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Posts
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portfolio
publications
Design of a Beyond-Line-of-Sight Microwave Propagation Study Across the Gulf of Mexico
Published in IEEE SoutheastCon 2018, 2018
The Florida Department of Transportation (FDOT) Intelligent Transportation System (ITS) uses statewide, redundant, physically separate, fiber and microwave communications networks for mission critical services. However, there are two specific geographical regions that do not support redundant, physically separate networks. These two regions are the Florida panhandle and the Florida Keys. It may be possible to remove this vulnerability and implement a redundant communication path by utilizing a beyond Line-of-Sight(b-LoS) microwave link. A b-LoS microwave link uses the atmospheric evaporative duct which can be present immediately above large bodies of water. A propagation study project is underway that will investigate using this evaporative duct to create a 500-mile microwave link, across the Gulf of Mexico, between Key West and Destin, Florida. Such a link could potentially create an opportunity to introduce redundancy for both vulnerable geographic regions at the same time. This study will require the remote operation of two temporary microwave propagation test stations over an extended period. The separate transmit and receive test stations will use two candidate microwave frequencies for one-way link tests between the two locations. At the end of the propagation study, the results will be published and recommendations on next steps will be presented to the FDOT.
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Utilizing Existing Commercial Geostationary Earth Orbit Fixed Satellite Services for Low Earth Orbit Satellite Communication Relays with Earth
Published in New Space, 2019
There are only a few ways that a low Earth orbit (LEO) satellite can communicate with Earth without a ground station network. A LEO satellite can link with other LEO satellites establishing a mesh network that connects with Earth, or LEO satellites can relay their traffic through one of only a few specialized existing or planned geostationary Earth orbit (GEO) or medium Earth orbit (MEO) relay satellites such as the Tracking and Data Relay Satellite System (TDRSS) and Audacy. Unfortunately, there is a real possibility that these limited choices for satellite communications will not accommodate all of the anticipated growth in LEO satellite deployments that are forecast for the next 10 years. The less efficient direct LEO to Earth communications link method will be used unless another solution can be found. A new option may be to leverage the on-orbit commercial GEO satellites that already support the fixed satellite services (FSSs) market. In this scenario, a LEO satellite would relay its communications through the GEO satellite and down to an Earth station, much the same way terrestrial very small aperture terminals, cruise ships, or jet airliners do today. Utilizing several of these commercial GEO satellites, a LEO satellite could communicate with Earth during a large portion of each orbit. There are some challenges with such a scheme, including regulatory hurdles, but if they could be overcome a significant resource of satellite communication services could be engaged to support the future growth of the satellite industry. Several new LEO to GEO relay methods have been proposed or are in development, requiring the deployment of new GEO relay satellites, but this article discusses the idea of utilizing the hundreds of existing FSS GEO satellites operating in C, Ku, and Ka band to leverage an existing resource for satellite communications with LEO satellites.
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Extremely Fast Convergence Rates for Extremum Seeking Control with Polyak-Ruppert Averaging
Published in arXiv, 2022
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as \(O(n^{-1})\). A deterministic counterpart known as quasi-stochastic approximation is a viable alternative in many applications, including gradient-free optimization and reinforcement learning. It was assumed in prior research that the optimal achievable convergence rate is \(O(n^{-2})\). It is shown in this paper that through design it is possible to obtain far faster convergence, of order \(O(n^{-4+\delta})\), with \(\delta>0\) arbitrary.
Two techniques are introduced for the first time to achieve this rate of convergence. The theory is also specialized within the context of gradient-free optimization, and tested on standard benchmarks. The main results are based on a combination of novel application of results from number theory and techniques adapted from stochastic approximation theory.
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Markovian Foundations for Quasi-Stochastic Approximation with Applications to Extremum Seeking Control
Published in ArXiv, 2022
This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the time-inhomogeneous ODE \(\tfrac{d}{dt} \Theta_t = \alpha f_t (\Theta_t)\), with state process \(\Theta\) evolving on \(\mathbb{R}^d\). Theory is based on an almost periodic vector field, so that in particular the time average of \(f_t(\theta)\) defines the time-homogeneous mean vector field \(\bar{f}\colon\mathbb{R}^d\to\mathbb{R}^d\) with \(\bar{f}(\theta^*) = 0\). Under smoothness assumptions on the functions involved, the following exact representation is obtained: \[\frac{d}{dt} \Theta_t = \alpha (\bar{f}(\Theta_t) -\alpha \overline{\Upsilon}_t + \alpha^2 \mathcal{W}_t^0 + \alpha \frac{d}{dt} \mathcal{W}_t^1 +\frac{d^2}{dt^2} \mathcal{W}_t^2) \] along with formulae for the smooth signals \(\{ \overline{\Upsilon}_t, \mathcal{W}_t^i : i=0, 1, 2\}\). This representation is based on the application of techniques from Markov processes, for which Poisson’s equation plays a central role. This new representation, combined with new conditions for ultimate boundedness, has many applications for furthering the theory of QSA and its applications, including the following implications that are developed in this paper:
- A proof that the estimation error \(\| \Theta_t - \theta^* \|\) is of order \(O(\alpha)\), but can be reduced to \(O(\alpha^2)\) using a second order linear filter.
- In application to extremum seeking control (an approach to gradient free optimization), it is found that the results do not apply because the standard algorithms are not Lipschitz continuous. A new approach is presented to ensure that the required Lipschitz bounds hold, and from this we obtain stability, transient bounds, asymptotic bias of order \(O(\alpha^2)\), and asymptotic variance of order \(O(\alpha^4)\).
- It is in general possible to obtain better than \(O(\alpha)\) bounds on error in traditional stochastic approximation when there is Markovian noise.
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Bias in Stochastic Approximation Cannot Be Eliminated With Averaging
Published in 2022 58th Annual Allerton Conference on Communication, Control, and Computing, 2022
This paper concerns bias and asymptotic statistics for stochastic approximation (SA) driven by Markovian noise. This extended abstract is organized into three parts:
- Background
- Asymptotic statistics with Markovian noise
- Quasi stochastic approximation.
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Approaching Quartic Convergence Rates for Quasi-Stochastic Approximation with Application to Gradient-Free Optimization
Published in Advances in Neural Information Processing Systems 35 (NeurIPS 2022), 2022
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as \(O(n^{-1})\). A deterministic counterpart known as quasi-stochastic approximation is a viable alternative in many applications, including gradient-free optimization and reinforcement learning. It was assumed in prior research that the optimal achievable convergence rate is \(O(n^{-2})\). It is shown in this paper that through design it is possible to obtain far faster convergence, of order \(O(n^{-4+\delta})\), with \(\delta>0\) arbitrary.
Two techniques are introduced for the first time to achieve this rate of convergence. The theory is also specialized within the context of gradient-free optimization, and tested on standard benchmarks. The main results are based on a combination of novel application of results from number theory and techniques adapted from stochastic approximation theory.
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The Curse of Memory in Stochastic Approximation: Extended Version
Published in ArXiv, 2023
Theory and application of stochastic approximation (SA) has grown within the control systems community since the earliest days of adaptive control.
This paper takes a new look at the topic, motivated by recent results establishing remarkable performance of SA with (sufficiently small) constant step-size \(\alpha>0\). If averaging is implemented to obtain the final parameter estimate, then the estimates are asymptotically unbiased with nearly optimal asymptotic covariance. These results have been obtained for random linear SA recursions with i.i.d. coefficients.
This paper obtains very different conclusions in the more common case of geometrically ergodic Markovian disturbance:
- the \(\textit{target bias}\) is identified, even in the case of non-linear SA, and is in general non-zero. The remaining results are established for linear SA recursions:
- the bivariate parameter-disturbance process is geometrically ergodic in a topological sense;
- the representation for bias has a simpler form in this case, and cannot be expected to be zero if there is multiplicative noise;
- the asymptotic covariance of the averaged parameters is within \(O(\alpha)\) of optimal. The error term is identified, and may be massive if mean dynamics are not well conditioned. The theory is illustrated with application to TD-learning.
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talks
Talk 1 on Relevant Topic in Your Field
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Conference Proceeding talk 3 on Relevant Topic in Your Field
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teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
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Teaching experience 2
Workshop, University 1, Department, 2015
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