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Neural Operators for Boundary Stabilization of Stop-and-Go Traffic 6

Neural Operators for Boundary Stabilization of Stop-and-Go T...

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6th annual learning for dynamics and control conference

作者： Zhang, Yihuai Zhong, Ruiguo Yu, Huan Hong Kong Univ Sci & Technol Thrust Intelligent Transportat Guangzhou Peoples R China Hong Kong Univ Sci & Technol Dept Civil & Environm Engn Guangzhou Peoples R China

this paper introduces a novel approach to PDE boundary control design using neural operators to alleviate stop-and-go traffic instabilities. Our framework leverages neural operators to design control strategies for traffic flow systems. the traffic dynamics are described by the Aw-RascleZhang (ARZ) model, which consists of second-order coupled hyperbolic partial differential equations (PDEs). the backstepping method which involves constructing and solving a backstepping control kernel is widely used for boundary control of such PDE systems, but it requires intensive depth of expertise and can be time-consuming. To overcome these challenges, we present two distinct neural operator (NO) learning schemes aimed at stabilizing the traffic PDE system. the first scheme embeds NO-approximated gain kernels within a predefined backstepping controller, while the second one directly learns a boundary control law. the Lyapunov analysis is conducted to evaluate the stability of the NO-approximated gain kernels and control law. It is proved that the NO-based closed-loop system is practical stable under certain approximation accuracy conditions. To validate the efficacy of the proposed approach, simulations are conducted to compare the performance of the two neural operator controllers with a PDE backstepping controller and a Proportional Integral (PI) controller. While the NO-approximated methods exhibit larger errors compared to the backstepping controller, they consistently outperform the PI controller, demonstrating faster computation speeds across all scenarios. this result suggests that neural operators can significantly expedite and simplify the process of obtaining boundary controllers for freeway traffic stabilization systems.

关键词： Intelligent traffic systems(ITS) Partial differential equations(PDEs) Neural operator Backstepping control

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Soft Convex Quantization: Revisiting Vector Quantization with Convex Optimization 6

Soft Convex Quantization: Revisiting Vector Quantization wit...

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6th annual learning for dynamics and control conference

作者： Gautam, Tanmay Pryzant, Reid Yang, Ziyi Zhu, Chenguang Sojoudi, Somayeh Microsoft Azure AI Redmond WA 98052 USA Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA

Vector Quantization (VQ) is a well-known technique in deep learning for extracting informative discrete latent representations. VQ-embedded models have shown impressive results in a range of applications including image and speech generation. VQ operates as a parametric K-means algorithm that quantizes inputs using a single codebook vector in the forward pass. While powerful, this technique faces practical challenges including codebook collapse, non-differentiability and lossy compression. To mitigate the aforementioned issues, we propose Soft Convex Quantization (SCQ) as a direct substitute for VQ. SCQ works like a differentiable convex optimization (DCO) layer: in the forward pass, we solve for the optimal convex combination of codebook vectors to quantize the inputs. In the backward pass, we leverage differentiability through the optimality conditions of the forward solution. We then introduce a scalable relaxation of the SCQ optimization and demonstrate its efficacy on the CIFAR-10, GTSRB and LSUN datasets. We train powerful SCQ autoencoder models that significantly outperform matched VQ architectures, observing an order of magnitude better image reconstruction and codebook usage with comparable quantization runtime.

关键词： Differentiable convex optimization vector quantization representation learning

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Signatures Meet Dynamic Programming: Generalizing Bellman Equations for Trajectory Following 6

Signatures Meet Dynamic Programming: Generalizing Bellman Eq...

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6th annual learning for dynamics and control conference

作者： Ohnishi, Motoya Akinola, Iretiayo Xu, Jie Mandlekar, Ajay Ramos, Fabio Univ Washington Seattle WA 98195 USA NVIDIA Santa Clara CA USA Univ Sydney Sydney NSW Australia

Path signatures have been proposed as a powerful representation of paths that efficiently captures the path's analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor products. Signatures have recently been widely adopted in machine learning problems for time series analysis. In this work we establish connections between value functions typically used in optimal control and intriguing properties of path signatures. these connections motivate our novel control framework with signature transforms that efficiently generalizes the Bellman equation to the space of trajectories. We analyze the properties and advantages of the framework, termed signature control. In particular, we demonstrate that (i) it can naturally deal with varying/adaptive time steps;(ii) it propagates higher-level information more efficiently than value function updates;(iii) it is robust to dynamical system misspecification over long rollouts. As a specific case of our framework, we devise a model predictive control method for path tracking. this method generalizes integral control, being suitable for problems with unknown disturbances. the proposed algorithms are tested in simulation, with differentiable physics models including typical control and robotics tasks such as point-mass, curve following for an ant model, and a robotic manipulator.

关键词： Decision making Path signature Bellman equation Integral control Model predictive control Robotics

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Adaptive neural network based control approach for building energy control under changing environmental conditions 6

Adaptive neural network based control approach for building ...

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6th annual learning for dynamics and control conference

作者： Frison, Lilli Goelzhaeuser, Simon Fraunhofer Inst Solar Energy Syst ISE Heidenhofstr 2 D-79110 Freiburg Germany IMTEK Dept Microsyst Engn Syst Control & Optimizat Lab Georges Koehler Allee 102 D-79110 Freiburg Germany

Deep neural networks are adept at modeling complex relationships between input and output variables. When trained on diverse datasets, they can understand not just the specifics of individual objects but also the broader principles governing an entire object class. this research applies this principle to building heating control, a domain marked by significant heterogeneity and constant environmental changes, including renovations and changes in user behavior. Our approach involves training the network on a wide range of data instances, enhancing its adaptability to newly distributed data representing unseen scenarios. We find that Transformer-based LSTM architectures are particularly adept for this task as they are able to remember previous tasks' learning. We propose a simple yet effective control algorithm that separates system identification and forecasting from the optimization-based control step. this separation simplifies the control process while ensuring robust performance. In a wide range of simulation experiments, we demonstrate that our "universally trained" neural network control can adjust to changing conditions, thus reducing the need for more complex continual learning techniques. Our results suggest that training neural networks on varied datasets empowers the network with the ability to generalize and adapt beyond specific training instances, which demonstrates their effectiveness in dynamic and heterogeneous environments.

关键词： learning based control adaptive control building energy control neural network based control

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Parameter-Adaptive Approximate MPC: Tuning Neural-Network controllers without Retraining 6

Parameter-Adaptive Approximate MPC: Tuning Neural-Network Co...

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6th annual learning for dynamics and control conference

作者： Hose, Henrik Graefe, Alexander Trimpe, Sebastian Rhein Westfal TH Aachen Inst Data Sci Mech Engn DSME Aachen Germany

Model Predictive control (MPC) is a method to control nonlinear systems with guaranteed stability and constraint satisfaction but suffers from high computation times. Approximate MPC (AMPC) with neural networks (NNs) has emerged to address this limitation, enabling deployment on resource-constrained embedded systems. However, when tuning AMPCs for real-world systems, large datasets need to be regenerated and the NN needs to be retrained at every tuning step. this work introduces a novel, parameter-adaptive AMPC architecture capable of online tuning without recomputing large datasets and retraining. By incorporating local sensitivities of nonlinear programs, the proposed method not only mimics optimal MPC inputs but also adjusts to known changes in physical parameters of the model using linear predictions while still guaranteeing stability. We showcase the effectiveness of parameter-adaptive AMPC by controlling the swing-ups of two different real cartpole systems with a severely resource-constrained microcontroller (MCU). We use the same NN across both system instances that have different parameters. this work not only represents the first experimental demonstration of AMPC for fast-moving systems on low-cost MCUs to the best of our knowledge, but also showcases generalization across system instances and variations through our parameter-adaptation method. Taken together, these contributions represent a marked step toward the practical application of AMPC in real-world systems.

关键词： Nonlinear model predictive control approximate MPC sensitivity machine learning

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Generalized Constraint for Probabilistic Safe Reinforcement learning 6

Generalized Constraint for Probabilistic Safe Reinforcement ...

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6th annual learning for dynamics and control conference

作者： Chen, Weiqin Paternain, Santiago Rensselaer Polytech Inst Dept Elect Comp & Syst Engn Troy NY 12180 USA

In this paper, we consider the problem of learning policies for probabilistic safe reinforcement learning (PSRL). Specifically, a safe policy or controller is one that, with high probability, maintains the trajectory of the agent in a given safe set. While the explicit gradient of the probabilistic constraint for solving PSRL directly exists, the high variance in the estimate of the gradient hinders its performance in problems with long-horizons. An alternative that is frequently explored in the literature is to consider a cumulative safe reinforcement learning (CSRL) setting. In this setting, the estimates of the constraint's gradient have less variance but are biased (worse solutions than the PSRL) and they provide an approximate solution since they solve a relaxation of the PSRL formulation. In this work, we propose a safe reinforcement learning framework with a generalized constraint for solving the PSRL problems, which we term Generalized Safe Reinforcement learning (GSRL). Our theoretical contributions substantiate that the proposed GSRL can recover both the PSRL and CSRL settings. In addition, it can be naturally combined with any state-of-the-art safe RL algorithms like PPO-Lagrangian, TD3-Lagrangian, CPO, PCPO, etc. We evaluate the GSRL by a series of empirical experiments in the well-known safe RL benchmark Bullet-Safety-Gym, which exhibit a better return-safety trade-off than both the PSRL and CSRL formulations.

关键词： Constrained Policy Optimization Safe Reinforcement learning Probabilistic Constraints

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Probably approximately correct stability of allocations in uncertain coalitional games with private sampling 6

Probably approximately correct stability of allocations in u...

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6th annual learning for dynamics and control conference

作者： Pantazis, George Fele, Filiberto Fabiani, Filippo Grammatico, Sergio Margellos, Kostas Delft Univ Technol Delft Ctr Syst & Control Delft Netherlands Univ Seville Dept Syst Engn & Automat Seville Spain IMT Sch Adv Studies Lucca Lucca Italy Univ Oxford Dept Engn Sci Oxford England

We study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology to study the out-of-sample coalitional rationality of allocations in the set of stable allocations (i.e., the core). Our analysis builds on the framework of probably approximately correct learning. Initially, we state a priori and a posteriori guarantees for the entire core. Furthermore, we provide a distributed algorithm to compute a compression set that determines the generalization properties of the a posteriori statements. We then refine our probabilistic robustness bounds by specialising the analysis to a single payoff allocation, taking, also in this case, both a priori and a posteriori approaches. Finally, we consider a relaxed zeta-core to include nearby allocations and also address the case of empty core. For this case, probabilistic statements are given on the eventual stability of allocations in the zeta-core.

关键词： Uncertain coalitional games Statistical learning Data privacy

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Towards Model-Free LQR control over Rate-Limited Channels 6

Towards Model-Free LQR Control over Rate-Limited Channels

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6th annual learning for dynamics and control conference

作者： Mitra, Aritra Ye, Lintao Gupta, Vijay North Carolina State Univ Dept Elect & Comp Engn Raleigh NC 27695 USA Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan Peoples R China Purdue Univ Elmore Family Sch Elect & Comp Engn W Lafayette IN 47907 USA

Given the success of model-free methods for control design in many problem settings, it is natural to ask how things will change if realistic communication channels are utilized for the transmission of gradients or policies. While the resulting problem has analogies with the formulations studied under the rubric of networked control systems, the rich literature in that area has typically assumed that the model of the system is known. As a step towards bridging the fields of model-free control design and networked control systems, we ask: Is it possible to solve basic control problems - such as the linear quadratic regulator (LQR) problem - in a model-free manner over a rate-limited channel? Toward answering this question, we study a setting where a worker agent transmits quantized policy gradients (of the LQR cost) to a server over a noiseless channel with a finite bit-rate. We propose a new algorithm titled Adaptively Quantized Gradient Descent (AQGD), and prove that above a certain finite threshold bit-rate, AQGD guarantees exponentially fast convergence to the globally optimal policy, with no deterioration of the exponent relative to the unquantized setting. More generally, our approach reveals the benefits of adaptive quantization in preserving fast linear convergence rates, and, as such, may be of independent interest to the literature on compressed optimization.

关键词： Model-free learning Quantized optimization Policy gradient algorithms for LQR Rate-limited channels

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Gradient Shaping for Multi-Constraint Safe Reinforcement learning 6

Gradient Shaping for Multi-Constraint Safe Reinforcement Lea...

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6th annual learning for dynamics and control conference

作者： Yao, Yihang Liu, Zuxin Cen, Zhepeng Huang, Peide Zhang, Tingnan Yu, Wenhao Zhao, Ding Carnegie Mellon Univ Pittsburgh PA 15213 USA Google Deepmind London England

Online safe reinforcement learning (RL) involves training a policy that maximizes task efficiency while satisfying constraints via interacting with the environments. In this paper, our focus lies in addressing the complex challenges associated with solving multi-constraint (MC) safe RL problems. We approach the safe RL problem from the perspective of Multi-Objective Optimization (MOO) and propose a unified framework designed for MC safe RL algorithms. this framework highlights the manipulation of gradients derived from constraints. Leveraging insights from this framework and recognizing the significance of redundant and conflicting constraint conditions, we introduce the Gradient Shaping (GradS) method for general Lagrangian-based safe RL algorithms to improve the training efficiency in terms of both reward and constraint satisfaction. Our extensive experimentation demonstrates the effectiveness of our proposed method in encouraging exploration and learning a policy that improves both safety and reward performance across various challenging MC safe RL tasks as well as good scalability to the number of constraints. the full paper with the appendix is available on our website: https://***/view/mc-grads/home.

关键词： Safe Reinforcement learning Multi-Objective Optimization Multi-task learning

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Global Rewards in Multi-Agent Deep Reinforcement learning for Autonomous Mobility on Demand Systems 6

Global Rewards in Multi-Agent Deep Reinforcement Learning fo...

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6th annual learning for dynamics and control conference

作者： Hoppe, Heiko Enders, Tobias Cappart, Quentin Schiffer, Maximilian Tech Univ Munich Munich Germany Polytech Montreal Montreal PQ Canada

We study vehicle dispatching in autonomous mobility on demand (AMoD) systems, where a central operator assigns vehicles to customer requests or rejects these with the aim of maximizing its total profit. Recent approaches use multi-agent deep reinforcement learning (MADRL) to realize scalable yet performant algorithms, but train agents based on local rewards, which distorts the reward signal with respect to the system-wide profit, leading to lower performance. We therefore propose a novel global-rewards-based MADRL algorithm for vehicle dispatching in AMoD systems, which resolves so far existing goal conflicts between the trained agents and the operator by assigning rewards to agents leveraging a counterfactual baseline. Our algorithm shows statistically significant improvements across various settings on real-world data compared to state-of-the-art MADRL algorithms with local rewards. We further provide a structural analysis which shows that the utilization of global rewards can improve implicit vehicle balancing and demand forecasting abilities. An extended version of our paper, including an appendix, can be found at https://***/abs/2312.08884. Our code is available at https://github. com/tumBAIS/GR-MADRL-AMoD.

关键词： multi-agent learning credit assignment deep reinforcement learning autonomous mobility on demand

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