arXiv subjects

Midhun T. Augustine

Publications and source records attributed to Midhun T. Augustine.

7 recordsLinked to original sources

arXiv2026

Discovering Nonlinear Static Relationships in Unlabeled Dataset using Autoencoder with Ordered Variance

This paper presents an autoencoder with ordered variance (AEO), in which the conventional reconstruction loss is augmented by a variance-based regularization term that promotes an ordered structure within the latent space. In this structure, the latent variables are ordered by their variance computed over the training data, facilitating systematic determination of the latent space dimensionality. The AEO is further extended using residual networks, resulting in a ResNet-based AEO (RAEO). Both AEO and RAEO green lead to discovery of nonlinear relationships among variables in unlabeled datasets, thereby enabling unsupervised static model extraction. Theoretical contributions include formal guarantees on the ordering of latent variances. The practical utility of the framework is demonstrated through its application to the identification of nonlinear steady-state models and their use in real-time optimization, with a continuous stirred tank reactor process serving as a representative case study.

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arXiv2026

State-Space Neural Network with Ordered Variance for Model Order Determination

This paper addresses the problem of identifying a nonlinear state-space model, along with an adequate model order, from a given input-output training dataset. To this end, a novel framework, termed state-space neural network with ordered variance (SSNNO), is proposed. In SSNNO, the state variables are ordered according to their variances computed using the training data. This ordering is achieved by introducing a variance-regularization term into the loss function used for SSNNO training and it facilitates a distinction between significant states, which exhibit high variance from the other residual states with near-zero variance. The number of significant states is indicative of a suitable model order. The variance-regularization mechanism is designed to minimize the number of significant state variables, thereby promoting a minimal order of the identified state-space model without significantly compromising its prediction accuracy. A systematic procedure is then introduced to obtain a reduced-order state-space model from the trained SSNNO, yielding a reduced-order SSNNO (R-SSNNO). The existence of an SSNNO with variance-ordered states, based solely on input-output data, as well as an upper bound on its output prediction error, are formally established. A practical and robust method is proposed for ensuring variance-ordered states in an SSNNO, even when the network is trained using local optimization algorithms. The effectiveness of the proposed method for identification of nonlinear state space models is demonstrated through simulation studies on a nonlinear continuous stirred-tank reactor process. The identified model is further used for state estimation and prediction in a model predictive control implementation.

eess.SY↗

arXiv2025

Predictive Controlled Music

This paper presents a new approach to algorithmic composition, called predictive controlled music (PCM), which combines model predictive control (MPC) with music generation. PCM uses dynamic models to predict and optimize the music generation process, where musical notes are computed in a manner similar to an MPC problem by optimizing a performance measure. A feedforward neural network-based assessment function is used to evaluate the generated musical score, which serves as the objective function of the PCM optimization problem. Furthermore, a recurrent neural network model is employed to capture the relationships among the variables in the musical notes, and this model is then used to define the constraints in the PCM. Similar to MPC, the proposed PCM computes musical notes in a receding-horizon manner, leading to feedback controlled prediction. Numerical examples are presented to illustrate the PCM generation method.

cs.SD↗

arXiv2025

Data-driven Model Predictive Control using MATLAB

This paper presents a comprehensive overview of data-driven model predictive control, highlighting state-of-the-art methodologies and their numerical implementation. The discussion begins with a brief review of conventional model predictive control (MPC), which discusses both linear MPC (LMPC) and nonlinear MPC (NMPC). This is followed by a section on data-driven LMPC, outlining fundamental concepts and the implementation of various approaches, including subspace predictive control and prediction error methods. Subsequently, the focus shifts to data-driven NMPC, emphasizing approaches based on neural network models. The paper concludes with a review of recent advancements in data-driven MPC and explores potential directions for future research.

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arXiv2023

Approximate Dynamic Programming based Model Predictive Control of Nonlinear systems

This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the proposed approach, the value function is approximated as a quadratic function for which the parametric matrix is computed using a switched system approximate of the nonlinear system. The approach is modified further using a multi-stage scheme to improve the control accuracy and an extension to incorporate state constraints. The MPC scheme is validated experimentally on a multi-tank system which is modeled as a third-order nonlinear system. The experimental results show the proposed MPC scheme results in significantly lesser online computation compared to the Nonlinear MPC scheme.

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arXiv2023

Model Predictive Control using MATLAB

This tutorial consists of a brief introduction to the modern control approach called model predictive control (MPC) and its numerical implementation using MATLAB. We discuss the basic concepts and numerical implementation of the two major classes of MPC: Linear MPC (LMPC) and Nonlinear MPC (NMPC). This includes the various aspects of MPC such as formulating the optimization problem, constraints handling, feasibility, stability, and optimality.

math.OC↗

arXiv2023

A Note on Linear Quadratic Regulator and Kalman Filter

Two central problems in modern control theory are the controller design problem: which deals with designing a control law for the dynamical system, and the state estimation problem (observer design problem): which deals with computing an estimate of the states of the dynamical system. The Linear Quadratic Regulator (LQR) and Kalman Filter (KF) solves these problems respectively for linear dynamical systems in an optimal manner, i.e., LQR is an optimal state feedback controller and KF is an optimal state estimator. In this note, we will be discussing the basic concepts, derivation, steady-state analysis, and numerical implementation of the LQR and KF.

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