arXiv subjects

Mohamed Naveed Gul Mohamed

Publications and source records attributed to Mohamed Naveed Gul Mohamed.

14 recordsLinked to original sources

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.

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arXiv2026

Collaborative Multi-Robot Non-Prehensile Manipulation via Flow-Matching Co-Generation

Coordinating a team of robots to reposition multiple objects in cluttered environments requires reasoning jointly about where robots should establish contact, how to manipulate objects once contact is made, and how to navigate safely and efficiently at scale. Prior approaches typically fall into two extremes -- either learning the entire task or relying on privileged information and hand-designed planners -- both of which struggle to handle diverse objects in long-horizon tasks. To address these challenges, we present a unified framework for collaborative multi-robot, multi-object non-prehensile manipulation that integrates flow-matching co-generation with anonymous multi-robot motion planning. Within this framework, a generative model co-generates contact formations and manipulation trajectories from visual observations, while a novel motion planner conveys robots at scale. Crucially, the same planner also supports coordination at the object level, assigning manipulated objects to larger target structures and thereby unifying robot- and object-level reasoning within a single algorithmic framework. Experiments in challenging simulated environments demonstrate that our approach outperforms baselines in both motion planning and manipulation tasks, highlighting the benefits of generative co-design and integrated planning for scaling collaborative manipulation to complex multi-agent, multi-object settings. Visit gco-paper.github.io for code and demonstrations.

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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.

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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.

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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.

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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.

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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.

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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.

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arXiv2024

On the Predictive Capability of Dynamic Mode Decomposition for Nonlinear Periodic Systems with Focus on Orbital Mechanics

This paper discusses the predictive capability of Dynamic Mode Decomposition (DMD) in the context of orbital mechanics. The focus is specifically on the Hankel variant of DMD which uses a stacked set of time-delayed observations for system identification and subsequent prediction. A theory on the minimum number of time delays required for accurate reconstruction of periodic trajectories of nonlinear systems is presented and corroborated using experimental analysis. In addition, the window size for training and prediction regions, respectively, is presented. The need for a meticulous approach while using DMD is emphasized by drawing comparisons between its performance on two candidate satellites, the ISS and MOLNIYA-3-50.

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arXiv2023

An Information-state based Approach to the Optimal Output Feedback Control of Nonlinear Systems

This paper develops a data-based approach to the closed-loop output feedback control of nonlinear dynamical systems with a partial nonlinear observation model. We propose an information state based approach to rigorously transform the partially observed problem into a fully observed problem where the information state consists of the past several observations and control inputs. We further show the equivalence of the transformed and the initial partially observed optimal control problems and provide the conditions to solve for the deterministic optimal solution. We develop a data based generalization of the iterative Linear Quadratic Regulator (iLQR) to partially observed systems using a local linear time varying model of the information state dynamics approximated by an Autoregressive moving average (ARMA) model, that is generated using only the input-output data. This open-loop trajectory optimization solution is then used to design a local feedback control law, and the composite law then provides an optimum solution to the partially observed feedback design problem. The efficacy of the developed method is shown by controlling complex high dimensional nonlinear dynamical systems in the presence of model and sensing uncertainty.

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arXiv2023

An Optimal Solution to Infinite Horizon Nonlinear Control Problems

In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set containing the origin, we establish an approximate regularized solution approach consisting of a ``finite free final time" optimal transfer problem to the terminal set, and an infinite horizon linear regulation problem within the terminal set, that is shown to render the origin globally asymptotically stable. Further, we show that the approximations converge to the true optimal cost function as the size of the terminal set decreases to zero. The approach is empirically evaluated on the pendulum and cart-pole swing-up problems to show that the finite time transfer is far shorter than the effective horizon required to solve the infinite horizon problem without the proposed regularization.

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arXiv2021

On the Convergence of Reinforcement Learning in Nonlinear Continuous State Space Problems

We consider the problem of Reinforcement Learning for nonlinear stochastic dynamical systems. We show that in the RL setting, there is an inherent ``Curse of Variance" in addition to Bellman's infamous ``Curse of Dimensionality", in particular, we show that the variance in the solution grows factorial-exponentially in the order of the approximation. A fundamental consequence is that this precludes the search for anything other than ``local" feedback solutions in RL, in order to control the explosive variance growth, and thus, ensure accuracy. We further show that the deterministic optimal control has a perturbation structure, in that the higher order terms do not affect the calculation of lower order terms, which can be utilized in RL to get accurate local solutions.

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arXiv2020

Experiments with Tractable Feedback in Robotic Planning under Uncertainty: Insights over a wide range of noise regimes (Extended Report)

We consider the problem of robotic planning under uncertainty. This problem may be posed as a stochastic optimal control problem, complete solution to which is fundamentally intractable owing to the infamous curse of dimensionality. We report the results of an extensive simulation study in which we have compared two methods, both of which aim to salvage tractability by using alternative, albeit inexact, means for treating feedback. The first is a recently proposed method based on a near-optimal "decoupling principle" for tractable feedback design, wherein a nominal open-loop problem is solved, followed by a linear feedback design around the open-loop. The second is Model Predictive Control (MPC), a widely-employed method that uses repeated re-computation of the nominal open-loop problem during execution to correct for noise, though when interpreted as feedback, this can only said to be an implicit form. We examine a much wider range of noise levels than have been previously reported and empirical evidence suggests that the decoupling method allows for tractable planning over a wide range of uncertainty conditions without unduly sacrificing performance.

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arXiv2019

Decoupling stochastic optimal control problems for efficient solution: insights from experiments across a wide range of noise regimes

We consider the problem of robotic planning under uncertainty in this paper. This problem may be posed as a stochastic optimal control problem, a solution to which is fundamentally intractable owing to the infamous "curse of dimensionality". Hence, we consider the extension of a "decoupling principle" that was recently proposed by some of the authors, wherein a nominal open-loop problem is solved followed by a linear feedback design around the open-loop, and which was shown to be near-optimal to second order in terms of a "small noise" parameter, to a much wider range of noise levels. Our empirical evidence suggests that this allows for tractable planning over a wide range of uncertainty conditions without unduly sacrificing performance.

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