Papers by Andrzej Banaszuk
Proceedings of the 2004 American Control Conference, 2004
In this paper, we consider the problem of controloriented modeling of the thermoacoustic dynamics... more In this paper, we consider the problem of controloriented modeling of the thermoacoustic dynamics of ducted, premixed bluffbody stabilized combustion. We make a simplifying assumption of ignoring the vortex dynamics, but retain the effects of burning and fuel actuation. The thermoacoustic model arises as an interconnection of acoustics and heatrelease submodels. For acoustics, we model the effects of mean reacting flow and for heat-release, we model the effects of distributed flame and fuel dynamics. We carry out a controloriented analysis of the resulting coupled thermoacoustic model that highlights the important role of density ratio in obtaining combustion instability.
2017 IEEE 56th Annual Conference on Decision and Control (CDC), 2017
This paper presents a novel Koopman operator theoretic approach for nonlinear constrained state e... more This paper presents a novel Koopman operator theoretic approach for nonlinear constrained state estimation (CSE) with non-convex state constraints. Exploiting linear representation induced by Koopman operator, we show that under certain conditions the CSE problem can be transformed into a higher dimensional but convex problem. This could provide significant benefit in real time applications. We numerically demonstrate the efficacy of proposed approach and report superior performance compared to convexification based on successive linearization.
An adaptive algorithm for control of combustion instability
... In particular, "parameter-dependent" models are desired that can be used to predict... more ... In particular, "parameter-dependent" models are desired that can be used to predict bifurcations of ... Our hope is that some of the methods developed in control theory of linear systems ... to capture the system behavior precluded the use of time-domain model validation techniques. ...
IFAC-PapersOnLine, 2016
In this paper we develop a new approach for observer synthesis for discrete time autonomous nonli... more In this paper we develop a new approach for observer synthesis for discrete time autonomous nonlinear systems based on Koopman operator theoretic framework. Koopman operator is a linear but an infinite-dimensional operator that governs the time evolution of system outputs in a linear fashion. We exploit this property to synthesize an observer form which enables the use of Luenberger/Kalman-like linear observers for nonlinear estimation. Using the techniques for Koopman eigenvalue/eigenfunction/mode computation, we describe a numerical procedure to construct such an observer form which is often valid in a large portion of state space or even globally. We numerically compare our approach with Extended Kalman Filter and report superior performance.
Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), 1997
... (See [l] for an application of Sobolev space techniques to a dual problem of approximate ... ... more ... (See [l] for an application of Sobolev space techniques to a dual problem of approximate ... Least squares integration of one-dimensional codistributions with application to approximate feedback linearization. ... Canonical form observer design for nonlinear time-variable systems. ...
2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004
We present a thermo-acoustic model on a cylindrical, or annular, domain capable of modeling insta... more We present a thermo-acoustic model on a cylindrical, or annular, domain capable of modeling instabilities of tangential acoustic modes. The model accounts for non-uniform density, damping, rotational flow, and heat-release coupling. It is shown that deliberately introducing spatial variations in some quantities have a similar effect to adding damping to the system. The effects of these symmetry-breaking concepts are evaluated
Proceedings of the 45th IEEE Conference on Decision and Control, 2006
We present a procedure for estimating nonlinear feedback parameters obtained from time series dat... more We present a procedure for estimating nonlinear feedback parameters obtained from time series data (power spectral density (PSD), and probability density function (pdf)) with application to the identification of the unsteady heat-release coupling of a limit-cycling thermoacoustic system. The limit cycling and Gaussian components are identified from the pdf of the output signal. The respective describing function gains, along with a phase-shifting element are fit to a nominal acoustic oscillator model by using the PSD. The nonlinear feedback parameters are determined from the describing function gains and their Gaussian and harmonic inputs. The estimation procedure is demonstrated on a benchmark oscillator problem and is applied to time-series data obtained from a limit-cycling combustor rig. Relations between the feedback parameters and the equivalence ratio are discussed
2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004
Page 1. Spectral Balance: a Frequency Domain Framework for Analysis of Nonlinear Dynamical System... more Page 1. Spectral Balance: a Frequency Domain Framework for Analysis of Nonlinear Dynamical Systems Andrzej Banaszuk Prashant G. Mehta Igor Mezic Abstract— A frequency-domain framework for analysis, computations ...
Proceedings of the 44th IEEE Conference on Decision and Control
In this paper we propose an efficient method of comparing data sets obtained from either an exper... more In this paper we propose an efficient method of comparing data sets obtained from either an experiment or simulation of dynamical system model for the purpose of model validation. The proposed approach is based on comparing the intrinsic geometry and the associated dynamics linked with the data sets, and requires no a priori knowledge of the qualitative behavior or the dimension of the phase space. The approach to data analysis is based on constructing a diffusion map defined on the graph of the data set as established in the work of Coifman, Lafon, et al.[5], [10]. Low dimensional embedding is done via a singular value decomposition of the approximate diffusion map. We propose some simple metrics constructed from the eigenvectors of the diffusion map that describe the geometric and spectral properties of the data. The approach is illustrated by comparison of candidate models to data of a combustion experiment that shows limit-cycling acoustic oscillations.
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)
ABSTRACT We present a formalism for comparing the asymptotic dynamics of dynamical systems with t... more ABSTRACT We present a formalism for comparing the asymptotic dynamics of dynamical systems with the physical systems that they model. There is often no need for the detailed (trajectory-wise) comparison of a dynamical system and the physical system that it models, but only comparison in statistical sense. For that purpose, invariant measures are typically considered. But, invariant measures usually can not be observed directly in an experiment. Thus, we base our formalism on time-averages obtained from a single observable. In particular, we constructively prove that, generically, a single observable is needed in order to recover an invariant ergodic measure. Pseudometrics on the space of dynamical systems can be defined using this formalism in order to compare their statistical behavior. We also identify the need to go beyond comparing only invariant ergodic measures of systems and introduce an ergodic-theoretic treatment of a class of spectral functionals that allow for this. The formalism is extended for a class of stochastic systems: discrete random dynamical systems. The ideas introduced can be used for parameter identification and model validation of driven nonlinear models with complicated behavior. As an illustration we provide an example in which we compare the asymptotic behavior of a combustion system measured experimentally with the asymptotic behavior of the model that is a stochastic control dynamical system
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)
Page 1. Proceedings of the 39* IEEE Conference on Decision and Control Sydney, Australia December... more Page 1. Proceedings of the 39* IEEE Conference on Decision and Control Sydney, Australia December, ZOO0 Controlling vortex motion and chaotic advection BERND R. NOACK~ IGOR MEZIe2 AND ANDRZEJ BANASZUK ...
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)
In this paper, we consider the problem of controlling the flame dynamics of a ducted, premixed, b... more In this paper, we consider the problem of controlling the flame dynamics of a ducted, premixed, bluffbody flameholder stabilized flame. The flame dynamics arise due to (complicated) interaction between the fluid dynamics and the inherent kinematical flame motion. For control oriented flame modelling, we make the simplifying assumption of ignoring the vortical component of the fluid dynamics in the problem,
2nd AIAA Flow Control Conference, 2004
This paper is aimed at understanding the role of physical processes of convection and diusion on ... more This paper is aimed at understanding the role of physical processes of convection and diusion on the fundamental limitations arising in fuel control of thermoacoustic instabilities. For this purpose, we develop a physics based reduced order \heat release" model that is analytical and incorporates a) distributed ame dynamics, b) exothermicity related dilatation eects, and c) distributed fuel dynamics including diusion. Results show that convection leads to the presence of distributed delay, while diusion, depending upon diffusivity and exothermicity constants, may lead to the presence of right half plane zeroes in the response of heat release to the fuel control command. We isolate these non-minimum phase aspects of dynamics and apply the theory of fundamental limitations to obtain conclusions on the impact of convection and diusion on ones ability to use fuel based feedback control in controlling heat release.
2008 American Control Conference, 2008
Providing real-time estimates of building occupancy to first responders during emergency events c... more Providing real-time estimates of building occupancy to first responders during emergency events can help in search and rescue, and egress management. This paper addresses the estimation of occupancy in each zone of a building, where the building is spatially divided into nonoverlapping zones that cover all areas of the building. Each zone contains video cameras located at each portal of the zone, where each camera has a signal processing algorithm that detects number of people passing through the portal in each direction. The technical approach of this paper is to develop a non-linear stochastic state-space model of people traffic during emergency egress, and apply the extended Kalman filter which uses the video signal processing outputs and the people traffic model. The approach is demonstrated on a 16,000 square-foot building that has typical occupancy of 100 people. The estimator is tested on data from an agent-based simulation, and on data from an actual fire alarm. The results show that better estimation accuracy is achieved compared to an estimation approach that uses only the video sensors.
ABSTRACT We present results on controllability and observability of point vortex motion actuated ... more ABSTRACT We present results on controllability and observability of point vortex motion actuated by external potential fields. Sufficient conditions for transformation of a point vortex system into the so-called flat coordinates which allow for simple description of controllability and observability of the system will be presented. Control of statistical, large-scale properties of point vortex systems is also considered. We present a number of examples of specific vortex configurations such as counterrotating vortex pairs.
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)
Abstract We present a distributed linear model of thermoacoustic instability in form of a set of ... more Abstract We present a distributed linear model of thermoacoustic instability in form of a set of coupled PDEs including an acoustic model based on potential Euler formulation, a fully distributed fuel transport model based on advection equation, and a fuel-sensitive heat ...
2008 47th IEEE Conference on Decision and Control, 2008
The purpose of this paper is to develop methods for model reduction for diffusion processes that ... more The purpose of this paper is to develop methods for model reduction for diffusion processes that exhibit cyclic behavior. For this purpose we extend techniques based on the spectral theory of Markov processes to the case of complex spectra. The main idea is to augment the state process for the diffusion with a clock process. For each complex eigenvalue for the original diffusion there exists a real eigenvalue for the augmented process. Results concerning metastability (or quasi-stationarity) are then applied to the augmented process. The results are illustrated through a linear diffusion, and an empirical model of combustion dynamics.
Waveform Relaxation is a parallelizable iterative method for solving large scale nonlinear system... more Waveform Relaxation is a parallelizable iterative method for solving large scale nonlinear systems. At each iteration, the system is decomposed into several subsystems each of which is evolved forward in time independently but coupled with the other subsystems through their solutions from the previous iteration. We derive a convergence criteria that reveals the influence of the mutual in- teraction between the subsystems and self-interaction of each subsystem. We propose a decomposition of the system that allows for faster convergence of the waveform relaxation method. This decomposition is based on a graph derived from the Jacobian of the system.
SIAM Journal on Control and Optimization, 1999
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Papers by Andrzej Banaszuk