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# Presentation Outline: Formally Verified Autonomous Hybrid Control for Nuclear Reactors
**Audience:** Engineering PhDs (not necessarily control, nuclear, or formal methods experts)
**Presentation Style:** Assertion-Evidence
---
## 1. Title Slide
**Assertion:** Autonomous Hybrid Control with Formal Safety Guarantees Enables Economic Viability of Next-Generation Nuclear Power
**Content:**
- Your name, affiliation
- Brief subtitle about bridging formal methods and control theory
---
## 2. The Economic Challenge
**Assertion:** Small modular reactors face an unsustainable staffing cost problem that threatens their economic viability
**Evidence:**
- Comparison chart: staffing costs per MW for conventional vs SMR
- Current requirement: 2+ ROs + 1 SRO per reactor
- Training timeline: up to 6 years to become a reactor operator
- Cost breakdown showing O&M as 23-30% of levelized cost
- Projected datacenter demand reaching 1,050 TWh by 2030 = $21-28B annually in O&M
**Key Message:** Automation is not optional—it's economically essential
---
## 3. The Safety Imperative
**Assertion:** Human operators are the root cause of 70-80% of nuclear incidents despite decades of training improvements
**Evidence:**
- Bar chart: 70-80% human error vs 20% equipment failure
- IAEA statement: "Human error was the root cause of all severe accidents"
- TMI case study visualization:
- 100+ simultaneous alarms
- 44% core meltdown
- 500-fold underestimation of risk
- Human Error Probability table showing degradation under stress:
- Optimal: 0.001-0.01
- Under accident conditions: 0.1-1.0 (essentially guaranteed failure)
**Key Message:** Training alone cannot overcome fundamental cognitive limitations
---
## 4. The Paradox
**Assertion:** Nuclear control faces a fundamental tension—human operators are both essential for flexibility and the primary source of failure
**Evidence:**
- Two-column comparison:
- LEFT: "Why we need humans" (judgment, adaptability, procedure interpretation)
- RIGHT: "Why humans fail" (cognitive limits, stress, 7±2 working memory, response time: seconds vs milliseconds)
- Current division of labor diagram:
- Automated: Emergency protection (trip systems, ECCS)
- Manual: Strategic operations (startup, mode transitions, power changes)
- Quote from TMI Commission about "ambiguity in responsibility"
**Key Message:** We need the reliability of automation with the sophistication of human decision-making
---
## 5. What Are Hybrid Control Systems?
**Assertion:** Hybrid systems combine continuous dynamics with discrete mode switching—exactly how nuclear plants operate
**Evidence:**
- Simple equations showing hybrid dynamics:
- Continuous: ẋ(t) = f(x(t), q(t), u(t))
- Discrete: q(k+1) = ν(x(k), q(k), u(k))
- Intuitive example diagram: Nuclear reactor startup
- Mode 1 (Cold Shutdown): Temperature control
- Transition condition: T > 400°F
- Mode 2 (Heatup): Ramp rate control
- Transition condition: Approach criticality
- Mode 3 (Low Power): Neutron flux control
- Contrast with pure continuous (traditional control) and pure discrete (software)
**Key Message:** Nuclear operations are inherently hybrid—continuous physics with discrete strategic decisions
---
## 6. The Gap in Current Approaches
**Assertion:** Existing methods can handle either continuous dynamics or discrete logic, but not both with formal guarantees
**Evidence:**
- Venn diagram showing the gap:
- Circle 1: Formal Methods (HARDENS) → Discrete logic verification ✓, Continuous dynamics ✗
- Circle 2: Control Theory → Continuous stability ✓, Discrete transitions ✗
- Gap in middle: Hybrid system verification
- HARDENS achievement summary:
- Complete RTS verification in 9 months
- Requirements → verified binaries
- BUT: No continuous dynamics, no closed-loop verification
- TRL 3-4, no experimental validation
**Key Message:** We can verify half the system with existing tools—we need to bridge the gap
---
## 7. Our Three-Thrust Approach
**Assertion:** Unifying discrete synthesis and continuous verification enables end-to-end correctness guarantees for hybrid systems
**Evidence:**
- Pipeline diagram with three stages:
**Thrust 1:** Procedures → Temporal Logic (FRET)
- Input: Written procedures
- Tool: NASA FRET (FRETish language)
- Output: LTL specifications
- Key feature: Realizability checking
**Thrust 2:** Temporal Logic → Discrete Automaton (Reactive Synthesis)
- Input: LTL specifications
- Tool: Strix (reactive synthesis)
- Output: Discrete state machine
- Key feature: Correct by construction
**Thrust 3:** Continuous Controllers + Verification
- Input: Discrete automaton + plant model
- Tools: Reachability analysis, barrier certificates
- Output: Verified continuous modes
- Key feature: Compositional verification
**Key Message:** Each piece uses state-of-the-art tools; innovation is in the integration
---
## 8. Thrust 1: From Procedures to Logic
**Assertion:** NASA's FRET tool systematically translates written procedures into unambiguous temporal logic specifications
**Evidence:**
- Side-by-side example:
- LEFT: Natural language: "If a high temperature alarm triggers, control rods must immediately insert and remain inserted until operator reset"
- RIGHT: Temporal logic: G(HighTemp → X(RodsInserted ∧ (¬RodsWithdrawn U OperatorReset)))
- FRETish structure diagram showing 6 required components:
- Scope | Condition | Component | Shall | Timing | Response
- Realizability checking benefits:
- Detects conflicting requirements
- Identifies undefined behaviors
- Finds "bugs" in procedures before implementation
**Key Message:** FRET bridges human-readable procedures and machine-verifiable specifications
---
## 9. Thrust 2: Synthesizing Discrete Controllers
**Assertion:** Reactive synthesis automatically generates provably correct discrete switching logic from temporal specifications
**Evidence:**
- What is reactive synthesis? Simple explanation:
- Input: Temporal logic formula (what should happen)
- Output: State machine (how to make it happen)
- Guarantee: If a solution exists, it is correct by construction
- Example automaton visualization for reactor mode transitions
- Nodes: Cold Shutdown, Heatup, Low Power, Full Power, SCRAM
- Edges: Transition conditions
- Highlight: This is the "operator's decision-making" automated
- Strix tool performance (SYNTCOMP winner)
**Key Message:** The discrete controller is mathematically guaranteed to follow procedures—no switching errors possible
---
## 10. Thrust 3: Continuous Mode Verification
**Assertion:** Continuous controllers are verified using three complementary techniques that avoid global trajectory analysis
**Evidence:**
- Three types of continuous modes based on transition objectives:
- **Stabilizing:** Stay in current mode (e.g., full-power operation)
- **Transitory:** Drive toward next mode (e.g., startup heatup)
- **Expulsory:** Force to safe mode (e.g., SCRAM)
- Three verification techniques:
1. **Reachability Analysis:**
- Computes reachable state sets
- Verifies boundary conditions are met
- Recent advances: Neural Hamilton-Jacobi for high dimensions
2. **Assume-Guarantee Contracts:**
- Each mode verified with input/output bounds
- Compositional: local verification, global guarantees
3. **Barrier Certificates:**
- Proves safe set forward invariance
- Guarantees transitions occur correctly
- Ensures stability across mode switches
**Key Message:** Local verification of each mode is tractable; composition ensures global correctness
---
## 11. Why This Works: The Key Insight
**Assertion:** Designing continuous controllers after synthesizing the discrete automaton enables local verification instead of intractable global analysis
**Evidence:**
- Problem with traditional approach:
- Design everything at once
- Verify entire trajectory through all modes
- Computationally intractable for complex systems
- Our approach:
- Discrete automaton defines transition boundaries
- Design each continuous mode to satisfy its local transitions
- Use assume-guarantee to chain modes together
- Barrier certificates prove transitions are safe
- Diagram showing modular verification:
- Each mode verified independently
- Interface contracts guarantee composition
- Total system correctness follows from local proofs
**Key Message:** Decomposition is the key to tractable verification
---
## 12. Demonstration: SmAHTR Startup
**Assertion:** Autonomous startup of a Small Modular Advanced High Temperature Reactor provides a rigorous test case spanning multiple coordinated modes
**Evidence:**
- Why SmAHTR?
- Well-documented startup procedures
- Multiple distinct operational modes
- Complex thermal-hydraulics + neutron kinetics
- Representative of next-gen reactor designs
- Startup sequence complexity:
- Cold conditions → Controlled heating → Approach criticality → Low-power physics → Full power
- Multiple coordinated subsystems
- Strict timing and temperature constraints
- Implementation platform:
- High-fidelity Simulink model (thermal-hydraulics + neutron kinetics)
- Emerson Ovation control hardware (industry standard)
- ARCADE integration (hardware-in-the-loop)
- Real-time performance validation
**Key Message:** This is not a toy problem—it's representative of actual deployment challenges
---
## 13. Expected Outcomes
**Assertion:** Success will be measured by progression to TRL 5, demonstrating practical feasibility beyond theoretical proof
**Evidence:**
- TRL progression chart:
- Starting point: TRL 2-3 (basic concepts, HARDENS as precedent)
- Target: TRL 5 (validated prototype in relevant environment)
- Gap: Experimental validation with continuous dynamics
- Three concrete deliverables:
**Outcome 1:** Procedure translation methodology
- Engineers can generate verified controllers from regulatory procedures
- No formal methods expertise required
**Outcome 2:** Continuous verification framework
- Standard control design + iterative verification
- Proof of safe mode transitions
**Outcome 3:** SmAHTR demonstration
- Autonomous startup on industrial hardware
- Hardware-in-the-loop validation
- Path to deployment
**Key Message:** TRL 5 proves both theoretical validity and practical implementability
---
## 14. Broader Impact: Beyond Nuclear
**Assertion:** This methodology generalizes to any safety-critical hybrid system with documented operational procedures
**Evidence:**
- Common pattern across domains:
- Written procedures exist
- Continuous dynamics + discrete decisions
- Safety is paramount
- Autonomy has economic benefits
- Application domains table:
- Chemical process control (batch processes, safety interlocks)
- Aerospace (flight phases, emergency procedures)
- Autonomous transportation (driving modes, emergency maneuvers)
- Medical devices (therapy modes, patient monitoring)
- Economic multiplier:
- Nuclear O&M: $21-28B annually (projected datacenter demand alone)
- Broader safety-critical infrastructure: Much larger
- Regulatory pathway:
- Proving concept in nuclear (highest safety bar)
- Establishes precedent for other industries
- Mathematical proof as regulatory evidence
**Key Message:** Nuclear is the proving ground; impact extends far beyond
---
## 15. Innovation Summary
**Assertion:** The innovation is not in individual techniques but in their systematic integration to bridge a fundamental gap in cyber-physical systems
**Evidence:**
- What's NOT new (but state-of-the-art):
- Temporal logic and reactive synthesis (computer science)
- Reachability analysis and barrier certificates (control theory)
- Hardware-in-the-loop validation (industry practice)
- What IS new:
- **Integration:** Unifying discrete and continuous verification
- **Methodology:** Systematic tool-supported workflow from procedures to verified controller
- **Decomposition:** Local verification with compositional guarantees
- **Practical:** Targets existing industrial hardware (Emerson Ovation)
- Comparison to HARDENS:
- HARDENS: Discrete only, TRL 3-4, no continuous dynamics
- This work: Full hybrid system, TRL 5, hardware-in-the-loop
- Key enabling insight:
- Automaton-first design enables tractable continuous verification
**Key Message:** Standing on the shoulders of giants to solve a previously intractable problem
---
## 16. Timeline and Feasibility
**Assertion:** This research is feasible within a PhD timeline given existing tools, models, and infrastructure access
**Evidence:**
- Existing infrastructure:
- University of Pittsburgh Cyber Energy Center
- Emerson control hardware access
- SmAHTR Simulink model already developed
- ARCADE platform operational
- Industry collaboration channels
- Tool maturity:
- FRET: Production-ready (NASA JPL)
- Strix: Competition-winning synthesis tool
- Reachability tools: Recent advances make high-dimensional systems tractable
- Risk mitigation:
- Start with simpler mode sequences, add complexity incrementally
- Extensive simulation before hardware-in-the-loop
- Fallback: Manual continuous controller design if synthesis proves intractable
- Precedent: HARDENS achieved similar scope in 9 months
**Key Message:** Ambitious but achievable with existing resources and tools
---
## 17. Conclusion: The Path Forward
**Assertion:** Formally verified autonomous hybrid control is essential for next-generation nuclear power and provides a template for broader safety-critical autonomy
**Evidence:**
- Three converging imperatives:
1. **Economic:** SMRs need autonomy to be viable ($21-28B annual O&M for datacenter demand)
2. **Safety:** Human error causes 70-80% of incidents; training can't fix cognitive limits
3. **Technical:** Tools now exist to verify hybrid systems; HARDENS proved discrete is feasible
- This research closes the gap:
- HARDENS + Continuous Verification = Complete Hybrid System
- Theory + Hardware-in-the-Loop = TRL 5
- Nuclear Demonstration = Pathway for broader adoption
- Vision: Control engineers generate high-assurance autonomous controllers from procedures
- No formal methods PhD required
- Mathematical proof of correctness included
- Deployable on existing industrial hardware
**Key Message:** The pieces exist; we're putting them together at the right time for the right application
---
## 18. Questions
**Assertion:** (Keep a few backup slides here for common questions)
Potential backup slides:
- Detailed FRET example
- Reactive synthesis algorithm overview
- Reachability analysis visualization
- Comparison with other autonomy approaches (ML, MPC, etc.)
- Regulatory acceptance pathway
- Scalability to larger systems