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1. Combining Learning and Model Based Multivariable Control

   https://doi.org/10.1109/CDC40024.2019.9028944  

   Venkatesh, G. S.; Steven Gray, W.; Duffaut Espinosa, Luis A. (December 2019, Proc. 58th IEEE Conference on Decision and Control)

   null (Ed.)

   Artificial neural networks have traditionally been used to implement machine learning algorithms. There are, however, alternatives to these biologically inspired machine learning architectures that offer potentially lower complexity and stronger theoretical underpinnings. One such option in the context of control is based on using a generic input-output model known as a Chen-Fliess functional series. The main goal of the paper is to describe a specific architecture that can be used in the multivariable setting to combine both learning and model based control. It builds on recent work by the authors showing that a certain monoid structure underlies any recursive implementation of such a system. The method is demonstrated using a two-input, two-output Lotka-Volterra system. 

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2. Combining Learning and Model Based Control: Case Study for Single-Input Lotka-Volterra System

   Gray, W. S.; Venkatesh, G. S.; Duffaut Espinosa, L. A. (July 2019, Proceedings of the ... American Control Conference)

   A hybrid control architecture for nonlinear dynamical systems is described which combines the advantages of model based control with those of real-time learning. The idea is to generate input-output data from an error system involving the plant and a proposed model. A discretized Chen-Fliess functional series is then identified from this data and used in conjunction with the model for predictive control. This method builds on the authors’ previous work on model-free control of a single-input, single-output Lotka-Volterra system.The problem is revisited here, but now with the introduction of a model for the dynamics. The single-input, multiple-output version of the problem is also investigated as a way to enhance closed-loop performance 

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3. Flat Outputs in Terms of SISO Operator Compositions

   https://doi.org/10.1109/CDC40024.2019.9028949  

   Gray, W. Steven (December 2019, Proc. 58th IEEE Conference on Decision and Control)

   null (Ed.)

   The goal of this paper is to use a flat coordinate system to show that a flat output for a SISO flat system can be written in terms of a certain composition of input-output operators. The work is partially motivated by the author’s recent work on computing the relative degree of interconnected systems. First the general smooth case is considered, followed by the control affine analytic case. The latter is more amenable to computations in terms of Chen-Fliess series. 

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4. Shuffle-Rational Series: Recognizability and Realizations

   https://doi.org/10.1109/ICSTCC50638.2020.9259634  

   Venkatesh, G. S.; Gray, W. Steven (October 2020, Proc. 24st International Conference on System Theory, Control and Computing)

   null (Ed.)

   The notion of a shuffle-rational formal power series is introduced. Then two equivalent characterizations are presented, one in terms of an analogue of Schützenberger’s recognizability of a series, and the other in the context of state space realizations of nonlinear input-output systems represented by Chen-Fliess series. An underlying computational framework is also described which employs the Hopf algebra associated with the shuffle group. As an application, it is shown how to model a bilinear system with output saturation in this context. 

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5. Nonlinear Matched Filters via Chen–Fliess Series

   Gray, W. Steven (December 2020, 2020 59th IEEE Conference on Decision and Control)

   null (Ed.)

   A class of nonlinear matched filters is introduced suitable for detection problems using Chen–Fliess functional series. Such series can be viewed as a noncommutative analogue of Taylor series. They are written in terms of a weighted sum of iterated integrals indexed by words over a noncommuting set of symbols. The primary goal is to identify within this class the set of filters which maximizes the signal-to-noise ratio at a given time instant in order to provide a statistic for detecting a known signal. 

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