arXiv subjects

Ravi Banavar

Publications and source records attributed to Ravi Banavar.

At least 19 recordsLinked to original sources

arXiv2026

Min-Max Grassmannian Optimization for Online Subspace Tracking

We propose GeRoST (Geometrically Robust Subspace Tracking), an online subspace tracking algorithm that models uncertainty in a subspace using a Grassmannian ball. We derive an exact scalar dual for the worst-case subspace problem, establish conditions for a unique worst-case subspace and a Riemannian gradient, and characterize the minimum radius needed to cover a dimensional extension of the target subspace. Each update uses either a spectral direction computed in a reduced subspace or the gradient of the window reconstruction loss. Our numerical experiments show that GeRoST achieves lower mean post-fault prediction error than GREAT in system identification. In video separation, it achieves higher precision and a better precision--recall balance, as measured by the F$_1$ score, than both GREAT and GRASTA at the reported thresholds, with lower recall and longer runtime.

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arXiv2026

Explicit Second-Order Bounds on the Domain of Validity for Lyapunov-Schmidt Reduction

Lyapunov-Schmidt reduction is a widely used dimensionality reduction technique for bifurcation analysis in high-dimensional systems. While classical formulations guarantee the local existence of reduced-order equations, they typically lack explicit quantitative estimates on the size of the neighbourhoods in which these representations faithfully capture the full bifurcation structure. In recent work, we have addressed this limitation by deriving bounds on the domain of validity of this reduction using first-order conditions on the vector field together with a quantitative result for the implicit function theorem. In this article we explore beyond, and adopt second-order conditions that incorporate the Hessians of the vector field to develop these bounds, and obtain a new set of results. We then investigate the applicability of these newly derived bounds to Hopfield-like networked dynamical systems, evaluate these bounds for pitchfork bifurcations on connected regular graphs, and finally examine the relationship between the two certified domains for this class of systems.

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arXiv2026

Quasi-Static Control of Discrete Cosserat Rod

In this paper, we design feedback control laws for soft robots modelled using the Cosserat rod theory, which is spatially discretised using the Piecewise Constant Strain (PCS) approach. The PCS approach approximates the nonlinear PDEs describing the Cosserat rod by a finite-dimensional system of nonlinear ODEs. This simplification results in a model describing soft robots which is similar to the serial rigid-link manipulators. We design feedback control laws for the quasi-static PCS model by using external wrenches as control inputs. The control laws are designed based on feedback linearisation in strain and task spaces. An extensive set of numerical results demonstrates the performance of the control laws for end-effector trajectory tracking and shape control of soft robots.

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arXiv2026

Tracking Control for a Dynamic Model of an Underwater Submersible

Underwater vehicles are naturally modelled as rigid bodies on SE(3) subjected to added mass effects. The passivity of the Hamiltonian structure of the system can be exploited to design energy-based stabilising controllers, however, the extension of these control designs to tracking control is not trivial since the error system for the classical error formulations is not itself Hamiltonian. In this paper, we show that a novel choice of error function leads to error dynamics that are Hamiltonian. We go on to derive an energy-based tracking control for a fully coupled model of a submersible vehicle. Asymptotic convergence of the control scheme is proved and the control is demonstrated in a simulation study of the Blue Robotics BlueROV2 Heavy submersible.

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arXiv2026

Synchronous Observer Design for Landmark-Inertial SLAM with Magnetometer and Intermittent GNSS Measurements

In Landmark-Inertial Simultaneous Localisation and Mapping (LI-SLAM), the positions of landmarks in the environment and the robot's pose relative to these landmarks are estimated using landmark position measurements, and measurements from the Inertial Measurement Unit (IMU). However, the robot and landmark positions in the inertial frame, and the yaw of the robot, are not observable in LI-SLAM. This paper proposes a nonlinear observer for LI-SLAM that overcomes the observability constraints with the addition of intermittent GNSS position and magnetometer measurements. The full-state error dynamics of the proposed observer is shown to be both almost-globally asymptotically stable and locally exponentially stable, and this is validated using simulations.

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arXiv2026

Bounds of Validity for Bifurcations of Equilibria in a Class of Networked Dynamical Systems

Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of validity for the classification of bifurcation diagrams in two classes of continuous-time networked dynamical systems, analogous in structure to the Hopfield and the Firing Rate dynamic neural network models. Our approach leverages recent advances in computing the bounds for the validity of Lyapunov-Schmidt reduction, a reduction method widely employed in nonlinear systems analysis. Using these bounds we rigorously characterize neighbourhoods around bifurcation points where predictions from reduced-order bifurcation equations remain reliable. We further demonstrate how these bounds can be applied to an illustrative family of nonlinear opinion dynamics on k-regular graphs, which emerges as a special case of the general framework. These results provide new analytical tools for quantifying the robustness of bifurcation phenomena in dynamics over networked systems and highlight the interplay between network structure and nonlinear dynamical behaviour.

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arXiv2025

Equivariant Tracking Control for Fully Actuated Mechanical Systems on Matrix Lie Groups

Mechanical control systems such as aerial, marine, space, and terrestrial robots often naturally admit a state-space that has the structure of a Lie group. The kinetic energy of such systems is commonly invariant to the induced action by the Lie group, and the system dynamics can be written as a coupled ordinary differential equation on the group and the dual space of its Lie algebra, termed a Lie-Poisson system. In this paper, we show that Lie-Poisson systems can also be written as a left-invariant system on a semi-direct Lie group structure placed on the trivialised cotangent bundle of the symmetry group. The authors do not know of a prior reference for this observation and we are confident the insight has never been exploited in the context of tracking control. We use this representation to build a right-invariant tracking error for the full state of a Lie-Poisson mechanical system and show that the error dynamics for this error are themselves of Lie-Poisson structure, albeit with time-varying inertia. This allows us to tackle the general trajectory tracking problem using an energy shaping design metholodology. To demonstrate the approach, we apply the proposed design methodology to a simple attitude tracking control.

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arXiv2025

Numerical Discretization Schemes that Preserve Flatness

Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems. Although many control systems evolve in continuous time, control implementation is performed digitally, requiring discretization. It is well known in the literature that discretization does not necessarily preserve structural properties, and it has been established that, in general, flatness is not preserved under discretization (whether exact or approximate). In this paper, inspired by our previous work [1] and based on the notion of discretization maps, we construct numerical schemes that preserve flatness.

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arXiv2025

Synchronous Observer Design for Landmark-Inertial SLAM with Almost-Global Convergence

Landmark Inertial Simultaneous Localisation and Mapping (LI-SLAM) is the problem of estimating the locations of landmarks in the environment and the robot's pose relative to those landmarks using landmark position measurements and measurements from Inertial Measurement Unit (IMU). This paper proposes a nonlinear observer for LI-SLAM posed in continuous time and analyses the observer in a base space that encodes all the observable states of LI-SLAM. The local exponential stability and almost-global asymptotic stability of the error dynamics in base space is established in the proof section and validated using simulations.

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arXiv2025

Robust Orientation Estimation with TRIAD-aided Manifold EKF

The manifold extended Kalman filter (Manifold EKF) has found extensive application for attitude determination. Magnetometers employed as sensors for such attitude determination are easily prone to disturbances by their sensitivity to calibration and external magnetic fields. The TRIAD (Tri-Axial Attitude Determination) algorithm is well known as a sub-optimal attitude estimator. In this article, we incorporate this sub-optimal feature of the TRIAD in mitigating the influence of the magnetometer reading in the pitch and roll axis determination in the Manifold EKF algorithm. We substantiate our results with experiments.

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arXiv2024

Feedback Linearizable Discretizations of Second Order Mechanical Systems using Retraction Maps

Mechanical systems are most often described by a set of continuous-time, nonlinear, second-order differential equations (SODEs) of a particular structure governed by the covariant derivative. The digital implementation of controllers for such systems requires a discrete model of the system and hence requires numerical discretization schemes. Feedback linearizability of such sampled systems, however, depends on the discretization scheme employed. In this article, we utilize retraction maps and their lifts to construct feedback linearizable discretizations for SODEs which can be applied to many mechanical systems.

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arXiv2024

Estimates on the domain of validity for Lyapunov-Schmidt reduction

Lyapunov-Schmidt reduction is a dimensionality reduction technique in nonlinear systems analysis that is commonly utilised in the study of bifurcation problems in high-dimensional systems. The method is a systematic procedure for reducing the dimensionality of systems of algebraic equations that have singular points, preserving essential features of their solution sets. In this article, we establish estimates for the region of validity of the reduction by leveraging recently derived bounds on the Implicit Function Theorem. We then apply these bounds to an illustrative example of a two-dimensional system with a pitchfork bifurcation.

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arXiv2024

Stability of multiplexed NCS based on an epsilon-greedy algorithm for communication selection

In this letter, we study a Networked Control System (NCS) with multiplexed communication and Bernoulli packet drops. Multiplexed communication refers to the constraint that transmission of a control signal and an observation signal cannot occur simultaneously due to the limited bandwidth. First, we propose an epsilon-greedy algorithm for the selection of the communication sequence that also ensures Mean Square Stability (MSS). We formulate the system as a Markovian Jump Linear System (MJLS) and provide the necessary conditions for MSS in terms of Linear Matrix Inequalities (LMIs) that need to be satisfied for three corner cases. We prove that the system is MSS for any convex combination of these three corner cases. Furthermore, we propose to use the epsilon-greedy algorithm with the epsilon that satisfies MSS conditions for training a Deep Q Network (DQN). The DQN is used to obtain an optimal communication sequence that minimizes a quadratic cost. We validate our approach with a numerical example that shows the efficacy of our method in comparison to the round-robin and a random scheme.

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arXiv2024

Constructing Dynamic Feedback Linearizable Discretizations

Dynamic feedback linearization-based methods allow us to design control algorithms for a fairly large class of nonlinear systems in continuous time. However, this feature does not extend to their sampled counterparts, i.e., for a given dynamically feedback linearizable continuous time system, its numerical discretization may fail to be so. In this article, we present a way to construct discretization schemes (accurate up to first order) that result in schemes that are feedback linearizable. This result is an extension of our previous work, where we had considered only static feedback linearizable systems. The result presented here applies to a fairly general class of nonlinear systems, in particular, our analysis applies to both endogenous and exogenous types of feedback. While the results in this article are presented on a control affine form of nonlinear systems, they can be readily modified to general nonlinear systems.

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arXiv2024

Exploiting Equivariance in the Design of Tracking Controllers for Euler-Poincare Systems on Matrix Lie Groups

The trajectory tracking problem is a fundamental control task in the study of mechanical systems. A key construction in tracking control is the error or difference between an actual and desired trajectory. This construction also lies at the heart of observer design and recent advances in the study of equivariant systems have provided a template for global error construction that exploits the symmetry structure of a group action if such a structure exists. Hamiltonian systems are posed on the cotangent bundle of configuration space of a mechanical system and symmetries for the full cotangent bundle are not commonly used in geometric control theory. In this paper, we propose a group structure on the cotangent bundle of a Lie group and leverage this to define momentum and configuration errors for trajectory tracking drawing on recent work on equivariant observer design. We show that this error definition leads to error dynamics that are themselves ``Euler-Poincare like'' and use these to derive simple, almost global trajectory tracking control for fully-actuated Euler-Poincare systems on a Lie group state space.

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arXiv2023

Implicit Function Theorem: Estimates on the size of the domain

In this article, we present explicit estimates of the size of the domain on which the Implicit Function Theorem and the Inverse Function Theorem are valid. For maps that are twice continuously differentiable, these estimates depend upon the magnitude of the first-order derivatives evaluated at the point of interest, and a bound on the second-order derivatives over a region of interest. One of the key contributions of this article is that the estimates presented require minimal numerical computation. In particular, these estimates are arrived at without any intermediate optimization procedures. We then present three applications in optimization and systems and control theory where the computation of such bounds turns out to be important. First, in electrical networks, the power flow operations can be written as Quadratically Constrained Quadratic Programs (QCQPs), and we utilize our bounds to compute the size of permissible power variations to ensure stable operations of the power system network. Second, the robustness margin of positive definite solutions to the Algebraic Riccati Equation (frequently encountered in control problems) subject to perturbations in the system matrices are computed with the aid of our bounds. Finally, we employ these bounds to provide quantitative estimates of the size of the domains for feedback linearization of discrete-time control systems.

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arXiv2023

A discrete-time Pontryagin maximum principle under rate constraints

Limited bandwidth and limited saturation in actuators are practical concerns in control systems. Mathematically, these limitations manifest as constraints being imposed on the control actions, their rates of change, and more generally, the global behavior of their paths. While the problem of actuator saturation has been studied extensively, little attention has been devoted to the problem of actuators having limited bandwidth. While attempts have been made in the direction of incorporating frequency constraints on state-action trajectories before, rate constraints on the control at the design stage have not been studied extensively in the discrete-time regime. This article contributes toward filling this lacuna. In particular, we establish a new discrete-time Pontryagin maximum principle with rate constraints being imposed on the control trajectories, and derive first-order necessary conditions for optimality. A brief discussion on the existence of optimal control is included, and numerical examples are provided to illustrate the results.

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arXiv2023

Constructing Feedback Linearizable Discretizations for Continuous-Time Systems using Retraction Maps

Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. Numerical discretization of the continuous system is an integral part of subsequent analysis. Feedback linearizability of such sampled systems is dependent upon the choice of discretization map or technique. In this article, for feedback linearizable continuous-time systems, we utilize the idea of retraction maps to construct discretizations that are feedback linearizable as well. We also propose a method to functionally compose discretizations to obtain higher-order integrators that are feedback linearizable.

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