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1. Sample Complexity Bound for Evaluating the Robust Observer’s Performance under Coprime Factors Uncertainty

   Sabau, Serban; Zhang, Yifei; Ukil, Sourav Kumar (June 2023, Proceedings of Machine Learning Research)

   Lawrence, N (Ed.)

   This paper addresses the end-to-end sample complexity bound for learning in closed loop the state estimator-based robust H2 controller for an unknown (possibly unstable) Linear Time Invariant (LTI) system, when given a fixed state-feedback gain. We build on the results from Ding et al. (1994) to bridge the gap between the parameterization of all state-estimators and the celebrated Youla parameterization. Refitting the expression of the relevant closed loop allows for the optimal linear observer problem given a fixed state feedback gain to be recast as a convex problem in the Youla parameter. The robust synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant, such that a min-max optimization problem is formulated for the robust H2 controller via an observer approach. The closed-loop identification scheme follows Zhang et al. (2021), where the nominal model of the true plant is identified by constructing a Hankel-like matrix from a single time-series of noisy, finite length input-output data by using the ordinary least squares algorithm from Sarkar et al. (2020). Finally, a H∞ bound on the estimated model error is provided, as the robust synthesis procedure requires bounded additive uncertainty on the coprime factors of the model. Reference Zhang et al. (2022b) is the extended version of this paper. 

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2. Sample Complexity of the Robust LQG Regulator with Coprime Factors Uncertainty

   Yifei Zhang, Sourav Ukil (January 2022, Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:943-953, 2022.)

   This paper addresses the end-to-end sample complexity bound for learning the H2 optimal controller (the Linear Quadratic Gaussian (LQG) problem) with unknown dynamics, for potentially unstable Linear Time Invariant (LTI) systems. The robust LQG synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant. The closed-loopi dentification of the nominal model of the true plant is performed by constructing a Hankel-like matrix from a single time-series of noisy finite length input-output data, using the ordinary least squares algorithm from Sarkar and Rakhlin (2019). Next, an H∞ bound on the estimated model error is provided and the robust controller is designed via convex optimization, much in the spirit of Mania et al. (2019) and Zheng et al. (2020b), while allowing for bounded additive uncertainty on the coprime factors of the model. Our conclusions are consistent with previous results on learning the LQG and LQR controllers. 

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3. Robust Online Convex Optimization for Disturbance Rejection

   https://doi.org/10.1109/CDC56724.2024.10886354  

   Lai, Joyce; Seiler, Peter (December 2024, IEEE)

   Online convex optimization (OCO) is a powerful tool for learning sequential data, making it ideal for high precision control applications where the disturbances are arbitrary and unknown in advance. However, the ability of OCO-based controllers to accurately learn the disturbance while maintaining closed-loop stability relies on having an accurate model of the plant. This paper studies the performance of OCO-based controllers for linear time-invariant (LTI) systems subject to disturbance and model uncertainty. The model uncertainty can cause the closed-loop to become unstable. We provide a sufficient condition for robust stability based on the small gain theorem. This condition is easily incorporated as an on-line constraint in the OCO controller. Finally, we verify via numerical simulations that imposing the robust stability condition on the OCO controller ensures closed-loop stability. 

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4. NeuroVectorizer: end-to-end vectorization with deep reinforcement learning

   https://doi.org/10.1145/3368826.3377928  

   Haj-Ali, Ameer; Ahmed, Nesreen K.; Willke, Ted; Shao, Yakun Sophia; Asanovic, Krste; Stoica, Ion (February 2020, CGO 2020: Proceedings of the 18th ACM/IEEE International Symposium on Code Generation and Optimization)

   null (Ed.)

   One of the key challenges arising when compilers vectorize loops for today’s SIMD-compatible architectures is to decide if vectorization or interleaving is beneficial. Then, the compiler has to determine the number of instructions to pack together and the interleaving level (stride). Compilers are designed today to use fixed-cost models that are based on heuristics to make vectorization decisions on loops. However, these models are unable to capture the data dependency, the computation graph, or the organization of instructions. Alternatively, software engineers often hand-write the vectorization factors of every loop. This, however, places a huge burden on them, since it requires prior experience and significantly increases the development time. In this work, we explore a novel approach for handling loop vectorization and propose an end-to-end solution using deep reinforcement learning (RL). We conjecture that deep RL can capture different instructions, dependencies, and data structures to enable learning a sophisticated model that can better predict the actual performance cost and determine the optimal vectorization factors. We develop an end-to-end framework, from code to vectorization, that integrates deep RL in the LLVM compiler. Our proposed framework takes benchmark codes as input and extracts the loop codes. These loop codes are then fed to a loop embedding generator that learns an embedding for these loops. Finally, the learned embeddings are used as input to a Deep RL agent, which dynamically determines the vectorization factors for all the loops. We further extend our framework to support random search, decision trees, supervised neural networks, and nearest-neighbor search. We evaluate our approaches against the currently used LLVM vectorizer and loop polyhedral optimization techniques. Our experiments show 1.29×−4.73× performance speedup compared to baseline and only 3% worse than the brute-force search on a wide range of benchmarks. 

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5. Feedback Oscillatory Control of Roll Instability During Stall Using the LIBRA Mechanism

   https://doi.org/10.2514/6.2023-1449  

   Abdelgalil, Mahmoud A.; Taha, Haithem E. (January 2023, AIAA SciTech)

   The goal of this paper is to design a stabilizing feedback controller of roll instability near stall. This problem becomes immensely challenging since the aileron sensitivity is vanishes and even reversed sign at stall. This challenge is overcome by employing the recently developed Lie Bracket Roll Augmentation (LIBRA) mechanism. In this mechanism,the nonlinear dynamics of the airplane near stall is exploited to achieve a rolling motion that is independent of the aileron sensitivity. Rather, it depends on the variation of the aileron sensitivity with the angle of attack which is non-zero at stall. The open loop characteristics of the LIBRA mechanism have been studied previously. The contribution of the current manuscript lies in using the LIBRA mechanism in a feedback fashion to stabilize the roll unstable dynamics near stall using a stabilization scheme based on motion planning techniques for highly oscillatory inputs. 

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