Adaptive Robust Model Predictive Control via Uncertainty Cancellation

• URL: http://arxiv.org/abs/2212.01371v1
• Date: Fri, 2 Dec 2022 18:54:23 GMT
• Title: Adaptive Robust Model Predictive Control via Uncertainty Cancellation
• Authors: Rohan Sinha, James Harrison, Spencer M. Richards, and Marco Pavone
• Abstract summary: We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws.
• Score: 25.736296938185074
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems commonly model the nonlinear effects of an unknown environment on a nominal system. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws pioneered in classical adaptive control to achieve significant performance improvements in the presence of uncertainties of large magnitude, a setting in which existing learning-based predictive control algorithms often struggle to guarantee safety. In contrast to previous work in robust adaptive MPC, our approach allows us to take advantage of structure (i.e., the numerical predictions) in the a priori unknown dynamics learned online through function approximation. Our approach also extends typical nonlinear adaptive control methods to systems with state and input constraints even when we cannot directly cancel the additive uncertain function from the dynamics. We apply contemporary statistical estimation techniques to certify the system's safety through persistent constraint satisfaction with high probability. Moreover, we propose using Bayesian meta-learning algorithms that learn calibrated model priors to help satisfy the assumptions of the control design in challenging settings. Finally, we show in simulation that our method can accommodate more significant unknown dynamics terms than existing methods and that the use of Bayesian meta-learning allows us to adapt to the test environments more rapidly.

Related papers

• Learning to Boost the Performance of Stable Nonlinear Systems [0.0]
  We tackle the performance-boosting problem with closed-loop stability guarantees. Our methods enable learning over arbitrarily deep neural network classes of performance-boosting controllers for stable nonlinear systems.
  arXiv  Detail & Related papers  (2024-05-01T21:11:29Z)
• Online Nonstochastic Model-Free Reinforcement Learning [35.377261344335736]
  We investigate robust model robustness guarantees for environments that may be dynamic or adversarial. We provide efficient and efficient algorithms for optimizing these policies. These are the best-known developments in having no dependence on the state-space dimension in having no dependence on the state-space.
  arXiv  Detail & Related papers  (2023-05-27T19:02:55Z)
• Learning-enhanced Nonlinear Model Predictive Control using Knowledge-based Neural Ordinary Differential Equations and Deep Ensembles [5.650647159993238]
  In this work, we leverage deep learning tools, namely knowledge-based neural ordinary differential equations (KNODE) and deep ensembles, to improve the prediction accuracy of a model predictive control (MPC) In particular, we learn an ensemble of KNODE models, which we refer to as the KNODE ensemble, to obtain an accurate prediction of the true system dynamics. We show that the KNODE ensemble provides more accurate predictions and illustrate the efficacy and closed-loop performance of the proposed nonlinear MPC framework.
  arXiv  Detail & Related papers  (2022-11-24T23:51:18Z)
• Sparsity in Partially Controllable Linear Systems [56.142264865866636]
  We study partially controllable linear dynamical systems specified by an underlying sparsity pattern. Our results characterize those state variables which are irrelevant for optimal control.
  arXiv  Detail & Related papers  (2021-10-12T16:41:47Z)
• 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)
• Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty [28.10549712956161]
  We propose a learning-based robust predictive control algorithm that can handle large uncertainty in the dynamics for a class of discrete-time systems. Motivated by an inability of existing learning-based predictive control algorithms to achieve safety guarantees in the presence of uncertainties of large magnitude, we achieve significant performance improvements.
  arXiv  Detail & Related papers  (2021-04-16T17:47:02Z)
• Closing the Closed-Loop Distribution Shift in Safe Imitation Learning [80.05727171757454]
  We treat safe optimization-based control strategies as experts in an imitation learning problem. We train a learned policy that can be cheaply evaluated at run-time and that provably satisfies the same safety guarantees as the expert.
  arXiv  Detail & Related papers  (2021-02-18T05:11:41Z)
• Improper Learning with Gradient-based Policy Optimization [62.50997487685586]
  We consider an improper reinforcement learning setting where the learner is given M base controllers for an unknown Markov Decision Process. We propose a gradient-based approach that operates over a class of improper mixtures of the controllers.
  arXiv  Detail & Related papers  (2021-02-16T14:53:55Z)
• Anticipating the Long-Term Effect of Online Learning in Control [75.6527644813815]
  AntLer is a design algorithm for learning-based control laws that anticipates learning. We show that AntLer approximates an optimal solution arbitrarily accurately with probability one.
  arXiv  Detail & Related papers  (2020-07-24T07:00:14Z)
• Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees [1.1086440815804224]
  We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems. We employ automatic differentiation to obtain direct policy gradients by backpropagating the model predictive control (MPC) loss function and constraints penalties through a differentiable closed-loop system dynamics model.
  arXiv  Detail & Related papers  (2020-04-23T14:24:44Z)
• Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting [91.43582419264763]
  We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model.
  arXiv  Detail & Related papers  (2020-03-12T19:56:38Z)

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.