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1. Nonparametric Adaptive Robust Control under Model Uncertainty

   https://doi.org/10.1137/22M1481609  

   Bayraktar, Erhan; Chen, Tao (October 2023, SIAM Journal on Control and Optimization)

   Yin, George (Ed.)

   We consider a discrete time stochastic Markovian control problem under model uncertainty. Such uncertainty not only comes from the fact that the true probability law of the underlying stochastic process is unknown, but the parametric family of probability distributions which the true law belongs to is also unknown. We propose a nonparametric adaptive robust control methodology to deal with such problem where the relevant system random noise is, for simplicity, assumed to be i.i.d. and onedimensional. Our approach hinges on the following building concepts: first, using the adaptive robust paradigm to incorporate online learning and uncertainty reduction into the robust control problem; second, learning the unknown probability law through the empirical distribution, and representing uncertainty reduction in terms of a sequence of Wasserstein balls around the empirical distribution; third, using Lagrangian duality to convert the optimization over Wasserstein balls to a scalar optimization problem, and adopting a machine learning technique to achieve efficient computation of the optimal control. We illustrate our methodology by considering a utility maximization problem. Numerical comparisons show that the nonparametric adaptive robust control approach is preferable to the traditional robust frameworks 

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2. Human Uncertainty-Aware MPC for Enhanced Human-Robot Collaborative Manipulation

   https://doi.org/10.1109/ICPS59941.2024.10640020  

   Mahmud, Al Jaber; Nguyen, Duc M; Veiga, Filipe; Xiao, Xuesu; Wang, Xuan (May 2024, IEEE)

   This paper presents the development of a novel control algorithm designed for tasks involving human-robot collaboration. By using an 8-DOF robotic arm, our approach aims to counteract human-induced uncertainties added to the robot's nominal trajectory. To address this challenge, we incorporate a variable within the regular Model Predictive Control (MPC) framework to account for human uncertainties, which are modeled as following a normal distribution with a non-zero mean and variance. Our solution involves formulating and solving an uncertainty-aware Discrete Algebraic Ricatti Equation (ua-DARE), which yields the optimal control law for all joints to mitigate the impact of these uncertainties. We validate our methodology through theoretical analysis, demonstrating the effectiveness of the ua-DARE in providing an optimal control strategy. Our approach is further validated through simulation experiments using a Fetch robot model, where the results highlight a significant improvement in performance over a baseline algorithm that does not consider human uncertainty while solving for optimal control law. 

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3. ALERA: Accelerated Reinforcement Learning Driven Adaptation to Electro-Mechanical Degradation in Nonlinear Control Systems Using Encoded State Space Error Signatures

   https://doi.org/10.1145/3338123  

   Banerjee, S. and (July 2019, ACM transactions on intelligent systems and technology)

   The successful deployment of autonomous real-time systems is contingent on their ability to recover from performance degradation of sensors, actuators, and other electro-mechanical subsystems with low latency. In this article, we introduce ALERA, a novel framework for real-time control law adaptation in nonlinear control systems assisted by system state encodings that generate an error signal when the code properties are violated in the presence of failures. The fundamental contributions of this methodology are twofold—first, we show that the time-domain error signal contains perturbed system parameters’ diagnostic information that can be used for quick control law adaptation to failure conditions and second, this quick adaptation is performed via reinforcement learning algorithms that relearn the control law of the perturbed system from a starting condition dictated by the diagnostic information, thus achieving significantly faster recovery. The fast (up to 80X faster than traditional reinforcement learning paradigms) performance recovery enabled by ALERA is demonstrated on an inverted pendulum balancing problem, a brake-by-wire system, and a self-balancing robot. 

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4. dSLAP: Distributed Safe Learning and Planning for Multi-robot Systems

   https://doi.org/10.1109/CDC51059.2022.9992938  

   Yuan, Zhenyuan; Zhu, Minghui (December 2022, IEEE 61st Conference on Decision and Control)

   This paper considers the problem where a group of mobile robots subject to unknown external disturbances aim to safely reach goal regions. We develop a distributed safe learning and planning algorithm that allows the robots to learn about the external unknown disturbances and safely navigate through the environment via their single trajectories. We use Gaussian process regression for online learning where variance is adopted to quantify the learning uncertainty. By leveraging set-valued analysis, the developed algorithm enables fast adaptation to newly learned models while avoiding collision against the learning uncertainty. Active learning is then applied to return a control policy such that the robots are able to actively explore the unknown disturbances and reach their goal regions in time. Sufficient conditions are established to guarantee the safety of the robots. A set of simulations are conducted for evaluation. 

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5. Provable Probabilistic Safety and Feasibility-Assured Control for Autonomous Vehicles using Exponential Control Barrier Functions

   https://doi.org/10.1109/IV51971.2022.9827424  

   Van Koevering, Spencer; Lyu, Yiwei; Luo, Wenhao; Dolan, John M. (June 2022, IEEE Intelligent Vehicles Symposium)

   With the increasing need for safe control in the domain of autonomous driving, model-based safety-critical control approaches are widely used, especially Control Barrier Function (CBF) based approaches. Among them, Exponential CBF (eCBF) is particularly popular due to its realistic applicability to high-relative-degree systems. However, for most of the optimization-based controllers utilizing CBF-based constraints, solution feasibility is a common issue raised from potential conflict among different constraints. Moreover, how to incorporate uncertainty into the eCBF-based constraints in high-relative-degree systems to account for safety remains an open challenge. In this paper, we present a novel approach to extend a eCBF-based safe critical controller to a probabilistic setting to handle potential motion uncertainty from system dynamics. More importantly, we leverage an optimization-based technique to provide a solution feasibility guarantee in run time, while ensuring probabilistic safety. Lane changing and intersection handling are demonstrated as two use cases, and experiment results are provided to show the effectiveness of the proposed approach. 

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