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Control Theory


Lessons from AlphaZero for Optimal, Model Predictive, and Adaptive Control

arXiv.org Artificial Intelligence

In this paper we aim to provide analysis and insights (often based on visualization), which explain the beneficial effects of on-line decision making on top of off-line training. In particular, through a unifying abstract mathematical framework, we show that the principal AlphaZero/TD-Gammon ideas of approximation in value space and rollout apply very broadly to deterministic and stochastic optimal control problems, involving both discrete and continuous search spaces. Moreover, these ideas can be effectively integrated with other important methodologies such as model predictive control, adaptive control, decentralized control, discrete and Bayesian optimization, neural network-based value and policy approximations, and heuristic algorithms for discrete optimization.


Stochastic Deep Model Reference Adaptive Control

arXiv.org Artificial Intelligence

In this paper, we present a Stochastic Deep Neural Network-based Model Reference Adaptive Control. Building on our work "Deep Model Reference Adaptive Control", we extend the controller capability by using Bayesian deep neural networks (DNN) to represent uncertainties and model non-linearities. Stochastic Deep Model Reference Adaptive Control uses a Lyapunov-based method to adapt the output-layer weights of the DNN model in real-time, while a data-driven supervised learning algorithm is used to update the inner-layers parameters. This asynchronous network update ensures boundedness and guaranteed tracking performance with a learning-based real-time feedback controller. A Bayesian approach to DNN learning helped avoid over-fitting the data and provide confidence intervals over the predictions. The controller's stochastic nature also ensured "Induced Persistency of excitation," leading to convergence of the overall system signal.


Meta-Adaptive Nonlinear Control: Theory and Algorithms

arXiv.org Artificial Intelligence

We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown $\textit{environment-dependent}$ nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task adaptive nonlinear control. OMAC can also be integrated with deep representation learning. Experiments show that OMAC significantly outperforms conventional adaptive control approaches which do not learn the shared representation.


Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls

arXiv.org Machine Learning

We study finite-time horizon continuous-time linear-convex reinforcement learning problems in an episodic setting. In this problem, the unknown linear jump-diffusion process is controlled subject to nonsmooth convex costs. We show that the associated linear-convex control problems admit Lipchitz continuous optimal feedback controls and further prove the Lipschitz stability of the feedback controls, i.e., the performance gap between applying feedback controls for an incorrect model and for the true model depends Lipschitz-continuously on the magnitude of perturbations in the model coefficients; the proof relies on a stability analysis of the associated forward-backward stochastic differential equation. We then propose a novel least-squares algorithm which achieves a regret of the order $O(\sqrt{N\ln N})$ on linear-convex learning problems with jumps, where $N$ is the number of learning episodes; the analysis leverages the Lipschitz stability of feedback controls and concentration properties of sub-Weibull random variables.


Towards a Dimension-Free Understanding of Adaptive Linear Control

arXiv.org Machine Learning

We study the problem of adaptive control of the linear quadratic regulator for systems in very high, or even infinite dimension. We demonstrate that while sublinear regret requires finite dimensional inputs, the ambient state dimension of the system need not be bounded in order to perform online control. We provide the first regret bounds for LQR which hold for infinite dimensional systems, replacing dependence on ambient dimension with more natural notions of problem complexity. Our guarantees arise from a novel perturbation bound for certainty equivalence which scales with the prediction error in estimating the system parameters, without requiring consistent parameter recovery in more stringent measures like the operator norm. When specialized to finite dimensional settings, our bounds recover near optimal dimension and time horizon dependence.


A Regret Minimization Approach to Iterative Learning Control

arXiv.org Machine Learning

We consider the setting of iterative learning control, or model-based policy learning in the presence of uncertain, time-varying dynamics. In this setting, we propose a new performance metric, planning regret, which replaces the standard stochastic uncertainty assumptions with worst case regret. Based on recent advances in non-stochastic control, we design a new iterative algorithm for minimizing planning regret that is more robust to model mismatch and uncertainty. We provide theoretical and empirical evidence that the proposed algorithm outperforms existing methods on several benchmarks.


Learning-based vs Model-free Adaptive Control of a MAV under Wind Gust

arXiv.org Artificial Intelligence

Navigation problems under unknown varying conditions are among the most important and well-studied problems in the control field. Classic model-based adaptive control methods can be applied only when a convenient model of the plant or environment is provided. Recent model-free adaptive control methods aim at removing this dependency by learning the physical characteristics of the plant and/or process directly from sensor feedback. Although there have been prior attempts at improving these techniques, it remains an open question as to whether it is possible to cope with real-world uncertainties in a control system that is fully based on either paradigm. We propose a conceptually simple learning-based approach composed of a full state feedback controller, tuned robustly by a deep reinforcement learning framework based on the Soft Actor-Critic algorithm. We compare it, in realistic simulations, to a model-free controller that uses the same deep reinforcement learning framework for the control of a micro aerial vehicle under wind gust. The results indicate the great potential of learning-based adaptive control methods in modern dynamical systems.


Safe and Efficient Model-free Adaptive Control via Bayesian Optimization

arXiv.org Artificial Intelligence

Adaptive control approaches yield high-performance controllers when a precise system model or suitable parametrizations of the controller are available. Existing data-driven approaches for adaptive control mostly augment standard model-based methods with additional information about uncertainties in the dynamics or about disturbances. In this work, we propose a purely data-driven, model-free approach for adaptive control. Tuning low-level controllers based solely on system data raises concerns on the underlying algorithm safety and computational performance. Thus, our approach builds on GoOSE, an algorithm for safe and sample-efficient Bayesian optimization. We introduce several computational and algorithmic modifications in GoOSE that enable its practical use on a rotational motion system. We numerically demonstrate for several types of disturbances that our approach is sample efficient, outperforms constrained Bayesian optimization in terms of safety, and achieves the performance optima computed by grid evaluation. We further demonstrate the proposed adaptive control approach experimentally on a rotational motion system.


Distributed Adaptive Control: An ideal Cognitive Architecture candidate for managing a robotic recycling plant

arXiv.org Artificial Intelligence

In the past decade, society has experienced notable growth in a variety of technological areas. However, the Fourth Industrial Revolution has not been embraced yet. Industry 4.0 imposes several challenges which include the necessity of new architectural models to tackle the uncertainty that open environments represent to cyber-physical systems (CPS). Waste Electrical and Electronic Equipment (WEEE) recycling plants stand for one of such open environments. Here, CPSs must work harmoniously in a changing environment, interacting with similar and not so similar CPSs, and adaptively collaborating with human workers. In this paper, we support the Distributed Adaptive Control (DAC) theory as a suitable Cognitive Architecture for managing a recycling plant. Specifically, a recursive implementation of DAC (between both singleagent and large-scale levels) is proposed to meet the expected demands of the European Project HR-Recycler. Additionally, with the aim of having a realistic benchmark for future implementations of the recursive DAC, a micro-recycling plant prototype is presented. Keywords: Cognitive Architecture, Distributed Adaptive Control, Recycling Plant, Navigation, Motor Control, Human-Robot Interaction.


Machine learning approach could improve radar in congested environments - Military Embedded Systems

#artificialintelligence

Research being conducted by the U.S. Army Combat Capabilities Development Command (DEVCOM) is focused on a new machine learning approach that could improve radar performance in congested environments. Researchers from DEVCOM, Army Research Laboratory, and Virginia Tech have developed an automatic way for radars to operate in congested and limited-spectrum environments created by commercial 4G LTE and future 5G communications systems. The researchers claim they examined how future Department of Defense radar systems will share the spectrum with commercial communications systems. The team used machine learning to learn the behavior of ever-changing interference in the spectrum and find clean spectrum to maximize the radar performance. Once clean spectrum is identified, waveforms can be modified to best fit into the spectrum.