28,919 research outputs found
Safe Learning of Quadrotor Dynamics Using Barrier Certificates
To effectively control complex dynamical systems, accurate nonlinear models
are typically needed. However, these models are not always known. In this
paper, we present a data-driven approach based on Gaussian processes that
learns models of quadrotors operating in partially unknown environments. What
makes this challenging is that if the learning process is not carefully
controlled, the system will go unstable, i.e., the quadcopter will crash. To
this end, barrier certificates are employed for safe learning. The barrier
certificates establish a non-conservative forward invariant safe region, in
which high probability safety guarantees are provided based on the statistics
of the Gaussian Process. A learning controller is designed to efficiently
explore those uncertain states and expand the barrier certified safe region
based on an adaptive sampling scheme. In addition, a recursive Gaussian Process
prediction method is developed to learn the complex quadrotor dynamics in
real-time. Simulation results are provided to demonstrate the effectiveness of
the proposed approach.Comment: Submitted to ICRA 2018, 8 page
On the Design of LQR Kernels for Efficient Controller Learning
Finding optimal feedback controllers for nonlinear dynamic systems from data
is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful
framework for direct controller tuning from experimental trials. For selecting
the next query point and finding the global optimum, BO relies on a
probabilistic description of the latent objective function, typically a
Gaussian process (GP). As is shown herein, GPs with a common kernel choice can,
however, lead to poor learning outcomes on standard quadratic control problems.
For a first-order system, we construct two kernels that specifically leverage
the structure of the well-known Linear Quadratic Regulator (LQR), yet retain
the flexibility of Bayesian nonparametric learning. Simulations of uncertain
linear and nonlinear systems demonstrate that the LQR kernels yield superior
learning performance.Comment: 8 pages, 5 figures, to appear in 56th IEEE Conference on Decision and
Control (CDC 2017
Kernel-Based Just-In-Time Learning for Passing Expectation Propagation Messages
We propose an efficient nonparametric strategy for learning a message
operator in expectation propagation (EP), which takes as input the set of
incoming messages to a factor node, and produces an outgoing message as output.
This learned operator replaces the multivariate integral required in classical
EP, which may not have an analytic expression. We use kernel-based regression,
which is trained on a set of probability distributions representing the
incoming messages, and the associated outgoing messages. The kernel approach
has two main advantages: first, it is fast, as it is implemented using a novel
two-layer random feature representation of the input message distributions;
second, it has principled uncertainty estimates, and can be cheaply updated
online, meaning it can request and incorporate new training data when it
encounters inputs on which it is uncertain. In experiments, our approach is
able to solve learning problems where a single message operator is required for
multiple, substantially different data sets (logistic regression for a variety
of classification problems), where it is essential to accurately assess
uncertainty and to efficiently and robustly update the message operator.Comment: accepted to UAI 2015. Correct typos. Add more content to the
appendix. Main results unchange
Dimension reduction for Gaussian process emulation: an application to the influence of bathymetry on tsunami heights
High accuracy complex computer models, or simulators, require large resources
in time and memory to produce realistic results. Statistical emulators are
computationally cheap approximations of such simulators. They can be built to
replace simulators for various purposes, such as the propagation of
uncertainties from inputs to outputs or the calibration of some internal
parameters against observations. However, when the input space is of high
dimension, the construction of an emulator can become prohibitively expensive.
In this paper, we introduce a joint framework merging emulation with dimension
reduction in order to overcome this hurdle. The gradient-based kernel dimension
reduction technique is chosen due to its ability to drastically decrease
dimensionality with little loss in information. The Gaussian process emulation
technique is combined with this dimension reduction approach. Our proposed
approach provides an answer to the dimension reduction issue in emulation for a
wide range of simulation problems that cannot be tackled using existing
methods. The efficiency and accuracy of the proposed framework is demonstrated
theoretically, and compared with other methods on an elliptic partial
differential equation (PDE) problem. We finally present a realistic application
to tsunami modeling. The uncertainties in the bathymetry (seafloor elevation)
are modeled as high-dimensional realizations of a spatial process using a
geostatistical approach. Our dimension-reduced emulation enables us to compute
the impact of these uncertainties on resulting possible tsunami wave heights
near-shore and on-shore. We observe a significant increase in the spread of
uncertainties in the tsunami heights due to the contribution of the bathymetry
uncertainties. These results highlight the need to include the effect of
uncertainties in the bathymetry in tsunami early warnings and risk assessments.Comment: 26 pages, 8 figures, 2 table
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