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In many machine learning applications, one wants to learn the unknown objective and constraint functions of an optimization problem from available data and then apply some technique to attain a local optimizer of the learned model. This work considers Gaussian processes as global surrogate models and utilizes them in conjunction with derivative-free trust-region methods. It is well known that derivative-free trust-region methods converge globally---provided the surrogate model is probabilistically fully linear. We prove that glspl{gp} are indeed probabilistically fully linear, thus resulting in fast (compared to linear or quadratic local surrogate models) and global convergence. We draw upon the optimization of a chemical reactor to demonstrate the efficiency of gls{gp}-based trust-region methods.
In this paper, a distributed learning leader-follower consensus protocol based on Gaussian process regression for a class of nonlinear multi-agent systems with unknown dynamics is designed. We propose a distributed learning approach to predict the re
This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in solving sophisticated event-based state estimation problems. An indirect modeling approach is developed, wherein a stat
In the interaction between control and mathematics, mathematical tools are fundamental for all the control methods, but it is unclear how control impacts mathematics. This is the first part of our paper that attempts to give an answer with focus on s
This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control. A trade-off should be decided between the control actions that (robustly) optim
We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher order schemes for SDEs based on It^o-Taylor expansion and iterated It^o