16,773 research outputs found
Bayesian frequentist bounds for machine learning and system identification
No full textEstimating a function from noisy measurements is a crucial problem in statistics and engineering, with an impact on machine learning predictions and identification of dynamical systems. In view of robust control design and safety-critical applications such as autonomous driving and smart healthcare, estimates are required to be complemented with uncertainty bounds quantifying their reliability. Most of the available results are derived by constraining the estimates to belong to a deterministic function space; however, the returned bounds often result overly conservative and, hence, of limited usefulness. An alternative is to use a Bayesian framework. The regions thereby obtained however require complete specification of prior distributions whose choice may significantly affect the probability of inclusion. This study presents a framework for the effective computation of regions that include the unknown function with exact probability. In this setting, the users not only have the freedom to modulate the amount of prior knowledge that informs the constructed regions but can, on a different plane, finely modulate their commitment to such information. The result is a versatile certified estimation framework capable of addressing a multitude of problems, ranging from parametric estimation (where the probabilistic guarantees can be issued under no commitment to the prior information) to non-parametric problems (that call for fine exploitation of prior information)
Bayesian Kernel-Based Linear Control Design
No full textRecent contributions have investigated the use of regularization in linear system identification. In particular, regularizing high-order FIR models to enforce stability while controlling complexity and regularity of the impulse response provides state-of-the-art performance in linear system identification. An advantage of such techniques is that they also enjoy a Bayesian interpretation that yields confidence intervals around the nominal system.In this work it is shown that these features can be useful for the design of a controller in a linear setting. In particular, the posterior distribution of the impulse response available from the Bayesian framework is exploited to perform control design using three different approaches; one of these is the minimization of the expected (posterior) distance from the desired closed loop system. Numerical studies illustrate the good performance of the proposed approaches
A New Model Selection Approach to Hybrid Kernel-Based Estimation
No full textGaussian regression combined with stochastic simulation schemes has proved to be an effective tool in hybrid systems estimation. In particular, recent works have shown that this approach can face effectively both the classification and estimation tasks jointly involved in this problem. In this paper, the combinatorial aspect arising in the choice between linear or nonlinear submodels is overcome with a new Gibbs sampling scheme. Numerical examples concerning the case of discontinuous (static) function estimation are provided to test this new approach
A convex approach to robust LQR
No full textIn this paper, we propose some new convex strategies for robust optimal control. In particular, we treat the problem of designing finite-horizon linear quadratic regulator (LQR) for uncertain discrete-time systems focusing on minimax strategies. A time-invariant linear control law is obtained just solving sequentially two convex optimization problems, hence obtaining a feedback law that takes into account all the available systems samples. In the case of stabilizable systems, we also generalize our approach by including additional constraints on the closed-loop stability in the optimization scheme. Extensions to time-variant control rules are also discussed, leading to novel and intriguing connections between optimal control and multitask learning
Kernel-based learning of orthogonal functions
Get PDFThe paper deals with the reconstruction of functions from sparse and noisy data in suitable intersections of Hilbert spaces that account for orthogonality constraints. Such problem is becoming more and more relevant in several areas like imaging, dictionary learning, compressed sensing. We propose a new approach where it is interpreted as a particular kernel-based multi-task learning problem, with regularization formulated in a reproducing kernel Hilbert space. Special penalty terms are then designed to induce orthogonality. We show that the problem can be given a Bayesian interpretation. This then permits to overcome nonconvexity through a novel Markov chain Monte Carlo scheme able to recover the posterior of the unknown functions and also to understand from data if the orthogonal constraints really hold
An Article About Albertus C. Van Raalte, Author Unknown, Except for Parts Taken from an Article by Anna C. Post
Get PDFAn article about Albertus C. Van Raalte, author unknown, except for parts taken from an article by Anna C. Post. The author knew first generation persons in the Holland settlement and therefore, the article has some value.https://digitalcommons.hope.edu/vrp_1890s/1012/thumbnail.jp
Active Learning-based Model Predictive Coverage Control
Get PDFThe problem of coverage control, i.e., of coordinating multiple agents to
optimally cover an area, arises in various applications. However, coverage
applications face two major challenges: (1) dealing with nonlinear dynamics
while respecting system and safety critical constraints, and (2) performing the
task in an initially unknown environment. We solve the coverage problem by
using a hierarchical framework, in which references are calculated at a central
server and passed to the agents' local model predictive control (MPC) tracking
schemes. Furthermore, to ensure that the environment is actively explored by
the agents a probabilistic exploration-exploitation trade-off is deployed. In
addition, we derive a control framework that avoids the hierarchical structure
by integrating the reference optimization in the MPC formulation. Active
learning is then performed drawing inspiration from Upper Confidence Bound
(UCB) approaches. For all developed control architectures, we guarantee
closed-loop constraint satisfaction and convergence to an optimal
configuration. Furthermore, all methods are tested and compared on hardware
using a miniature car platform.Comment: Extended version of accepted paper in IEEE Transactions on Automatic
Control, 202
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