Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States

• URL: http://arxiv.org/abs/2303.17963v4
• Date: Tue, 6 Aug 2024 06:28:57 GMT
• Title: Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States
• Authors: Robert Lefringhausen, Supitsana Srithasan, Armin Lederer, Sandra Hirche,
• Abstract summary: This paper proposes a novel method for the computation of an optimal input trajectory for unknown nonlinear systems with latent states. The effectiveness of the proposed method is demonstrated in a numerical simulation.
• Score: 4.4820711784498
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: As control engineering methods are applied to increasingly complex systems, data-driven approaches for system identification appear as a promising alternative to physics-based modeling. While the Bayesian approaches prevalent for safety-critical applications usually rely on the availability of state measurements, the states of a complex system are often not directly measurable. It may then be necessary to jointly estimate the dynamics and the latent state, making the quantification of uncertainties and the design of controllers with formal performance guarantees considerably more challenging. This paper proposes a novel method for the computation of an optimal input trajectory for unknown nonlinear systems with latent states based on a combination of particle Markov chain Monte Carlo methods and scenario theory. Probabilistic performance guarantees are derived for the resulting input trajectory, and an approach to validate the performance of arbitrary control laws is presented. The effectiveness of the proposed method is demonstrated in a numerical simulation.

Related papers

• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings [0.24578723416255752]
  We develop scalable formal verification algorithms without shifting the problem to unrealistic assumptions. In a pursuit of developing scalable formal verification algorithms without shifting the problem to unrealistic assumptions, we employ the concept of barrier certificates. We show how to solve the resulting program efficiently using sum-of-squares optimization and a Gaussian process envelope.
  arXiv  Detail & Related papers  (2024-03-15T17:32:02Z)
• In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution States [84.24300005271185]
  We propose a control filter that wraps any reference policy and effectively encourages the system to stay in-distribution with respect to offline-collected safe demonstrations. Our method is effective for two different visuomotor control tasks in simulation environments, including both top-down and egocentric view settings.
  arXiv  Detail & Related papers  (2023-01-27T22:28:19Z)
• Adaptive Robust Model Predictive Control via Uncertainty Cancellation [25.736296938185074]
  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.
  arXiv  Detail & Related papers  (2022-12-02T18:54:23Z)
• 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)
• The Impact of Data on the Stability of Learning-Based Control- Extended Version [63.97366815968177]
  We propose a Lyapunov-based measure for quantifying the impact of data on the certifiable control performance. By modeling unknown system dynamics through Gaussian processes, we can determine the interrelation between model uncertainty and satisfaction of stability conditions.
  arXiv  Detail & Related papers  (2020-11-20T19:10:01Z)
• Efficient falsification approach for autonomous vehicle validation using a parameter optimisation technique based on reinforcement learning [6.198523595657983]
  The widescale deployment of Autonomous Vehicles (AV) appears to be imminent despite many safety challenges that are yet to be resolved. The uncertainties in the behaviour of the traffic participants and the dynamic world cause reactions in advanced autonomous systems. This paper presents an efficient falsification method to evaluate the System Under Test.
  arXiv  Detail & Related papers  (2020-11-16T02:56:13Z)
• 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.