1. hyper A Useful Toolbox for Hybrid Systems
Shankar Sastry, Jonathan Sprinkle,
Mike Eklund, Ian Mitchell
UC Berkeley
November 2004
Shankar Sastry, UC Berkeley

2. What Are Hybrid Systems?
Dynamical systems with interacting continuous and discrete dynamics
November 2004
Shankar Sastry, UC Berkeley

3. Why are Hybrid Systems Hard?
All implicit error in continuous analysis, coupled with switching criteria, leads to possible catastrophic error X1
Numerical Solution
Real Solution
t = t* X2
November 2004
Shankar Sastry, UC Berkeley
Slide by Rafael Garcia

4. Why are Hybrid Systems Hard?
Zeno behavior
Event transitions happen so rapidly that the simulator grinds to a halt
A Toolbox should detect this
November 2004
Shankar Sastry, UC Berkeley
Slide by Edward Lee

5. Shankar Sastry, UC Berkeley
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: observers[Bemporad, Koutsoukos, Vidal]
Computer Science[ Biswas, Karsai, Zhao]
November 2004
Shankar Sastry, UC Berkeley

6. Shankar Sastry, UC Berkeley
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)
November 2004
Shankar Sastry, UC Berkeley

7. 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:
November 2004
Shankar Sastry, UC Berkeley
Slide by Edward Lee

8. Shankar Sastry, UC Berkeley
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
November 2004
Shankar Sastry, UC Berkeley

9. Example Integration: HyVisual
Ptolemy II’s HyVisual
November 2004
Shankar Sastry, UC Berkeley
Slide by Edward Lee

10. Shankar Sastry, UC Berkeley
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
November 2004
Shankar Sastry, UC Berkeley

11. 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
November 2004
Shankar Sastry, UC Berkeley

12. Example Integration: A Toolbox of LSM
Ian Mitchell’s Toolbox of Level Set Methods
Numerical algorithms for dynamic implicit surfaces and Hamilton-Jacobi partial differential equations
November 2004
Shankar Sastry, UC Berkeley

13. Shankar Sastry, UC Berkeley
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)
November 2004
Shankar Sastry, UC Berkeley

14. 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
November 2004
Shankar Sastry, UC Berkeley

15. 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
November 2004
Shankar Sastry, UC Berkeley

16. Shankar Sastry, UC Berkeley
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
- Should be highly robust, with respect to many different KINDS of systems (hybrid, discrete, stochastically driven, etc.) -
November 2004
Shankar Sastry, UC Berkeley

17. Shankar Sastry, UC Berkeley
Hyper Framework
Interoperability
Interfaces
November 2004
Shankar Sastry, UC Berkeley

18. Shankar Sastry, UC Berkeley
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
November 2004
Shankar Sastry, UC Berkeley

19. Shankar Sastry, UC Berkeley
Conclusions
Not trying to build Rome in 1 day
Focused application to certain capabilities at first
Concentration on not solving all the world’s problems at once
Restricting initial release to useful and mature tools
Immediately providing two diverse toolbox integrations as examples to others
November 2004
Shankar Sastry, UC Berkeley

20. Shankar Sastry, UC Berkeley
November 2004
Shankar Sastry, UC Berkeley

21. Shankar Sastry, UC Berkeley
BASE Package
Simulators
Matlab, HyVisual
Simulators
Matlab, HyVisual
Simulators
Matlab, HyVisual
CORE
Extraction
model database
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
November 2004
Shankar Sastry, UC Berkeley