Stabilization of Cascaded Two-Port Networked Systems Against Nonlinear Perturbations

A networked control system (NCS) consisting of cascaded two-port communication channels between the plant and controller is modeled and analyzed. Towards this end, the robust stability of a standard closed-loop system in the presence of conelike perturbations on the system graphs is investigated. The underlying geometric insights are then exploited to analyze the two-port NCS. It is shown that the robust stability of the two-port NCS can be guaranteed when the nonlinear uncertainties in the transmission matrices are sufficiently small in norm. The stability condition, given in the form of "arcsin" of the uncertainty bounds, is both necessary and sufficient.Comment: 8 pages, in preparation for journal submissio

A Behavioral Approach to Robust Machine Learning

Machine learning is revolutionizing almost all fields of science and technology and has been proposed as a pathway to solving many previously intractable problems such as autonomous driving and other complex robotics tasks. While the field has demonstrated impressive results on certain problems, many of these results have not translated to applications in physical systems, partly due to the cost of system fail- ure and partly due to the difficulty of ensuring reliable and robust model behavior. Deep neural networks, for instance, have simultaneously demonstrated both incredible performance in game playing and image processing, and remarkable fragility. This combination of high average performance and a catastrophically bad worst case performance presents a serious danger as deep neural networks are currently being used in safety critical tasks such as assisted driving. In this thesis, we propose a new approach to training models that have built in robustness guarantees. Our approach to ensuring stability and robustness of the models trained is distinct from prior methods; where prior methods learn a model and then attempt to verify robustness/stability, we directly optimize over sets of models where the necessary properties are known to hold. Specifically, we apply methods from robust and nonlinear control to the analysis and synthesis of recurrent neural networks, equilibrium neural networks, and recurrent equilibrium neural networks. The techniques developed allow us to enforce properties such as incremental stability, incremental passivity, and incremental l2 gain bounds / Lipschitz bounds. A central consideration in the development of our model sets is the difficulty of fitting models. All models can be placed in the image of a convex set, or even R^N , allowing useful properties to be easily imposed during the training procedure via simple interior point methods, penalty methods, or unconstrained optimization. In the final chapter, we study the problem of learning networks of interacting models with guarantees that the resulting networked system is stable and/or monotone, i.e., the order relations between states are preserved. While our approach to learning in this chapter is similar to the previous chapters, the model set that we propose has a separable structure that allows for the scalable and distributed identification of large-scale systems via the alternating directions method of multipliers (ADMM)

An extension of the structured singular value to nonlinear systems with application to robust flutter analysis

The paper discusses an extension of μ (or structured singular value), a well-established technique from robust control for the study of linear systems subject to structured uncertainty, to nonlinear polynomial problems. Robustness is a multifaceted concept in the nonlinear context, and in this work the point of view of bifurcation theory is assumed. The latter is concerned with the study of qualitative changes of the steady-state solutions of a nonlinear system, so-called bifurcations. The practical goal motivating the work is to assess the effect of modeling uncertainties on flutter, a dynamic instability prompted by an adverse coupling between aerodynamic, elastic, and inertial forces, when considering the system as nonlinear. Specifically, the onset of flutter in nonlinear systems is generally associated with limit cycle oscillations emanating from a Hopf bifurcation point. Leveraging μ and its complementary modeling paradigm, namely linear fractional transformation, this work proposes an approach to compute margins to the occurrence of Hopf bifurcations for uncertain nonlinear systems. An application to the typical section case study with linear unsteady aerodynamic and hardening nonlinearities in the structural parameters will be presented to demonstrate the applicability of the approach.This work has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant agreement no. 636307, project FLEXOP. Open access funding provided by Swiss Federal Institute of Technology Zurich