Risk-Aware Fixed-Time Stabilization of Stochastic Systems with Measurement Uncertainty

Konsep Inti

The paper introduces novel classes of risk-aware fixed-time control Lyapunov functions (RA-FxT-CLFs) and risk-aware path-integral control Lyapunov functions (RA-PI-CLFs) to certify that a stochastic, nonlinear system's trajectories reach a goal set within a fixed-time with a specified probability, despite the presence of measurement uncertainty.

Abstrak

The paper addresses the problem of risk-aware fixed-time stabilization of a class of uncertain, output-feedback nonlinear systems modeled via stochastic differential equations.
Key highlights:

It introduces novel classes of RA-FxT-CLFs and RA-PI-CLFs to certify that a system is both stable in probability and probabilistically fixed-time convergent to a goal set.
It proves that the use of either RA-FxT-CLFs or RA-PI-CLFs for control design ensures the goal set is rendered probabilistically fixed-time stable with a specified probability.
The theoretical results are verified through an empirical study on an illustrative, stochastic, nonlinear system, and the proposed controllers are evaluated against an existing method.
The methods are demonstrated on a simulated fixed-wing aerial robot to highlight their ability to certify the probability that the system safely reaches its goal.

Statistik

The paper does not contain any explicit numerical data or statistics to extract.

Kutipan

"it introduces novel classes of risk-aware fixed-time control Lyapunov functions (RA-FxT-CLFs) and risk-aware path-integral control Lyapunov functions (RA-PI-CLFs) for the fixed-time stabilization of a generic class of stochastic, nonlinear systems to a goal set under the additional effect of stochastic measurement noise"
"it proves how the use of either RA-FxT-CLFs or RA-PI-CLFs for control design certifies that their associated goal set is probabilistically FxTS with probability pg, i.e., that the system trajectories reach the goal set within the given fixed-time with probability pg"

Wawasan Utama Disaring Dari

Risk-Aware Fixed-Time Stabilization of Stochastic Systems under Measurement Uncertainty

by Mitchell Bla... pada arxiv.org 04-01-2024

https://arxiv.org/pdf/2403.20258.pdf

Pertanyaan yang Lebih Dalam

How can the conservatism associated with the proposed RA-FxT-CLF and RA-PI-CLF approaches be reduced?

The conservatism in the RA-FxT-CLF and RA-PI-CLF approaches can be reduced through several strategies:

Refinement of Uncertainty Models: By improving the accuracy of the stochastic models used to represent uncertainties in the system, the conservative assumptions can be minimized. This can involve better estimation techniques, more sophisticated modeling of noise, and incorporating more realistic scenarios into the analysis.

Optimization of Control Parameters: Fine-tuning the control parameters used in the Lyapunov-based methods can help in achieving a better balance between risk aversion and system performance. This optimization process can be iterative and involve simulations to find the optimal set of parameters.

Adaptive Control Strategies: Implementing adaptive control strategies that adjust the control actions based on real-time feedback and system behavior can help in dynamically reducing conservatism while ensuring stability and convergence.

Incorporation of Learning Algorithms: Utilizing machine learning algorithms to adaptively learn and update the control policies based on system responses can lead to more efficient and less conservative control strategies over time.

Hybrid Approaches: Combining the Lyapunov-based methods with other control techniques like model predictive control or reinforcement learning can offer a more comprehensive approach to reducing conservatism while maintaining stability guarantees.

How can the proposed methods be combined with risk-aware barrier functions to handle state constraints?

The combination of the proposed risk-aware fixed-time stabilization methods with risk-aware barrier functions can provide a robust framework for handling state constraints in control systems. Here's how they can be integrated:

Barrier Function as a Constraint: The risk-aware barrier function can be used to define constraints that the system must adhere to while moving towards the goal set. By incorporating these constraints into the Lyapunov-based control design, the system can navigate towards the goal while avoiding unsafe regions defined by the barrier function.

Joint Optimization: A joint optimization framework can be developed where the Lyapunov-based controller and the barrier function constraints are optimized simultaneously. This optimization process aims to find control inputs that not only stabilize the system within a fixed time but also ensure that state constraints are not violated.

Adaptive Weighting: The weighting between the Lyapunov function and the barrier function can be dynamically adjusted based on the risk level and the proximity to state constraints. This adaptive weighting mechanism allows for flexible control strategies that prioritize safety while maintaining stability and convergence.

Hierarchical Control Architecture: Implementing a hierarchical control architecture where the barrier function acts as a higher-level safety controller while the Lyapunov-based controller operates at a lower level for stabilization can provide a structured approach to handling state constraints in a risk-aware manner.

What are the potential applications of the risk-aware fixed-time stabilization techniques beyond the aerial robotics example presented in the paper?

The risk-aware fixed-time stabilization techniques proposed in the paper have broad applications beyond aerial robotics. Some potential areas where these techniques can be applied include:

Autonomous Vehicles: Implementing risk-aware fixed-time stabilization in autonomous cars, drones, or marine vessels can enhance safety and reliability in navigation tasks, especially in dynamic and uncertain environments.

Financial Systems: Applying these techniques in financial systems can help in managing risk in trading algorithms, portfolio optimization, and risk assessment models, ensuring stable and predictable outcomes within specified time frames.

Healthcare Systems: Utilizing risk-aware fixed-time stabilization in medical devices, patient monitoring systems, and healthcare robots can improve patient safety, treatment delivery, and operational efficiency in healthcare settings.

Manufacturing and Industrial Processes: Implementing these techniques in control systems for manufacturing processes, industrial robots, and supply chain management can optimize production efficiency, reduce downtime, and ensure timely completion of tasks while considering safety and risk factors.

Energy Systems: Applying risk-aware fixed-time stabilization in energy grid management, renewable energy systems, and smart grid technologies can enhance grid stability, optimize energy distribution, and mitigate risks associated with power generation and transmission.

Overall, the techniques have the potential to be beneficial in various domains where stability, safety, and time-critical performance are essential requirements.