Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework

• URL: http://arxiv.org/abs/2409.08616v1
• Date: Fri, 13 Sep 2024 08:15:20 GMT
• Title: Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework
• Authors: Manish Prajapat, Amon Lahr, Johannes Köhler, Andreas Krause, Melanie N. Zeilinger,
• Abstract summary: We propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. We highlight the improved reachable set approximation compared to existing methods, as well as real-time feasible times.
• Score: 35.79393879150088
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller's safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GP-MPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as real-time feasible computation times, using two numerical examples.

Related papers

• Last-Iterate Global Convergence of Policy Gradients for Constrained Reinforcement Learning [62.81324245896717]
  We introduce an exploration-agnostic algorithm, called C-PG, which exhibits global last-ite convergence guarantees under (weak) gradient domination assumptions. We numerically validate our algorithms on constrained control problems, and compare them with state-of-the-art baselines.
  arXiv  Detail & Related papers  (2024-07-15T14:54:57Z)
• Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models [14.790031018404942]
  This paper presents an adaptive online learning framework for systems with uncertain parameters. We first integrate a forgetting factor to refine a variational sparse GP algorithm. In the second phase, we propose a safety filter based on high-order control barrier functions.
  arXiv  Detail & Related papers  (2024-02-29T08:25:32Z)
• Probabilistic Reach-Avoid for Bayesian Neural Networks [71.67052234622781]
  We show that an optimal synthesis algorithm can provide more than a four-fold increase in the number of certifiable states. The algorithm is able to provide more than a three-fold increase in the average guaranteed reach-avoid probability.
  arXiv  Detail & Related papers  (2023-10-03T10:52:21Z)
• Model Predictive Control with Gaussian-Process-Supported Dynamical Constraints for Autonomous Vehicles [82.65261980827594]
  We propose a model predictive control approach for autonomous vehicles that exploits learned Gaussian processes for predicting human driving behavior. A multi-mode predictive control approach considers the possible intentions of the human drivers.
  arXiv  Detail & Related papers  (2023-03-08T17:14:57Z)
• GPU-Accelerated Policy Optimization via Batch Automatic Differentiation of Gaussian Processes for Real-World Control [8.720903734757627]
  We develop a policy optimization method by leveraging fast predictive sampling methods to process batches of trajectories in every forward pass. We demonstrate the effectiveness of our approach in training policies on a set of reference-tracking control experiments with a heavy-duty machine.
  arXiv  Detail & Related papers  (2022-02-28T09:31:15Z)
• Robust and Adaptive Temporal-Difference Learning Using An Ensemble of Gaussian Processes [70.80716221080118]
  The paper takes a generative perspective on policy evaluation via temporal-difference (TD) learning. The OS-GPTD approach is developed to estimate the value function for a given policy by observing a sequence of state-reward pairs. To alleviate the limited expressiveness associated with a single fixed kernel, a weighted ensemble (E) of GP priors is employed to yield an alternative scheme.
  arXiv  Detail & Related papers  (2021-12-01T23:15:09Z)
• Gaussian Processes to speed up MCMC with automatic exploratory-exploitation effect [1.0742675209112622]
  We present a two-stage Metropolis-Hastings algorithm for sampling probabilistic models. The key feature of the approach is the ability to learn the target distribution from scratch while sampling.
  arXiv  Detail & Related papers  (2021-09-28T17:43:25Z)
• Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
  Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
  arXiv  Detail & Related papers  (2021-05-17T08:36:18Z)
• Adversarial Robustness Guarantees for Gaussian Processes [22.403365399119107]
  Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. We present a framework to analyse adversarial robustness of GPs, defined as invariance of the model's decision to bounded perturbations. We develop a branch-and-bound scheme to refine the bounds and show, for any $epsilon > 0$, that our algorithm is guaranteed to converge to values $epsilon$-close to the actual values in finitely many iterations.
  arXiv  Detail & Related papers  (2021-04-07T15:14:56Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.