Optimal Control Envelope Synthesis for Hybrid Systems via Angelic Refinements

Core Concepts

This paper presents an approach called Control Envelope Synthesis via Angelic Refinements (CESAR) that synthesizes provably correct control envelopes for hybrid systems. The control envelopes characterize families of safe controllers and are used to monitor untrusted controllers at runtime. CESAR fills in the blanks of a hybrid system's sketch to maximize the flexibility of the control envelope while establishing the desired safety condition.

Abstract

The paper introduces CESAR, an approach for synthesizing provably correct control envelopes for hybrid systems. Control envelopes characterize families of safe controllers and are used to monitor untrusted controllers at runtime.
The key insights are:

CESAR fills in the blanks of a hybrid system's sketch, specifying the desired shape of the control envelope, the possible control actions, and the system's differential equations.
To maximize the flexibility of the control envelope, CESAR synthesizes conditions saying which control action can be chosen when, as permissively as possible while establishing the desired safety condition.
CESAR uses hybrid systems game theory to implicitly characterize an optimal safe control envelope, from which explicit solutions can be derived via symbolic execution and sound, systematic game refinements.
CESAR is demonstrated on a range of safe control envelope synthesis examples with different control challenges, including benchmarks with non-solvable dynamics and those requiring a sequence of clever control actions.

Stats

A > 0 ∧B > 0 ∧T > 0 ∧v ≥0
e - p > v^2/2B
e - p > vT + AT^2/2 + (v + AT)^2/2B
V > 0 ∧T > 0
y > -R ∧|x| < R
V T < 2R ∧(x > -R ∧|y| < R)

Quotes

"Control envelopes allow the verification of abstractions of control systems, isolating the parts relevant to the safety feature of interest, without involving the full complexity of a specific control implementation."
"The full control system is then monitored for adherence to the safe control envelope at runtime."

Key Insights Distilled From

CESAR

by Adit... at arxiv.org 04-08-2024

https://arxiv.org/pdf/2311.02833.pdf

Deeper Inquiries

How can CESAR be extended to handle more complex hybrid system dynamics, such as those involving partial differential equations or stochastic elements?

To handle more complex hybrid system dynamics, CESAR can be extended in several ways. One approach is to incorporate techniques for dealing with partial differential equations (PDEs) into the synthesis process. This could involve developing methods to symbolically reason about PDEs, similar to how CESAR currently handles ordinary differential equations (ODEs). By integrating tools for PDE analysis and solution, CESAR could be adapted to synthesize control envelopes for systems with PDE dynamics.
Additionally, to address stochastic elements in hybrid systems, CESAR could be enhanced to incorporate probabilistic reasoning and stochastic modeling techniques. This would involve integrating probabilistic models, such as Markov decision processes or stochastic differential equations, into the synthesis process. By considering the uncertainty and randomness inherent in stochastic systems, CESAR could provide control strategies that are robust to probabilistic variations in system behavior.

What are the limitations of the current approach in terms of scalability and the types of control strategies it can handle? How could it be improved to address these limitations?

One limitation of the current approach is scalability, particularly when dealing with complex systems or large state spaces. As the complexity of the system increases, the computational resources required for synthesis also increase, leading to scalability challenges. To address this limitation, CESAR could benefit from optimization techniques, parallel computing, and algorithmic improvements to enhance efficiency and reduce computational overhead.
In terms of control strategies, the current approach may have limitations in handling certain types of non-linear or hybrid control strategies that require sophisticated reasoning. To improve this, CESAR could be enhanced with advanced control synthesis algorithms, such as reinforcement learning or model predictive control, to handle a broader range of control strategies. By integrating these advanced techniques, CESAR could provide more comprehensive solutions for complex control problems.

What are the potential applications of CESAR beyond the safe control of hybrid systems, such as in the design of robust control systems or the verification of machine learning-based controllers?

Beyond safe control of hybrid systems, CESAR has potential applications in various domains related to control systems and verification. One application is in the design of robust control systems, where CESAR can be used to synthesize control envelopes that ensure system stability and performance under uncertain conditions. By incorporating robustness criteria into the synthesis process, CESAR can help design controllers that are resilient to disturbances and uncertainties.
Another application is in the verification of machine learning-based controllers. CESAR can be utilized to verify the safety and correctness of controllers generated by machine learning algorithms. By synthesizing control envelopes that encapsulate the safety requirements of the system, CESAR can provide a formal verification framework for ensuring the reliability of machine learning-based controllers in safety-critical applications. This can help bridge the gap between the black-box nature of machine learning models and the need for formal guarantees in control systems.