arXiv subjects

Aleksandar Haber

Publications and source records attributed to Aleksandar Haber.

15 recordsLinked to original sources

arXiv2025

Global network control from local information

In the classical control of network systems, the control actions on a node are determined as a function of the states of all nodes in the network. Motivated by applications where the global state cannot be reconstructed in real time due to limitations in the collection, communication, and processing of data, here we introduce a control approach in which the control actions can be computed as a function of the states of the nodes within a limited state information neighborhood. The trade-off between the control performance and the size of this neighborhood is primarily determined by the condition number of the controllability Gramian. Our theoretical results are supported by simulations on regular and random networks and are further illustrated by an application to the control of power-grid synchronization. We demonstrate that for well-conditioned Gramians, there is no significant loss of control performance as the size of the state information neighborhood is reduced, allowing efficient control of large networks using only local information.

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arXiv2023

State-Robust Observability Measures for Sensor Selection in Nonlinear Dynamic Systems

This paper explores the problem of selecting sensor nodes for a general class of nonlinear dynamical networks. In particular, we study the problem by utilizing altered definitions of observability and open-loop lifted observers. The approach is performed by discretizing the system's dynamics using the implicit Runge-Kutta method and by introducing a state-averaged observability measure. The observability measure is computed for a number of perturbed initial states in the vicinity of the system's true initial state. The sensor node selection problem is revealed to retain the submodular and modular properties of the original problem. This allows the problem to be solved efficiently using a greedy algorithm with a guaranteed performance bound while showing an augmented robustness to unknown or uncertain initial conditions. The validity of this approach is numerically demonstrated on a $H_{2}/O_{2}$ combustion reaction network.

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arXiv2023

Data-driven Estimation, Tracking, and System Identification of Deterministic and Stochastic Optical Spot Dynamics

Stabilization, disturbance rejection, and control of optical beams and optical spots are ubiquitous problems that are crucial for the development of optical systems for ground and space telescopes, free-space optical communication terminals, precise beam steering systems, and other types of optical systems. High-performance disturbance rejection and control of optical spots require the development of disturbance estimation and data-driven Kalman filter methods. Motivated by this, we propose a unified and experimentally verified data-driven framework for optical-spot disturbance modeling and tuning of covariance matrices of Kalman filters. Our approach is based on covariance estimation, nonlinear optimization, and subspace identification methods. Also, we use spectral factorization methods to emulate optical-spot disturbances with a desired power spectral density in an optical laboratory environment. We test the effectiveness of the proposed approaches on an experimental setup consisting of a piezo tip-tilt mirror, piezo linear actuator, and a CMOS camera.

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arXiv2022

Subspace identification of low-dimensional Structural-Thermal-Optical-Performance (STOP) models of reflective optics

In this paper, we investigate the feasibility of using subspace system identification techniques for estimating transient Structural-Thermal-Optical Performance (STOP) models of reflective optics. As a test case, we use a Newtonian telescope structure. This work is motivated by the need for the development of model-based data-driven techniques for prediction, estimation, and control of thermal effects and thermally-induced wavefront aberrations in optical systems, such as ground and space telescopes, optical instruments operating in harsh environments, optical lithography machines, and optical components of high-power laser systems. We estimate and validate a state-space model of a transient STOP dynamics. First, we model the system in COMSOL Multiphysics. Then, we use LiveLink for MATLAB software module to export the wavefront aberrations data from COMSOL to MATLAB. This data is used to test the subspace identification method that is implemented in Python. One of the main challenges in modeling and estimation of STOP models is that they are inherently large-dimensional. The large-scale nature of STOP models originates from the coupling of optical, thermal, and structural phenomena and physical processes. Our results show that large-dimensional STOP dynamics of the considered optical system can be accurately estimated by low-dimensional state-space models. Due to their low-dimensional nature and state-space forms, these models can effectively be used for the prediction, estimation, and control of thermally-induced wavefront aberrations. The developed MATLAB, COMSOL, and Python codes are available online.

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arXiv2022

A novel method for adaptive control of deformable mirrors

For sufficiently wide ranges of applied control signals (control voltages), MEMS and piezoelectric Deformable Mirrors (DMs), exhibit nonlinear behavior. The nonlinear behavior manifests itself in nonlinear actuator couplings, nonlinear actuator deformation characteristics, and in the case of piezoelectric DMs, hysteresis. Furthermore, in a number of situations, DM behavior can change over time, and this requires a procedure for updating the DM models on the basis of the observed data. If not properly modeled and if not taken into account when designing control algorithms, nonlinearities, and time-varying DM behavior, can significantly degrade the achievable closed-loop performance of Adaptive Optics (AO) systems. Widely used approaches for DM control are based on pre-estimated linear time-invariant DM models in the form of influence matrices. Often, these models are not being updated during system operation. Consequently, when the nonlinear DM behavior is excited by control signals with wide operating ranges, or when the DM behavior changes over time, the state-of-the-art DM control approaches relying upon linear control methods, might not be able to produce a satisfactory closed-loop performance of an AO system. Motivated by these key facts, we present a novel method for data-driven DM control. Our approach combines a simple open-loop control method with a recursive least squares method for dynamically updating the DM model. The DM model is constantly being updated on the basis of the dynamically changing DM operating points. That is, the proposed method updates both the control actions and the DM model during the system operation. We experimentally verify this approach on a Boston Micromachines MEMS DM with 140 actuators. Preliminary experimental results reported in this manuscript demonstrate good potential for using the developed method for DM control.

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arXiv2021

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

In this paper, we develop a novel data-driven method for Deformable Mirror (DM) control. The developed method updates both the DM model and DM control actions that produce desired mirror surface shapes. The novel method explicitly takes into account actuator constraints and couples a feedback control algorithm with an algorithm for recursive estimation of DM influence function models. In addition to this, we explore the possibility of using Walsh basis functions for DM control. By expressing the desired and observed mirror surface shapes as sums of Walsh pattern matrices, we formulate the control problem in the 2D Walsh basis domain. We thoroughly experimentally verify the developed approach on a 140-actuator MEMS DM, developed by Boston Micromachines. Our results show that the novel method produces the root-mean-square surface error in the $14-40$ nanometer range. These results can additionally be improved by tuning the control and estimation parameters. The developed approach is also applicable to other DM types, such as for example, segmented DMs.

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arXiv2021

Joint Sensor Node Selection and State Estimation for Nonlinear Networks and Systems

State estimation and sensor selection problems for nonlinear networks and systems are ubiquitous problems that are important for the control, monitoring, analysis, and prediction of a large number of engineered and physical systems. Sensor selection problems are extensively studied for linear networks. However, less attention has been dedicated to networks with nonlinear dynamics. Furthermore, widely used sensor selection methods relying on structural (graph-based) observability approaches might produce far from optimal results when applied to nonlinear network dynamics. In addition, state estimation and sensor selection problems are often treated separately, and this might decrease the overall estimation performance. To address these challenges, we develop a novel methodology for selecting sensor nodes for networks with nonlinear dynamics. Our main idea is to incorporate the sensor selection problem into an initial state estimation problem. The resulting mixed-integer nonlinear optimization problem is approximately solved using three methods. The good numerical performance of our approach is demonstrated by testing the algorithms on prototypical Duffing oscillator, associative memory, and chemical reaction networks. The developed codes are available online.

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arXiv2020

Control Node Selection Algorithm for Nonlinear Dynamic Networks

The coupled problems of selecting control nodes and designing control actions for nonlinear network dynamics are fundamental scientific problems with applications in many diverse fields. These problems are thoroughly studied for linear dynamics; however, in spite of a number of open research questions, methods for nonlinear network dynamics are less developed. As observed by various studies, the prevailing graph-based controllability approaches for selecting control nodes might result in significantly suboptimal control performance for nonlinear dynamics. Herein we present a new, intuitive, and simple method for simultaneous control node selection and control sequence design for complex networks with nonlinear dynamics. The method is developed by incorporating the control node selection problem into an open-loop predictive control cost function and by solving the resulting mixed-integer optimization problem using a mesh adaptive direct search method. The developed framework is numerically robust and can deal with stiff networks, networks with non-smooth dynamics, as well as with control and actuator constraints. Good numerical performance of the method is demonstrated by testing it on prototypical Duffing oscillator and associative memory networks. The developed codes that can easily be adapted to models of other complex systems are available online.

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arXiv2019

Steady-State Control and Machine Learning of Large-Scale Deformable Mirror Models

We use Machine Learning (ML) and system identification validation approaches to estimate neural network models of large-scale Deformable Mirrors (DMs) used in Adaptive Optics (AO) systems. To obtain the training, validation, and test data sets, we simulate a realistic large-scale Finite Element (FE) model of a faceplate DM. The estimated models reproduce the input-output behavior of Vector AutoRegressive with eXogenous (VARX) input models and can be used for the design of high-performance AO systems. We address the model order selection and overfitting problems. We also provide an FE based approach for computing steady-state control signals that produce the desired wavefront shape. This approach can be used to predict the steady-state DM correction performance for different actuator spacings and configurations. The presented methods are tested on models with thousands of state variables and hundreds of actuators. The numerical simulations are performed on low-cost high-performance graphic processing units and implemented using the TensorFlow machine learning framework. The used codes are available online. The approaches presented in this paper are useful for the design and optimization of high-performance DMs and AO systems.

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arXiv2019

Subspace Identification of Temperature Dynamics

Data-driven modeling and control of temperature dynamics in mechatronics systems and industrial processes are challenging control engineering problems. This is mainly because the temperature dynamics is inherently infinite-dimensional, nonlinear, spatially distributed, and coupled with other physical processes. Furthermore, the dominant time constants are usually long, implying that in practice due to various economic and time constraints, we can only collect a relatively small number of data samples that can be used for data-driven modeling. Finally, since sensing and actuation of temperature dynamics are often spatially discrete, special attention needs to be given to sensor (actuator) placement and identifiability problems. Motivated by these challenges, in this manuscript, we consider the problem of data-driven modeling and validation of temperature dynamics. We have developed an experimental setup consisting of a long aluminum bar whose temperature dynamics is influenced by spatially distributed heat actuators and whose temperature is sensed by spatially distributed thermocouples. We address the noise reduction problem and perform step response and nonlinearity analyses. We combine predictor based subspace identification methods with time series analysis methods to identify a multiple-input multiple-output system model. We provide detailed treatments of model structure selection, validation, and residual analysis problems under different modeling and prediction scenarios. Our extensive experimental results show that the temperature dynamics of the experimental setup can be relatively accurately estimated by low-order models.

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arXiv2018

Sparsity Preserving Optimal Control of Discretized PDE Systems

We focus on the problem of optimal control of large-scale systems whose models are obtained by discretization of partial differential equations using the Finite Element (FE) or Finite Difference (FD) methods. The motivation for studying this pressing problem originates from the fact that the classical numerical tools used to solve low-dimensional optimal control problems are computationally infeasible for large-scale systems. Furthermore, although the matrices of large-scale FE or FD models are usually sparse banded or highly structured, the optimal control solution computed using the classical methods is dense and unstructured. Consequently, it is not suitable for efficient centralized and distributed real-time implementations. We show that the a priori (sparsity) patterns of the exact solutions of the generalized Lyapunov equations for FE and FD models are banded matrices. The a priori pattern predicts the dominant non-zero entries of the exact solution. We furthermore show that for well-conditioned problems, the a priori patterns are not only banded but also sparse matrices. On the basis of these results, we develop two computationally efficient methods for computing sparse approximate solutions of generalized Lyapunov equations. Using these two methods and the inexact Newton method, we show that the solution of the generalized Riccati equation can be approximated by a banded matrix. This enables us to develop a novel computationally efficient optimal control approach that is able to preserve the sparsity of the control law. We perform extensive numerical experiments that demonstrate the effectiveness of our approach.

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arXiv2017

State observation and sensor selection for nonlinear networks

A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system. However, network states are usually unknown, and only a fraction of the state variables are directly measurable. The observability problem concerns reconstructing the network state from this limited information. Here, we propose a general optimization-based approach for observing the states of nonlinear networks and for optimally selecting the observed variables. Our results reveal several fundamental limitations in network observability, such as the trade-off between the fraction of observed variables and the observation length on one side, and the estimation error on the other side. We also show that owing to the crucial role played by the dynamics, purely graph- theoretic observability approaches cannot provide conclusions about one's practical ability to estimate the states. We demonstrate the effectiveness of our methods by finding the key components in biological and combustion reaction networks from which we determine the full system state. Our results can lead to the design of novel sensing principles that can greatly advance prediction and control of the dynamics of such networks.

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arXiv2016

Sparse solution of the Lyapunov equation for large-scale interconnected systems

We consider the problem of computing an approximate banded solution of the continuous-time Lyapunov equation $\underline{A}\underline{X}+\underline{X}\underline{A}^{T}=\underline{P}$, where the coefficient matrices $\underline{A}$ and $\underline{P}$ are large, symmetric banded matrices. The (sparsity) pattern of $\underline{A}$ describes the interconnection structure of a large-scale interconnected system. Recently, it has been shown that the entries of the solution $\underline{X}$ are spatially localized or decaying away from a banded pattern. We show that the decay of the entries of $\underline{X}$ is faster if the condition number of $\underline{A}$ is smaller. By exploiting the decay of entries of $\underline{X}$, we develop two computationally efficient methods for approximating $\underline{X}$ by a banded matrix. For a well-conditioned and sparse banded $\underline{A}$, the computational and memory complexities of the methods scale linearly with the state dimension. We perform extensive numerical experiments that confirm this, and that demonstrate the effectiveness of the developed methods. The methods proposed in this paper can be generalized to (sparsity) patterns of $\underline{A}$ and $\underline{P}$ that are more general than banded matrices. The results of this paper open the possibility for developing computationally efficient methods for approximating the solution of the large-scale Riccati equation by a sparse matrix.

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arXiv2014

Sparse approximate inverses of Gramians and impulse response matrices of large-scale interconnected systems

In this paper we show that inverses of well-conditioned, finite-time Gramians and impulse response matrices of large-scale interconnected systems described by sparse state-space models, can be approximated by sparse matrices. The approximation methodology established in this paper opens the door to the development of novel methods for distributed estimation, identification and control of large-scale interconnected systems. The novel estimators (controllers) compute local estimates (control actions) simply as linear combinations of inputs and outputs (states) of local subsystems. The size of these local data sets essentially depends on the condition number of the finite-time observability (controllability) Gramian. Furthermore, the developed theory shows that the sparsity patterns of the system matrices of the distributed estimators (controllers) are primarily determined by the sparsity patterns of state-space matrices of large-scale systems. The computational and memory complexity of the approximation algorithms are $O(N)$, where $N$ is the number of local subsystems of the interconnected system. Consequently, the proposed approximation methodology is computationally feasible for interconnected systems with an extremely large number of local subsystems.

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arXiv2014

Subspace identification of large-scale interconnected systems

We propose a decentralized subspace algorithm for identification of large-scale, interconnected systems that are described by sparse (multi) banded state-space matrices. First, we prove that the state of a local subsystem can be approximated by a linear combination of inputs and outputs of the local subsystems that are in its neighborhood. Furthermore, we prove that for interconnected systems with well-conditioned, finite-time observability Gramians (or observability matrices), the size of this neighborhood is relatively small. On the basis of these results, we develop a subspace identification algorithm that identifies a state-space model of a local subsystem from the local input-output data. Consequently, the developed algorithm is computationally feasible for interconnected systems with a large number of local subsystems. Numerical results confirm the effectiveness of the new identification algorithm.

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