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Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models

Core Concepts
The author presents an adaptive online learning framework for safety-critical control in non-stationary environments using Gaussian processes. The approach involves two phases: a novel sparse Gaussian process framework and a safety filter based on high order control barrier functions.
The paper introduces an adaptive online learning framework for safety-critical control in uncertain systems. It consists of two phases: one focusing on a sparse Gaussian process framework and the other proposing a safety filter based on high order control barrier functions. The efficacy of the algorithm is demonstrated through real-time obstacle avoidance experiments. Key points: Introduction to adaptive online learning for safety-critical control. Two-phase approach involving sparse Gaussian processes and high order control barrier functions. Demonstration of algorithm effectiveness through obstacle avoidance experiments.
Time complexity reduced from O(NM^2) to O(M^3) MSE comparison: AFVSGP (0.5863), VSGP (1.4844), GP (6.6029), SOGP (0.8118) Training time comparison: AFVSGP (0.00613s), VSGP (0.03562s), GP, SOGP (not specified)
"Control barrier functions offer a framework for ensuring state forward-invariance." "Gaussian processes stand out for modeling complex functions with minimal prior knowledge." "Our proposed algorithm demonstrates real-time adaptability in obstacle avoidance tasks."

Deeper Inquiries

How can the adaptive selection of training data reflect the evolving nature of the environment?

In the context of safety-critical control systems, adaptive selection of training data is crucial to ensure that the model remains relevant and effective in dynamic environments. By continuously updating and modifying the training dataset based on new incoming data points, the model can adapt to changes in its surroundings. This adaptability allows for a more accurate representation of the system's behavior, especially when dealing with uncertain parameters or non-stationary conditions. The process involves evaluating which data points are most informative and representative at any given time, reflecting the evolving nature of the environment by capturing real-time dynamics.

How can Gaussian processes be used for safety-critical control?

While Gaussian processes (GPs) offer a powerful Bayesian approach for modeling complex functions with minimal prior knowledge, there are certain counterarguments against their use in safety-critical control applications. One primary concern is related to computational complexity, as GPs typically require extensive offline learning strategies and may struggle to adapt quickly to changing environments in real-time scenarios. Additionally, GPs have limitations when handling high-dimensional nonlinear models efficiently due to their inherent scalability issues.

How can forgetting mechanisms be applied beyond safety-critical control?

Forgetting mechanisms play a vital role in enhancing adaptability and efficiency in learning algorithms by selectively discarding outdated information while retaining essential knowledge. Beyond safety-critical control applications, forgetting mechanisms can be applied across various domains such as: Machine Learning: In online learning tasks where continuous updates are required, forgetting mechanisms help prevent model degradation over time. Natural Language Processing: Forgetting irrelevant context from previous sentences during text generation tasks could improve language models' performance. Financial Forecasting: Removing outdated market trends from predictive models using forgetting mechanisms ensures more accurate predictions. Healthcare: In medical diagnosis systems that need constant updates based on new patient data, forgetting mechanisms aid in maintaining relevance and accuracy. By incorporating forgetting mechanisms into different fields, systems can stay agile and responsive to changes while optimizing resource utilization effectively.