insikt - Algorithms and Data Structures - # Robust Predictive Safety Filter for Nonlinear Systems

A Robust and Efficient Predictive Safety Filter for Time-Varying Nonlinear Systems with Bounded Disturbances

Q: How can the proposed robust predictive safety filter be extended to handle stochastic disturbances or uncertainties beyond bounded perturbations

To extend the proposed robust predictive safety filter to handle stochastic disturbances or uncertainties beyond bounded perturbations, we can incorporate probabilistic methods into the safety filter design. By introducing probabilistic models for the disturbances, such as Gaussian processes or Monte Carlo simulations, we can account for the uncertainty in the system dynamics. This would involve modifying the barrier function formulation to include probabilistic guarantees of safety, rather than strict bounds on disturbances. Additionally, techniques from robust control theory, such as robust MPC or H-infinity control, can be integrated to handle uncertainties in a more systematic manner. By combining these approaches, the safety filter can adapt to a wider range of disturbances and uncertainties, providing a more robust and reliable control strategy.

Q: What are the trade-offs between the conservatism of the 1-step robust safety filter and the computational complexity of the N-step robust predictive safety filter

The trade-offs between the conservatism of the 1-step robust safety filter and the computational complexity of the N-step robust predictive safety filter are crucial considerations in control system design. The 1-step robust safety filter tends to be more conservative as it enforces safety at each time step independently, leading to a more cautious control strategy. On the other hand, the N-step robust predictive safety filter allows for more flexibility in the system's behavior over a longer prediction horizon, potentially leading to less conservative control actions. However, this comes at the cost of increased computational complexity, as the optimization problem grows with the prediction horizon. Balancing these trade-offs involves understanding the specific requirements of the system and the level of conservatism acceptable for the application. For safety-critical systems where any risk of violation is unacceptable, a more conservative approach with the 1-step filter may be preferred. In contrast, for systems where performance is a priority and some level of risk can be tolerated, the N-step predictive safety filter can offer a more efficient solution. By adjusting the prediction horizon and tuning the constraints in the safety filter, a balance can be achieved between conservatism and computational complexity to meet the specific needs of the application.

Q: How can these be balanced for different applications

The event-triggered framework can be further optimized to reduce online computations by incorporating machine learning techniques to predict when the safety filter is likely to be triggered. By training a model on historical data of system behavior and safety filter activations, the system can learn patterns and trends that indicate when a safety violation is imminent. This predictive model can then be used to selectively activate the safety filter only when necessary, reducing the overall computational load. Additionally, adaptive event-triggering thresholds can be implemented based on the system's current state and the level of uncertainty in the disturbances. By dynamically adjusting the triggering conditions, the system can optimize the balance between safety enforcement and computational efficiency. This adaptive approach ensures that the safety filter is activated only when the risk of a safety violation is significant, leading to more efficient utilization of computational resources.

Centrala begrepp

The proposed robust predictive safety filter ensures that the system states remain within a safe region in the presence of bounded disturbances, even for time-varying nonlinear systems with time-varying constraints.

Sammanfattning

The paper presents a novel robust predictive safety filter that extends existing work on control barrier functions to address bounded perturbations and time-varying systems and constraints. The key contributions are:

Robust predictive safety filter for time-varying nonlinear systems and time-varying constraints: The proposed approach uses robust, discrete-time barrier functions to ensure safety in the presence of bounded disturbances. This extends previous work that was limited to time-invariant systems.
1-step robust safety filter: The authors also develop a simplified 1-step robust safety filter that can be more efficiently implemented by only checking the safety condition around the boundary of the safe set.
Event-triggered implementation: An event-triggered control policy is proposed that only solves the safety filter optimization problem when necessary, reducing online computational requirements.

The safety filter is demonstrated on a two-tank system, a building system, and a single integrator example, showing its effectiveness in ensuring constraint satisfaction under bounded disturbances.

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Statistik

The paper provides the following key metrics and figures:

Lipschitz constants Lx
f, Ld, Lx
b, and Lx
h are used to bound the system dynamics, disturbance, and constraint functions.
The N-step prediction horizon is used to relax conservatism in the safety filter.
The robust terminal safe set X N
f (k) is defined to ensure safety at the end of the prediction horizon.

Citat

"The proposed safety filter extends upon existing work to reject disturbances for discrete-time, time-varying nonlinear systems with time-varying constraints."
"The event triggering only requires solving the safety filter optimization problem if the nominal control performs an unsafe action."

Viktiga insikter från

A Robust, Efficient Predictive Safety Filter

by Wenceslao Sh... på arxiv.org 04-29-2024

https://arxiv.org/pdf/2311.08496.pdf

A Robust, Efficient Predictive Safety Filter

Djupare frågor

How can the proposed robust predictive safety filter be extended to handle stochastic disturbances or uncertainties beyond bounded perturbations

To extend the proposed robust predictive safety filter to handle stochastic disturbances or uncertainties beyond bounded perturbations, we can incorporate probabilistic methods into the safety filter design. By introducing probabilistic models for the disturbances, such as Gaussian processes or Monte Carlo simulations, we can account for the uncertainty in the system dynamics. This would involve modifying the barrier function formulation to include probabilistic guarantees of safety, rather than strict bounds on disturbances. Additionally, techniques from robust control theory, such as robust MPC or H-infinity control, can be integrated to handle uncertainties in a more systematic manner. By combining these approaches, the safety filter can adapt to a wider range of disturbances and uncertainties, providing a more robust and reliable control strategy.

What are the trade-offs between the conservatism of the 1-step robust safety filter and the computational complexity of the N-step robust predictive safety filter

The trade-offs between the conservatism of the 1-step robust safety filter and the computational complexity of the N-step robust predictive safety filter are crucial considerations in control system design. The 1-step robust safety filter tends to be more conservative as it enforces safety at each time step independently, leading to a more cautious control strategy. On the other hand, the N-step robust predictive safety filter allows for more flexibility in the system's behavior over a longer prediction horizon, potentially leading to less conservative control actions. However, this comes at the cost of increased computational complexity, as the optimization problem grows with the prediction horizon.
Balancing these trade-offs involves understanding the specific requirements of the system and the level of conservatism acceptable for the application. For safety-critical systems where any risk of violation is unacceptable, a more conservative approach with the 1-step filter may be preferred. In contrast, for systems where performance is a priority and some level of risk can be tolerated, the N-step predictive safety filter can offer a more efficient solution. By adjusting the prediction horizon and tuning the constraints in the safety filter, a balance can be achieved between conservatism and computational complexity to meet the specific needs of the application.

How can these be balanced for different applications

The event-triggered framework can be further optimized to reduce online computations by incorporating machine learning techniques to predict when the safety filter is likely to be triggered. By training a model on historical data of system behavior and safety filter activations, the system can learn patterns and trends that indicate when a safety violation is imminent. This predictive model can then be used to selectively activate the safety filter only when necessary, reducing the overall computational load.
Additionally, adaptive event-triggering thresholds can be implemented based on the system's current state and the level of uncertainty in the disturbances. By dynamically adjusting the triggering conditions, the system can optimize the balance between safety enforcement and computational efficiency. This adaptive approach ensures that the safety filter is activated only when the risk of a safety violation is significant, leading to more efficient utilization of computational resources.