Probabilistic Safe Fault-Tolerant Control: A Gaussian Process-Based Approach
- Publication Type:
- Thesis
- Issue Date:
- 2025
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Fault-tolerant control (FTC) aims to preserve system functionality and ensure stability in the presence of unknown faults, such as actuator faults. However, existing FTC methods do not explicitly guarantee safety and may fail to mitigate potential risks to surrounding systems in practical environments. Accordingly, this research investigates the impact of unknown actuator gain and bias faults on system dynamics, which may result from partial degradation of physical components or long-term wear. In addition, model uncertainty is an inherent property of systems due to randomness and limited system knowledge, which degrades the performance of FTC methods. Two types of uncertainty are considered in this thesis: aleatoric uncertainty, arising from randomness, and epistemic uncertainty, resulting from incomplete system knowledge. To address these challenges, probabilistically safe FTC methods, which integrate GPs and control barrier functions (CBFs) into FTC frameworks, are proposed to ensure safe and reliable control of autonomous systems.
Firstly, this thesis proposes probabilistic adaptive FTC approaches to compensate for unknown actuator bias faults and to approximate unknown system dynamics through GP regression. Since GPs are sensitive to the quality and quantity of training data, two data collection strategies are investigated: offline data collection and online event-triggered learning. Sufficient conditions are derived to ensure the probabilistic stability of the closed-loop system. Secondly, to ensure both stability and safety of systems with high relative degrees, a learning-based safe FTC method is presented by integrating a high-order CBF (HOCBF) method and GP regression into the FTC framework. Theoretical feasibility conditions are derived to ensure probabilistic constraint satisfaction. Thirdly, a novel GP-based safe control approach is proposed to handle challenges arising from actuator gain faults. The approach incorporates the CBF method and online fault parameter estimation and is further extended to the HOCBF framework. Several theoretical results are derived to ensure stability of the estimator and probabilistic safety of uncertain systems. Lastly, to overcome the conservative assumptions about the structure of model uncertainty, particularly those adopted in HOCBF methods, a novel unified GP modelling strategy with compound kernels is introduced and integrated with HOCBFs into the FTC framework. Theoretical conditions are established to guarantee its feasibility. Numerical examples demonstrate the effectiveness and competitiveness of proposed methods compared to existing methods.
Overall, this thesis proposes novel methodologies to address unknown actuator faults and model uncertainty, with a focus on enhancing the safety and stability of autonomous systems in practical environments.
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