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1. L1-GP: L1 Adaptive Control with Bayesian Learning

   Gahlawat, Aditya; Zhao, Pan; Patterson, Andrew; Hovakimyan, Naira; Theodorou, Evangelos (June 2020, Learning for Dynamics and Control Conference)

   We present L1-GP, an architecture based on L1 adaptive control and Gaussian Process Regression (GPR) for safe simultaneous control and learning. On one hand, the L1 adaptive control provides stability and transient performance guarantees, which allows for GPR to efficiently and safely learn the uncertain dynamics. On the other hand, the learned dynamics can be conveniently incorporated into the L1 control architecture without sacrificing robustness and tracking performance. Subsequently, the learned dynamics can lead to less conservative designs for performance/robustness tradeoff. We illustrate the efficacy of the proposed architecture via numerical simulations. 

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2. ROBUST MODEL BASED REINFORCEMENT LEARNING USING L1 ADAPTIVE CONTROL

   Sung, Minjun; Karumanchi, Sambhu_Harimanas; Gahlawat, Aditya; Hovakimyan, Naira (January 2024, International Conference on learning representations, openreview.net)

   We introduce L1-MBRL, a control-theoretic augmentation scheme for Model-Based Reinforcement Learning (MBRL) algorithms. Unlike model-free approaches, MBRL algorithms learn a model of the transition function using data and use it to design a control input. Our approach generates a series of approximate control-affine models of the learned transition function according to the proposed switching law. Using the approximate model, control input produced by the underlying MBRL is perturbed by the L1 adaptive control, which is designed to enhance the robustness of the system against uncertainties. Importantly, this approach is agnostic to the choice of MBRL algorithm, enabling the use of the scheme with various MBRL algorithms. MBRL algorithms with L1 augmentation exhibit enhanced performance and sample efficiency across multiple MuJoCo environments, outperforming the original MBRL algorithms, both with and without system noise. 

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3. A Multirate Adaptive Control for MIMO Systems with Application to Cyber-Physical Security

   https://doi.org/10.1109/CDC.2018.8619570  

   Jafarnejadsani, Hamidreza; Lee, Hanmin; Hovakimyan, Naira; Voulgaris, Petros (December 2018, 2018 IEEE Conference on Decision and Control)

   This paper proposes a multirate output-feedback controller for multi-input multi-output (MIMO) systems, possibly with non-minimum-phase zeros, using the L1 adaptive control structure. The analysis of stability and robustness of the sampled-data controller reveals that under certain conditions the performance of a continuous-time reference system is uniformly recovered as the sampling time goes to zero. The controller is designed for detection and mitigation of actuator attacks. By considering a multirate formulation, stealthy zero-dynamics attacks become detectable. The experimental results from the flight test of a small quadrotor are provided. The tests show that the multirate L1 controller can effectively detect the zero-dynamics actuator attack and recover stability of the quadrotor. 

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4. Adaptive MPPI Architecture for Robust and Agile Control of Multirotors

   https://doi.org/10.1109/IROS45743.2020.9341154  

   Pravitra, Jintasit; Ackerman, Kasey A.; Cao, Chengyu; Hovakimyan, Naira; Theodorou, Evangelos A. (October 2020, IEEE International Workshop on Intelligent Robots and Systems)

   null (Ed.)

   This paper presents a multirotor control architecture, where Model Predictive Path Integral Control (MPPI) and ℒ 1 adaptive control are combined to achieve both fast model predictive trajectory planning and robust trajectory tracking. MPPI provides a framework to solve nonlinear MPC with complex cost functions in real-time. However, it often lacks robustness, especially when the simulated dynamics are different from the true dynamics. We show that the ℒ 1 adaptive controller robustifies the architecture, allowing the overall system to behave similar to the nominal system simulated with MPPI. The architecture is validated in a simulated multirotor racing environment. 

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5. Contraction L1-Adaptive Control using Gaussian Processes. In Learning for Dynamics and Control

   Gahlawat, A. (January 2021, Proceedings of Machine Learning Research)

   null (Ed.)

   We present a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based L1-adaptive (CL1) control and Bayesian learning in the form of Gaussian process (GP) regression. The CL1 controller ensures that control objectives are met while providing safety certificates. Furthermore, the controller incorporates any available data into GP models of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients. Keywords: Safe Learning, Planning, Adaptive Control, Gaussian Process Regression 

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