An official website of the United States government
We study the task of learning state representations from potentially high-dimensional observations, with the goal of controlling an unknown partially observable system. We pursue a direct latent model learning approach, where a dynamic model in some latent state space is learned by predicting quantities directly related to planning (e.g., costs) without reconstructing the observations. In particular, we focus on an intuitive cost-driven state representation learning method for solving Linear Quadratic Gaussian (LQG) control, one of the most fundamental partially observable control problems. As our main results, we establish finite-sample guarantees of finding a near-optimal state representation function and a near-optimal controller using the directly learned latent model. To the best of our knowledge, despite various empirical successes, prior to this work it was unclear if such a cost-driven latent model learner enjoys finite-sample guarantees. Our work underscores the value of predicting multi-step costs, an idea that is key to our theory, and notably also an idea that is known to be empirically valuable for learning state representations.
more »
« less
Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control
We present a straightforward and efficient way to control unstable robotic systems using an estimated dynamics model. Specifically, we show how to exploit the differentiability of Gaussian Processes to create a state-dependent linearized approximation of the true continuous dynamics that can be integrated with model predictive control. Our approach is compatible with most Gaussian process approaches for system identification, and can learn an accurate model using modest amounts of training data. We validate our approach by learning the dynamics of an unstable system such as a segway with a 7-D state space and 2-D input space (using only one minute of data), and we show that the resulting controller is robust to unmodelled dynamics and disturbances, while state-of-the-art control methods based on nominal models can fail under small perturbations. Code is open sourced at https://github.com/learning-and-control/core.
more »
« less
- PAR ID:
- 10329341
- Date Published:
- Journal Name:
- Proceedings of the IEEERSJ International Conference on Intelligent Robots and Systems
- ISSN:
- 2153-0858
- Page Range / eLocation ID:
- 3896-3903
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This paper investigates data-efficient methods for learning robust control policies. Reinforcement learning has emerged as an effective approach to learn control policies by interacting directly with the plant, but it requires a significant number of example trajectories to converge to the optimal policy. Combining model-free reinforcement learning with model-based control methods achieves better data-efficiency via simultaneous system identification and controller synthesis. We study a novel approach that exploits the existence of approximate physics models to accelerate the learning of control policies. The proposed approach consists of iterating through three key steps: evaluating a selected policy on the real-world plant and recording trajectories, building a Gaussian process model to predict the reality-gap of a parametric physics model in the neighborhood of the selected policy, and synthesizing a new policy using reinforcement learning on the refined physics model that most likely approximates the real plant. The approach converges to an optimal policy as well as an approximate physics model. The real world experiments are limited to evaluating only promising candidate policies, and the use of Gaussian processes minimizes the number of required real world trajectories. We demonstrate the effectiveness of our techniques on a set of simulation case-studies using OpenAI gym environments.more » « less
-
Summary Scenario‐based model predictive control (MPC) methods can mitigate the conservativeness inherent to open‐loop robust MPC. Yet, the scenarios are often generated offline based on worst‐case uncertainty descriptions obtaineda priori, which can in turn limit the improvements in the robust control performance. To this end, this paper presents a learning‐based, adaptive‐scenario‐tree model predictive control approach for uncertain nonlinear systems with time‐varying and/or hard‐to‐model dynamics. Bayesian neural networks (BNNs) are used to learn a state‐ and input‐dependent description of model uncertainty, namely the mismatch between a nominal (physics‐based or data‐driven) model of a system and its actual dynamics. We first present a new approach for training robust BNNs (RBNNs) using probabilistic Lipschitz bounds to provide a less conservative uncertainty quantification. Then, we present an approach to evaluate the credible intervals of RBNN predictions and determine the number of samples required for estimating the credible intervals given a credible level. The performance of RBNNs is evaluated with respect to that of standard BNNs and Gaussian process (GP) as a basis of comparison. The RBNN description of plant‐model mismatch with verified accurate credible intervals is employed to generate adaptive scenarios online for scenario‐based MPC (sMPC). The proposed sMPC approach with adaptive scenario tree can improve the robust control performance with respect to sMPC with a fixed, worst‐case scenario tree and with respect to an adaptive‐scenario‐based MPC (asMPC) using GP regression on a cold atmospheric plasma system. Furthermore, closed‐loop simulation results illustrate that robust model uncertainty learning via RBNNs can enhance the probability of constraint satisfaction of asMPC.more » « less
-
null (Ed.)Safety is a critical component in today's autonomous and robotic systems. Many modern controllers endowed with notions of guaranteed safety properties rely on accurate mathematical models of these nonlinear dynamical systems. However, model uncertainty is always a persistent challenge weakening theoretical guarantees and compromising safety. For safety-critical systems, this is an even bigger challenge. Typically, safety is ensured by constraining the system states within a safe constraint set defined a priori by relying on the model of the system. A popular approach is to use Control Barrier Functions (CBFs) that encode safety using a smooth function. However, CBFs fail in the presence of model uncertainties. Moreover, an inaccurate model can either lead to incorrect notions of safety or worse, incur system critical failures. Addressing these drawbacks, we present a novel safety formulation that leverages properties of CBFs and positive definite kernels to design Gaussian CBFs. The underlying kernels are updated online by learning the unmodeled dynamics using Gaussian Processes (GPs). While CBFs guarantee forward invariance, the hyperparameters estimated using GPs update the kernel online and thereby adjust the relative notion of safety. We demonstrate our proposed technique on a safety-critical quadrotor on SO(3) in the presence of model uncertainty in simulation. With the kernel update performed online, safety is preserved for the system.more » « less
-
This work introduces a data-driven control approach for stabilizing high-dimensional dynamical systems from scarce data. The proposed context-aware controller inference approach is based on the observation that controllers need to act locally only on the unstable dynamics to stabilize systems. This means it is sufficient to learn the unstable dynamics alone, which are typically confined to much lower dimensional spaces than the high-dimensional state spaces of all system dynamics and thus few data samples are sufficient to identify them. Numerical experiments demonstrate that context-aware controller inference learns stabilizing controllers from orders of magnitude fewer data samples than traditional data-driven control techniques and variants of reinforcement learning. The experiments further show that the low data requirements of context-aware controller inference are especially beneficial in data-scarce engineering problems with complex physics, for which learning complete system dynamics is often intractable in terms of data and training costs.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IROS51168.2021.9636786
