MathematicalSystems.jl

MathematicalSystems is a Julia package for mathematical systems interfaces.

Features

• Generic and flexible systems definitions, while being fast and type stable.
• Types for mathematical systems modeling: continuous, discrete, controlled, descriptor systems, etc.
• Iterator interfaces to handle constant or time-varying inputs.

Ecosystem

The following packages use MathematicalSystems.jl:

• Dionysos.jl – Optimal control of cyber-physical systems
• HybridSystems.jl – Hybrid Systems definitions in Julia
• ReachabilityAnalysis.jl – Methods to compute sets of states reachable by dynamical systems
• SpaceExParser.jl – SpaceEx modeling language parser
• StructuralDynamicsODESolvers.jl – Numerical integration methods for structural dynamics problems
• SwitchOnSafety.jl – Computing controlled invariant sets of Hybrid Systems using Sum Of Squares Programming

Manual Outline

• Overview of System Types
• • Using the @system Macro
  • Inputs
  • Summary Tables

Library Outline

• Types
• • Abstract Systems
  • Continuous Systems
  • Discrete Systems
  • Initial Value Problems
  • Identity Operator
  • Input Types
  • Maps
  • Systems with Output
  • Vector Fields
  • Macros
• Methods
• • States
  • Inputs
  • Noises
  • Output
  • Traits
  • Maps
  • Successor
  • Vector Field
  • Discretization
  • Internal Methods
• Internals
• • Expression Handling
  • Querying Expressions
  • Evaluation of AbstractSystem at Given State
  • Naming Convention for Systems' Fields