stochastic processes
- transition probability matrix
- United States
- United States president
- user actions
- variable memory
- voters

## Sound Invariant Generation for Continuous and Hybrid Systems

Invariant generation is crucial to the success of rigorous deductive verification tools for cyber-physical system. We develop a dedicated invariant generation toolbox for the KeYmaera X theorem prover which combines many custom invariant generation methods under a unified framework. Additionally, we develop a generalization of the method of barrier certificates (vector barrier certificates), building on R. Bellman's work on vector Lyapunov functions.

- canonical dynamic system
- canonical dynamic systems
- composability
- convergence
- convergence analysis
- covergence
- differential equation
- differential equations
- Dynamical Systems
- EKF
- EKF parameter estimation
- extended Kalman filter
- Heuristic algorithms
- Kalman filters
- Mathematical model
- Metrics
- Nonlinear dynamical systems
- nonlinear filters
- parameter estimation
- pubcrawl
- resilience
- Resiliency

- chaos
- chaotic communication
- chaotic cryptography
- chaotic differential equations
- chaotic ODEs
- chaotic pseudorandom number generators
- chaotic system
- composability
- Correlation
- Correlation analysis
- correlation analysis methods
- differential equations
- dynamical chaos
- generation process
- generator architecture
- Generators
- Metrics
- NIST
- NIST statistical test suite
- nonlinear control systems
- normalization factor
- normalization technique
- numerical integration
- numerical simulation
- numerical solution
- probability
- pseudo-random number generator
- pseudorandom binary sequence generator
- pubcrawl
- random number generation
- Random sequences
- Resiliency
- Rössler attractors
- Rössler system
- semi-implicit ODE solver
- semiimplicit ODE solvers
- semiimplicit symmetric composition D-method
- state variables values
- statistical testing
- Thomas attractor
- Thomas attractors

- continuous time system
- continuous time systems
- contracts
- differential equations
- financial management
- g-expectation framework
- Knightian uncertainty
- optimal contract
- optimal contracts
- optimal control
- optimal control theory
- optimisation
- optimization
- principal-agent problems
- pubcrawl170107
- pubcrawl170108
- TV
- uncertainty
- Yttrium

- bang-bang control
- bang-bang controls
- control systems
- decision-making problem
- differential equations
- Differential game
- differential game-based strategy
- Differential Games
- epidemic theory
- Games
- Grippers
- invasive software
- malware
- Malware propagation
- malware propagation model
- malware propagation prevention
- malware-defense differential game
- optimal control problem
- optimal dynamic strategy
- overall cost minimization
- saddle-point
- sensor node characteristics
- Silicon
- sleep mode
- telecommunication control
- telecommunication security
- traditional epidemic theory
- wireless sensor networks
- WSN

## Differential Radical Invariants: Safety Verification and Design of Correct Hybrid Systems

## Abstract:

The verification of hybrid systems requires ways of handling both the discrete and continuous dynamics, e.g., by proofs, abstraction, or approximation. Fundamentally, however, the study of the safety of hybrid systems can be shown to reduce constructively to the problem of generating invariants for their differ- ential equations. We recently focused on this core problem. We study the case of algebraic invariant equation, i.e. invariants described by a polynomial equation of the form p = 0 for a polynomial p.

- CPS Domains
- Automotive
- Hybrid Models
- Avionics
- Composition
- Semantics
- Modeling
- Wireless Sensing and Actuation
- Robotics
- Transportation
- Validation and Verification
- CPS Technologies
- Education
- Foundations
- Algebraic Sets
- Carnegie Mellon University
- differential equations
- formal verification
- hybrid systems
- nvariant Generation
- 0931985
- National CPS PI Meeting 2014
- 2014
- CPSPI MTG 2014 Posters, Videos and Abstracts
- Academia
- Abstract
- Poster