Title: hyper A Useful Toolbox for Hybrid Systems
1hyperA Useful Toolbox for Hybrid Systems
- Shankar Sastry, Jonathan Sprinkle,
- Mike Eklund, Ian Mitchell
- UC Berkeley
2What Are Hybrid Systems?
- Dynamical systems with interacting continuous and
discrete dynamics
3Why are Hybrid Systems Hard?
- All implicit error in continuous analysis,
coupled with switching criteria, leads to
possible catastrophic error
Slide by Rafael Garcia
4Why 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
5What 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
6Tool 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)
7Tool 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
8Tool 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
9Example Integration HyVisual
- Ptolemy IIs HyVisual
- http//ptolemy.eecs.berkeley.edu/hyvisual/
Slide by Edward Lee
10HyVisual
- 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
11HyVisual 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
12Example 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
13Level 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)
14Reachable 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
15Level 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
16Hyper 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
17Hyper Framework
Interoperability Interfaces
18Hyper 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
19Conclusions
- 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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21BASE 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