arXiv subjects

Suman Chakravorty

Publications and source records attributed to Suman Chakravorty.

At least 19 recordsLinked to original sources

arXiv2026

Refining GLSDC for Orbit Determination

This paper investigates the ambiguity of noisy short-arc angles-only orbit determination for a Molniya-orbit case study. Conventional Gauss Initial Orbit Determination followed by Gaussian Least-Squares Differential Correction is first shown to be unreliable under high-noise short-arc conditions, frequently failing to converge or converging to hyperbolic local solutions. To explore the candidate solution space, a Lambert-based initialization procedure is used over a grid of assumed ranges and angular-observation pairs, and the resulting states are refined using nonlinear least-squares optimization. The unconstrained solution set reveals multiple orbit families, including reentry elliptic, bounded elliptic, xGEO elliptic, and hyperbolic trajectories, all of which can reproduce the observed angular arc with comparable residuals. The solutions exhibit a structured range-velocity relationship, indicating that the angular measurements primarily constrain apparent line-of-sight motion rather than absolute range. Finally, physically motivated constraints are introduced to isolate Molniya-like bounded elliptic solutions. The results demonstrate that short-arc angles-only orbit determination is fundamentally non-unique without a priori information and that constraints should be interpreted as orbit-family selection tools rather than proof of uniqueness.

math.DS↗

arXiv2026

On Data-Driven Model Identification for Nonlinear Optimal Control

In this paper, we study the use of nonlinear model identification techniques for the optimal control of nonlinear systems, also known as model-based Reinforcement Learning. We show that the nonlinear model identification problem is equivalent to estimating the generalized moments of an underlying sampling distribution and is bound to suffer from ill-conditioning and variance when approximating a system to high order and over a large domain, requiring samples combinatorial-exponential in the order of the approximation and domain size: a ``Curse of Variance and Ill-Conditioning (COVIC)" that shows up even in very low dimensional problems, quite apart from the usual ``Curse of Dimensionality". We show that the iterative identification of ``local" linear time varying (LTV) models around the current estimate of the optimal trajectory, coupled with a suitable optimal control algorithm such as iterative LQR (ILQR), alleviates these issues and is sufficient to locally accurately solve the underlying optimal control problem.

math.OC↗

arXiv2026

A Two-Stage, Model-Based Reinforcement Learning Approach for Active Flow Control of Bluff Body Wakes

This paper develops a data-driven, output-feedback approach to the infinite-horizon optimal control of high-dimensional nonlinear systems with unknown and unstable equilibria, using sparse partial observations. The approach builds on the transfer-plus-regulation decomposition of the infinite-horizon problem: a finite-horizon nonlinear transfer drives the system into a region where the dynamics are well-approximated by a linear model about the unknown operating point, and an infinite-horizon linear regulator identified within that region completes stabilization. We extend this framework to the partially observed setting by combining an ARMA-based information-state construction with a two-stage control architecture: an iterative linear quadratic regulator (iLQR) approach on the information state drives the system to the equilibrium neighborhood, discovered implicitly without prior knowledge of the target, and a locally identified time-invariant ARMA model provides the infinite-horizon regulator for asymptotic stabilization. The method requires no adjoint solver, reduced-order model, or full-state access. We validate the approach on high-fidelity Navier-Stokes simulations of the cylinder wake at $\mathrm{Re}=100$ using only eight surface pressure sensors, an order of magnitude fewer than recent model-based RL methods. The controller achieves complete suppression of vortex-shedding-induced lift oscillations and a $44\%$ reduction in total drag relative to the uncontrolled baseline.

eess.SY↗

arXiv2026

Hybrid Particle Gaussian Mixture (H-PGM) Solution for Cislunar Target Tracking

Gauss's method of orbit determination (OD) is one of the most popular, minimal assumption target tracking techniques in astrodynamics, especially for generating an initial state estimate. However, due to Gauss's method's assumption of Keplerian motion (part of the larger two-body problem), this method cannot be applied in a cislunar environment, where three body, non-planar effects dominate. In this work, we showcase a hybrid Particle Gaussian Mixture (H-PGM) filtering method, a purely recursive probabilistic OD framework that relies upon a sequential combination of the Markov Chain Monte Carlo (MCMC) based Particle Gaussian Mixture-II (PGM-II) and Kalman update based Particle Gaussian Mixture-I (PGM-I) filters. This method allows us to fuse probabilistic information with angles-only observations from terrestrial telescopes for short- and long-term cislunar target tracking. This method also allows us to fuse other target \textit{a priori} information in an effort to reduce target uncertainty in the short term. This hybrid filtering technique is demonstrated for several popular and important cislunar orbit regimes and compared with several homogeneous and hybrid filtering frameworks.

astro-ph.EP↗

arXiv2026

A Sequential Quadratic Programming Perspective on Optimal Control

This paper investigates the performance of Newton's method, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP) in solving discrete-time optimal control problems. We offer a unified perspective on these approaches, centered on the understanding that each method ultimately solves a sequence of quadratic programs. Building upon previous comparative works, this paper contributes additional mathematical explanations and results to the analysis. In particular, it is shown that iLQR is a principled Sequential Quadratic Programming (SQP) approach, rather than merely an approximation of DDP that neglects Hessian terms. This characteristic guarantees that iLQR will always produce a cost-descent direction and converge to an optimum, under some mild assumptions. In contrast, Newton's method and DDP lack these guarantees, especially when initialized far from an optimum. A series of numerical examples are presented to corroborate the mathematical reasoning and analysis developed in the paper.

math.OC↗

arXiv2026

State Forecasting in an Estimation Framework with Surrogate Sensor Modeling

In recent years, computational power and data availability breakthroughs have revolutionized our ability to analyze complex physical systems through the inverse problem approach. Data-driven techniques like system identification and machine learning play an important role in this field, allowing us to gain insights into previously inaccessible phenomena. However, a major hurdle remains: How can meaningful information from partial measurements be extracted? In the aerospace domain, the challenge of state estimation is particularly pronounced due to the limited availability of observational data and the constraints imposed by sensor capabilities for tracking resident space objects (RSOs). To address these limitations, advanced compensation methodologies are required. Currently, range and bearing measurements obtained from radar and optical systems constitute the primary observational tools in the space situational awareness (SSA) community. In this work, we propose a novel framework that integrates a simplified reference dynamics model with a data-driven surrogate measurement model. This fusion process leverages the strengths of both models to estimate complex dynamical behaviors under conditions of partial observability. Extensive numerical experiments were conducted across multiple datasets to validate the proposed framework. The results demonstrate its efficacy in accurately reconstructing system dynamics from incomplete measurement data. Furthermore, to ensure the robustness of the framework, an initial consistency analysis of the surrogate modeling approach is presented. By addressing the current challenges and refining the integration of data-driven techniques with traditional physics-based modeling, this framework aims to advance state estimation methodologies in the aerospace sector.

eess.SY↗

arXiv2026

A Hybrid Particle Gaussian Mixture Filtering Method for Cislunar Orbit Determination Under Extreme Uncertainty

Gauss's method of orbit determination (OD) and its variants are among the most popular initial state estimation techniques for astronomers and engineers alike. However, owing to its assumptions regarding the two-body problem, Gauss's method is inapplicable in the cislunar domain, where three body effects dominate. We introduce a hybrid Particle Gaussian Mixture filtering method, a purely recursive probabilistic orbit determination framework based on a combination of the Markov Chain Monte Carlo based Particle Gaussian Mixture-II (PGM-II) and Particle Gaussian Mixture-I (PGM-I) filters. This method enables us to fuse probabilistic information with angles-only observations from terrestrial telescopes for short and long-term cislunar target tracking. We demonstrate this technique on an important cislunar orbit regime.

stat.AP↗

arXiv2026

Probabilistic Methods for Initial Orbit Determination and Orbit Determination in Cislunar Space

In orbital mechanics, Gauss's method for orbit determination (OD) is a popular, minimal assumption solution for obtaining the initial state estimate of a passing resident space object (RSO). Since much of the cislunar domain relies on three-body dynamics, a key assumption of Gauss's method is rendered incompatible, creating a need for a new, minimal assumption method for initial orbit determination (IOD). In this work, we present a framework for short and long term probabilistic target tracking in cislunar space which produces an initial state estimate with as few assumptions as possible. Specifically, we propose an IOD method involving the kinematic fitting of several series of noisy, consecutive ground-based observations. Once a probabilistic initial state estimate in the form of a particle cloud is formed, we apply the powerful Particle Gaussian Mixture (PGM) Filter to reduce the uncertainty of our state estimate over time. This combined IOD/OD framework is demonstrated for several classes of trajectories in cislunar space and compared to better-known filtering frameworks.

astro-ph.EP↗

arXiv2026

An Optimal Solution to Infinite Horizon Nonholonomic and Discounted Nonlinear Control Problems

This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we establish a regularized solution approach consisting of a ``finite free final time" optimal transfer problem to the terminal set, which renders the set globally asymptotically stable. Further, we show that the approximations converge to the optimal infinite horizon cost as the size of the terminal set decreases to zero. We also perform the analysis for the discounted problem and show that the terminal set is asymptotically stable only for a subset of the state space and not globally. The theory is empirically evaluated on various nonholonomic robotic systems to show that the cost of our approximate problem converges and the transfer time into the terminal set is dependent on the initial state of the system, necessitating the free final time formulation. We also do comparisons of our free-final time approach with nonlinear MPC.

math.OC↗

arXiv2026

Safe Optimal Control using Log Barrier Constrained iLQR

This paper presents a constrained iterative Linear Quadratic Regulator (iLQR) framework for nonlinear optimal control problems with box constraints on both states and control inputs. We incorporate logarithmic barrier functions into the stage cost to enforce box constraints (upper and lower bounds on variables), yielding a smooth interior-point formulation that integrates seamlessly with the standard iLQR backward-forward pass. The Hessian contributions from the log barriers are positive definite, preserving and enhancing the positive definiteness of the quadratic approximations in iLQR and providing an intrinsic regularization effect that improves numerical stability and convergence. Moreover, since the negative logarithm is convex, the addition of log barrier terms preserves convexity if the cost is already convex. We further analyze how the barrier-augmented iLQR naturally adapts feedback gains near constraint boundaries. In particular, at convergence, the feedback terms associated with saturated control channels go to zero, recovering a purely feedforward behavior whenever control is saturated. Numerical examples on constrained nonlinear control problems demonstrate that the proposed method reliably respects box constraints and maintains favorable convergence properties.

math.OC↗

arXiv2025

Optimal Control with Lyapunov Stability Guarantees for Space Applications

This paper investigates the infinite horizon optimal control problem (OCP) for space applications characterized by nonlinear dynamics. The proposed approach divides the problem into a finite horizon OCP with a regularized terminal cost, guiding the system towards a terminal set, and an infinite horizon linear regulation phase within this set. This strategy guarantees global asymptotic stability under specific assumptions. Our method maintains the system's fully nonlinear dynamics until it reaches the terminal set, where the system dynamics is linearized. As the terminal set converges to the origin, the difference in optimal cost incurred reduces to zero, guaranteeing an efficient and stable solution. The approach is tested through simulations on three problems: spacecraft attitude control, rendezvous maneuver, and soft landing. In spacecraft attitude control, we focus on achieving precise orientation and stabilization. For rendezvous maneuvers, we address the navigation of a chaser to meet a target spacecraft. For the soft landing problem, we ensure a controlled descent and touchdown on a planetary surface. We provide numerical results confirming the effectiveness of the proposed method in managing these nonlinear dynamics problems, offering robust solutions essential for successful space missions.

math.OC↗

arXiv2025

A Sequential Quadratic Programming Perspective on Optimal Control

This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between Newton's method, the iterative LQR (iLQR), and Differential Dynamic Programming (DDP) approaches to solve the problem. It is shown that the iLQR is a principled SQP approach, rather than simply an approximation of DDP by neglecting the Hessian terms, to solve optimal control problems that can be guaranteed to always produce a cost-descent direction and converge to an optimum; while Newton's approach or DDP do not have similar guarantees, especially far from an optimum. Our empirical evaluations on the pendulum and cart-pole swing-up tasks serve to corroborate the SQP-based analysis proposed in this paper.

math.OC↗

arXiv2025

Sensor Fusion Methods for Gaussian Mixture Models

Consensus is a popular technique for distributed state estimation. This formulation allows networks of connected agents or sensors to exchange information about the distribution of a set of targets with their immediate neighbors without the need of a centralized node or layer. We present decentralized consensus-based fusion techniques for a system whose target prior estimates are a weighted mixture of Gaussian probability density functions (PDFs) for the following cases: 1) in which all agents have the same a priori Gaussian mixture estimate of the target, and 2) in which agents have different a priori Gaussian mixture estimates of the target. For the second case, we present a formulation that fuses each agent's a priori estimate without using local observations such that each agent's posterior estimate is the same across the network.

eess.SY↗

arXiv2025

A Reduced Order Iterative Linear Quadratic Regulator (ILQR) Technique for the Optimal Control of Nonlinear Partial Differential Equations

In this paper, we introduce a reduced order model-based reinforcement learning (MBRL) approach, utilizing the Iterative Linear Quadratic Regulator (ILQR) algorithm for the optimal control of nonlinear partial differential equations (PDEs). The approach proposes a novel modification of the ILQR technique: it uses the Method of Snapshots to identify a reduced order Linear Time Varying (LTV) approximation of the nonlinear PDE dynamics around a current estimate of the optimal trajectory, utilizes the identified LTV model to solve a time-varying reduced order LQR problem to obtain an improved estimate of the optimal trajectory along with a new reduced basis, and iterates till convergence. The convergence behavior of the reduced order approach is analyzed and the algorithm is shown to converge to a limit set that is dependent on the truncation error in the reduction. The proposed approach is tested on the viscous Burger's equation and two phase-field models for microstructure evolution in materials, and the results show that there is a significant reduction in the computational burden over the standard ILQR approach, without significantly sacrificing performance.

eess.SY↗

arXiv2024

Time-delayed Dynamic Mode Decomposition for families of periodic trajectories in Cislunar Space

In recent years, the development of the Lunar Gateway and Artemis missions has renewed interest in lunar exploration, including both manned and unmanned missions. This interest necessitates accurate initial orbit determination (IOD) and orbit prediction (OP) in this domain, which faces significant challenges such as severe nonlinearity, sensitivity to initial conditions, large state-space volume, and sparse, faint, and unreliable measurements. This paper explores the capability of data-driven Koopman operator-based approximations for OP in these scenarios. Three stable periodic trajectories from distinct cislunar families are analyzed. The analysis includes theoretical justification for using a linear time-invariant system as the data-driven surrogate. This theoretical framework is supported by experimental validation. Furthermore, the accuracy is assessed by comparing the spectral content captured to period estimates derived from the fast Fourier transform (FFT) and Poincare-like sections.

eess.SY↗

arXiv2024

On the Feedback Law in Stochastic Optimal Nonlinear Control

We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman's "curse of dimensionality". We present a result that shows that repeatedly solving an open-loop deterministic problem from the current state with progressively shorter horizons, similar to Model Predictive Control (MPC), results in a feedback policy that is $O(ε^4)$ near to the true global stochastic optimal policy, where $ε$ is a perturbation parameter modulating the noise. We also show that the optimal deterministic feedback problem has a perturbation structure such that higher-order terms of the feedback law do not affect lower-order terms and that this structure is lost in the optimal stochastic feedback problem. Consequently, solving the Stochastic Dynamic Programming problem is highly susceptible to noise, even in low dimensional problems, and in practice, the MPC-type feedback law offers superior performance even for high noise levels.

eess.SY↗

arXiv2024

Convexity in Optimal Control Problems

This paper investigates the central role played by the Hamiltonian in continuous-time nonlinear optimal control problems. We show that the strict convexity of the Hamiltonian in the control variable is a sufficient condition for the existence of a unique optimal trajectory, and the nonlinearity/non-convexity of the dynamics and the cost are immaterial. The analysis is extended to discrete-time problems, revealing that discretization destroys the convex Hamiltonian structure, leading to multiple spurious optima, unless the time discretization is sufficiently small. We present simulated results comparing the "indirect" Iterative Linear Quadratic Regulator (iLQR) and the "direct" Sequential Quadratic Programming (SQP) approach for solving the optimal control problem for the cartpole and pendulum models to validate the theoretical analysis. Results show that the ILQR always converges to the "globally" optimum solution while the SQP approach gets stuck in spurious minima given multiple random initial guesses for a time discretization that is insufficiently small, while both converge to the same unique solution if the discretization is sufficiently small.

math.OC↗

arXiv2024

An Information-State Based Approach to Linear Time Varying System Identification and Control

This paper considers the problem of system identification for linear time varying systems. We propose a new system realization approach that uses an "information-state" as the state vector, where the "information-state" is composed of a finite number of past inputs and outputs. The system identification algorithm uses input-output data to fit an autoregressive moving average model (ARMA) to represent the current output in terms of finite past inputs and outputs. This information-state-based approach allows us to directly realize a state-space model using the estimated time varying ARMA paramters linear time varying (LTV) systems. The paper develops the theoretical foundation for using ARMA parameters-based system representation using only the concept of linear observability, details the reasoning for exact output modeling using only the finite history, and shows that there is no need to separate the free and the forced response for identification. The paper also discusses the implications of using the information-state system for optimal output feedback control and shows that the solution obtained using a suitably posed information state problem is optimal for the original problem. The proposed approach is tested on various different systems, and the performance is compared with state-of-the-art LTV system identification techniques.

eess.SY↗