hyper A Useful Toolbox for Hybrid Systems

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hyperA Useful Toolbox for Hybrid Systems

• Shankar Sastry, Jonathan Sprinkle,
• Mike Eklund, Ian Mitchell
• UC Berkeley

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What Are Hybrid Systems?

• Dynamical systems with interacting continuous and
  discrete dynamics

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Why are Hybrid Systems Hard?

• All implicit error in continuous analysis,
  coupled with switching criteria, leads to
  possible catastrophic error

Slide by Rafael Garcia
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Why are Hybrid Systems Hard?

• Zeno behavior
• Event transitions happen so rapidly that the
  simulator grinds to a halt
• A Toolbox should detect this

Slide by Edward Lee
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What are the pieces?

• Modeling Simulation
• Control classify discrete phenomena, existence
  and uniqueness of execution, Zeno Branicky,
  Brockett, van der Schaft, Astrom
• Computer Science composition and abstraction
  operations Alur-Henzinger, Lynch, Sifakis,
  Sztipanovits,Varaiya
• Analysis Verification
• Control stability, Lyapunov techniques
  Antsaklis, Branicky, Michel, LMI techniques
  Johansson-Rantzer, optimal control Branicky,
  Sussmann, Caines
• Computer Science Algorithmic Alur-Henzinger,
  Sifakis, Pappas-Lafferrier-Sastry or deductive
  methods Lynch, Manna, Pnuelli
• Controller Synthesis
• Control optimal control Branicky-Mitter,
  Bensoussan-Menaldi, hierarchical control
  Caines, Pappas-Sastry, supervisory control
  Lemmon-Antsaklis, model predictive techniques
  Morari Bemporad, safety specifications
  Lygeros-Tomlin-Sastry
• Computer Science algorithmic synthesis Maler,
  Pnueli, Asarin, Wong-Toi
• Observability and Diagnosability
• Control observersBemporad, Koutsoukos, Vidal
• Computer Science Biswas, Karsai, Zhao

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Tool Integration

• No one tool exists for all of these
• Several academic toolmakers created HSIF
• Hybrid Systems Interchange Format
• Failed to mature for a few reasons
• Tool-specific, and Tool-driven, not capability
  driven
• Not enough programming power behind it
• No thought to coverage of corner cases (Lee,
  Zheng)

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Tool Integration
Example correct output

• What is needed is a framework that utilizes
  interchange format
• Must support what we know about hybrid systems
  semantics, encourage tools integration
• Implicit tool semantics makes fully meaningful
  translation impossible, or impractical
• The proper specification of the semantics of an
  interchange format would ease this difficulty
• Leverage HSIF as a learning tool for the semantic
  specification of the hyper core

RK 2
-
3 variable
-
step solver and
breakpoint solver determine
sample times
Note two values at
Note two values at
the same time
the same time
Incorrect output
Slide by Edward Lee
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Tool Integration

• What about industry-standard tools?
• Many big industries are bound to Matlab, but
  clamoring for verification/synthesis capabilities
• Suggests a real need for getting this interchange
  piece right and showing examples for how to do
  the interchange with existing tools or toolboxes

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Example Integration HyVisual

• Ptolemy IIs HyVisual
• http//ptolemy.eecs.berkeley.edu/hyvisual/

Slide by Edward Lee
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HyVisual

• Clear contribution
• well-defined simulation and semantic behavior
• Assets
• Platform-independent model editing
• Visualization tools
• Reasoned meaning of hierarchical containment
• Well-formulated for the business of numerical
  solutions and execution of complex, nonlinear,
  deterministic hybrid systems

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HyVisual Integration Benefits

• Contains a rich set of examples of hybrid systems
• Useful for other tool integrations
• Platform independent, open source
• Lacks synthesis/runtime tools, so could then
  integrate with other tools with these capabilities

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Example Integration A Toolbox of LSM

• Ian Mitchells Toolbox of Level Set Methods
• http//www.cs.ubc.ca/mitchell/ToolboxLS/
• Numerical algorithms for dynamic implicit
  surfaces and Hamilton-Jacobi partial differential
  equations

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Level Set Methods

• Clear contribution
• Leverage level sets to perform reachability
  calculations for hybrid systems
• Assets
• Computationally sound for low dimensions
• Works in Matlab (no toolboxes required)

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Reachable sets how they are calculated
Time dependent H-J equation

• First order hyperbolic PDE
• Solution can form kinks (discontinuous
  derivatives)
• For the backwards reachable set, find the
  viscosity solution Crandall, Evans, Lions,
• Level set methods
• Convergent numerical algorithms to compute the
  viscosity solution Osher, Sethian,
• Non-oscillatory, high accuracy spatial derivative
  approximation
• Stable, consistent numerical Hamiltonian
• Variation diminishing, high order, explicit time
  integration

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Level Set Methods Integration Benefits

• Give additional capability to tools such as
  HyVisual
• Add a hybrid systems (rather than numerical)
  front-end to the LSM Toolbox
• Provide controller synthesis capability, as well
  as safety calculations

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Hyper Framework

• A new toolbox/toolsuite with the following
  characteristics
• High performance simulation
• High robustness factor
• High level modeling (with refinement)
• High number of interacting tools
• Provide a formal interchange between tools
• Low-level fundamental model specifications (a
  core)
• Requires a set of implementable functions to
  call
• Add a base package with interfaces for
  interoperability, and a lightweight editor
• Include industrial-strength solvers through
  transformations

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Hyper Framework
Interoperability Interfaces
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Hyper Framework

• Extensible to other tools
• Existing examples for integration through
  HyVisual/T-LSM
• A more focused, useful, core interchange format
• When integrated, allows persistence of legacy
  models in industry (Matlab/Simulink), now with
  advantage(s) of synthesis/verification
• Newer/faster tools can be tested against known
  true
• Check for same behavior
• Can be used for regression testing

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Conclusions

• Not trying to build Rome in 1 day
• Focused application to certain capabilities at
  first
• Concentration on not solving all the worlds
  problems at once
• Restricting initial release to useful and mature
  tools
• Immediately providing two diverse toolbox
  integrations as examples to others

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BASE Package
Simulators Matlab, HyVisual
Simulators Matlab, HyVisual
Simulators Matlab, HyVisual
CORE
Extraction
modeldatabase
Verification Engine HyTech, LSM, CheckMate
Verification Engine HyTech, LSM, CheckMate
Verification Engine HyTech, LSM, CheckMate
Manipulation
Visualization
Editor
Transformations XSL, GReAT
Transformations XSL, GReAT
Transformations XSL, GReAT