Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees

• URL: http://arxiv.org/abs/2111.00411v1
• Date: Sun, 31 Oct 2021 05:52:42 GMT
• Title: Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees
• Authors: Yingying Li, Subhro Das, Jeff Shamma, Na Li
• Abstract summary: We study the adaptive control of an unknown linear system with a quadratic cost function subject to safety constraints on both the states and actions. Our algorithm is implemented on a single trajectory and does not require system restarts.
• Score: 11.627320138064684
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the adaptive control of an unknown linear system with a quadratic cost function subject to safety constraints on both the states and actions. The challenges of this problem arise from the tension among safety, exploration, performance, and computation. To address these challenges, we propose a polynomial-time algorithm that guarantees feasibility and constraint satisfaction with high probability under proper conditions. Our algorithm is implemented on a single trajectory and does not require system restarts. Further, we analyze the regret of our learning algorithm compared to the optimal safe linear controller with known model information. The proposed algorithm can achieve a $\tilde O(T^{2/3})$ regret, where $T$ is the number of stages and $\tilde O(\cdot)$ absorbs some logarithmic terms of $T$.

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