arXiv subjects

Ramachandran Anantharaman

Publications and source records attributed to Ramachandran Anantharaman.

10 recordsLinked to original sources

arXiv2026

Identification of Nonlinear Acyclic Networks in Continuous Time from Nonzero Initial Conditions and Full Excitations

We propose a method to identify nonlinear acyclic networks in continuous time when the dynamics are located on the edges and all the nodes are excited. We show that it is necessary and sufficient to measure all the sinks to identify any tree in continuous time when the functions associated with the dynamics are analytic and satisfy $f(0)=0$, which is analogous to the discrete-time case. For general directed acyclic graphs (DAGs), we show that it is necessary and sufficient to measure all sinks, assuming that the dynamics are not linear (a condition that can be relaxed for trees). Then, based on the measurement of higher order derivatives and nonzero initial conditions, we introduce a method for the identification of trees, which allows us to recover the nonlinear functions located in the edges of the network under the assumption of dictionary functions. Finally, we propose a method to identify multiple parallel paths of the same length between two nodes, which allow us to identify any DAG when combined with the algorithm for the identification of trees. Several examples are added to illustrate the results.

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arXiv2025

Data-Driven Modeling of Photosynthesis Regulation Under Oscillating Light Condition - Part I: In-Silico Exploration

This paper explores the application of data-driven system identification techniques in the frequency domain to obtain simplified, control-oriented models of photosynthesis regulation under oscillating light conditions. In-silico datasets are generated using simulations of the physics-based Basic DREAM Model (BDM) Funete et al.[2024], with light intensity signals -- comprising DC (static) and AC (modulated) components as input and chlorophyll fluorescence (ChlF) as output. Using these data, the Best Linear Approximation (BLA) method is employed to estimate second-order linear time-invariant (LTI) transfer function models across different operating conditions defined by DC levels and modulation frequencies of light intensity. Building on these local models, a Linear Parameter-Varying (LPV) representation is constructed, in which the scheduling parameter is defined by the DC values of the light intensity, providing a compact state-space representation of the system dynamics.

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arXiv2025

Hierarchical Decentralized Stochastic Control for Cyber-Physical Systems

This paper introduces a two-timescale hierarchical decentralized control architecture for Cyber-Physical Systems (CPS). The system consists of a global controller (GC), and N local controllers (LCs). The GC operates at a slower timescale, imposing budget constraints on the actions of LCs, which function at a faster timescale. Applications can be found in energy grid planning, wildfire management, and other decentralized resource allocation problems. We propose and analyze two optimization frameworks for this setting: COpt and FOpt. In COpt, both GC and LCs together optimize infinite-horizon discounted rewards, while in FOpt the LCs optimize finite-horizon episodic rewards, and the GC optimizes infinite-horizon rewards. Although both frameworks share identical reward functions, their differing horizons can lead to different optimal policies. In particular, FOpt grants greater autonomy to LCs by allowing their policies to be determined only by local objectives, unlike COpt. To our knowledge, these frameworks have not been studied in the literature. We establish the formulations, prove the existence of optimal policies, and prove the convergence of their value iteration algorithms. We further show that COpt always achieves a higher value function than FOpt and derive explicit bounds on their difference. Finally, we establish a set of sufficient structural conditions under which the two frameworks become equivalent.

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arXiv2025

Estimation of Heat Transfer Coefficient in Heat Exchangers from closed-loop data using Neural Networks

Heat exchangers (HEXs) play a central role in process industries for thermal energy transfer. Fouling, the gradual accumulation of solids on heat transfer surfaces, causes a time-varying decrease in the overall heat transfer coefficient (U(t)), significantly impacting the efficiency of heat transfer. Good estimation and modeling of fouling (the heat transfer coefficient) will lead to better fouling mitigation strategies. This study investigates the identifiability of the time-varying $U(t)$ in HEXs from closed-loop operational data, without external excitation of reference signals or knowledge of the controller parameters. We establish that while the complete system model cannot be identified under these given constraints, the time-varying heat transfer coefficient $U(t)$ remains identifiable. Further, we propose a neural network based architecture, called (Per-PINN), for estimation and modeling the heat transfer coefficient from the closed-loop system data. This Per-PINN model is shown to perform better than the existing Physics-Informed Neural Networks (PINN) based models for inverse parameter learning as it inherently fixes the underlying physical equations and learns only the time-varying parameter U(t).

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arXiv2024

Koopman operator based identification of nonlinear networks

In this work, we develop a method to identify continuous-time nonlinear networked dynamics via the Koopman operator framework. The proposed technique consists of two steps: the first step identifies the neighbors of each node, and the second step identifies the local dynamics at each node from a predefined set of dictionary functions. The technique can be used to either identify the Boolean network of interactions (first step) or to solve the complete network identification problem that amounts to estimating the local node dynamics and the nature of the node interactions (first and second steps). Under a sparsity assumption, the data required to identify the complete network dynamics is significantly less than the total number of dictionary functions describing the dynamics. This makes the proposed approach attractive for identifying large dimensional networks with sparse interconnections. The accuracy and performance of the proposed identification technique are demonstrated with several examples.

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arXiv2024

Dynamic Mode Decomposition with Non-uniform Sampling

Dynamic Mode Decomposition (DMD) and its extensions (EDMD) have been at the forefront of data-based approaches to Koopman operators. Most (E)DMD algorithms assume that the entire state is sampled at a uniform sampling rate. In this paper, we provide an algorithm where the entire state is not uniformly sampled, with individual components of the states measured at individual (but known) sampling rates. We propose a two-step DMD algorithm where the first step performs Hankel DMD on individual state components to estimate them at specified time instants. With the entire state reconstructed at the same time instants, we compute the (E)DMD for the system with the estimated data in the second step.

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arXiv2024

On Linear Representation, Complexity and Inversion of maps over finite fields

This paper defines a linear representation for nonlinear maps $F:\mathbb{F}^n\rightarrow\mathbb{F}^n$ where $\mathbb{F}$ is a finite field, in terms of matrices over $\mathbb{F}$. This linear representation of the map $F$ associates a unique number $N$ and a unique matrix $M$ in $\mathbb{F}^{N\times N}$, called the Linear Complexity and the Linear Representation of $F$ respectively, and shows that the compositional powers $F^{(k)}$ are represented by matrix powers $M^k$. It is shown that for a permutation map $F$ with representation $M$, the inverse map has the linear representation $M^{-1}$. This framework of representation is extended to a parameterized family of maps $F_λ(x): \mathbb{F} \to \mathbb{F}$, defined in terms of a parameter $λ\in \mathbb{F}$, leading to the definition of an analogous linear complexity of the map $F_λ(x)$, and a parameter-dependent matrix representation $M_λ$ defined over the univariate polynomial ring $\mathbb{F}[λ]$. Such a representation leads to the construction of a parametric inverse of such maps where the condition for invertibility is expressed through the unimodularity of this matrix representation $M_λ$. Apart from computing the compositional inverses of permutation polynomials, this linear representation is also used to compute the cycle structures of the permutation map. Lastly, this representation is extended to a representation of the cyclic group generated by a permutation map $F$, and to the group generated by a finite number of permutation maps over $\mathbb{F}$.

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arXiv2024

Observability of Nonlinear Dynamical Systems over Finite Fields

This paper discusses the observability of nonlinear Dynamical Systems over Finite Fields (DSFF) through the Koopman operator framework. In this work, given a nonlinear DSFF, we construct a linear system of the smallest dimension, called the Linear Output Realization (LOR), which can generate all the output sequences of the original nonlinear system through proper choices of initial conditions (of the associated LOR). We provide necessary and sufficient conditions for the observability of a nonlinear system and establish that the maximum number of outputs sufficient for computing the initial condition is precisely equal to the dimension of the LOR. Further, when the system is not known to be observable, we provide necessary and sufficient conditions for the unique reconstruction of initial conditions for specific output sequences.

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arXiv2020

Koopman operator approach for computing structure of solutions and Observability of non-linear finite state system

Given a discrete dynamical system defined by a map in a vector space over a finite field called Finite State Systems (FSS), a dual linear system over the space of functions on the state space is constructed using the dual map. This system constitutes the well known Koopman linear system framework of dynamical systems, hence called the Koopman linear system (KLS). It is first shown that several structural properties of solutions of the FSS can be inferred from the solutions of the KLS. The problems of computation of structural parameters of solutions of non-linear FSS are computationally hard and hence become infeasible as the number of variables increases. In contrast, it has been well known that these problems can be solved by linear algebra for linear FSS in terms of elementary divisors of matrices and their orders. In the next step, the KLS is reduced to the smallest order (called RO-KLS) while still retaining all the information of the parameters of structure of solutions of the FSS. Hence when the order of the RO-KLS is sufficiently small, the above computational problems of non-linear FSS are practically feasible. Next, it is shown that the observability of the non-linear FSS with an output function is equivalent to that of the RO-KLS with an appropriate linear output map. Hence, the problem of non-linear observability is solved by an observer design for the equivalent RO-KLS. Such a construction should have striking applications to realistic FSS arising in Cryptology and Biological networks.

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arXiv2019

Analysis of Periodic Feedback Shift Registers

This paper develops methods for analyzing periodic orbits of states of linear feedback shift registers with periodic coefficients and estimating their lengths. These shift registers are among the simplest nonlinear feedback shift registers (FSRs) whose orbit lengths can be determined by feasible computation. In general such a problem for nonlinear FSRs involves infeasible computation. The dynamical systems whose model includes such FSRs are termed as Periodic Finite State systems (PFSS). This paper advances theory of such dynamical systems. Due to the finite field valued coefficients, the theory of such systems turns out to be radically different from that of linear continuous or discrete time periodic systems with real coefficients well known in literature. A special finite field version of the Floquet theory of such periodic systems is developed and the structure of trajectories of the PFSS is analyzed through that of a shift invariant linear system after Floquet transformation. The concept of extension of a dynamical system is proposed for such systems whenever the equivalent shift invariant system can be obtained over an extension field.

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