arXiv subjects

Ankit Goel

Publications and source records attributed to Ankit Goel.

At least 37 records · Page 2Linked to original sources

arXiv2025

Computing Invariant Zeros of a MIMO Linear System Using State-Space Realization

Poles of a multi-input multi-output (MIMO) linear system can be computed by solving an eigenvalue problem; however, the problem of computing its invariant zeros is equivalent to a generalized eigenvalue problem. This paper revisits the problem of computing the invariant zeros by solving an eigenvalue problem. We introduce a realization called the invariant zero form in which the system's invariant zeros are isolated in a partition of the transformed dynamics matrix. It is shown that the invariant zeros are then the eigenvalues of a partition of the transformed dynamics matrix. Although the paper's main result is proved only for square MIMO systems, the technique can be heuristically extended to nonsquare MIMO systems, as shown in the numerical examples.

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arXiv2025

Swarm-optimized Adaptive Augmentation of Missile Autopilot

This paper considers the problem of optimizing a missile autopilot. In particular, the paper investigates the application of an online learning technique to learn and optimize the gains of a three-loop topology autopilot for a planar missile modeled with nonlinear dynamics and nonlinear aerodynamics forces and moments. The classical autopilot for a missile is based on a three-loop topology, where each loop consists of tunable proportional gains. An adaptive three-loop autopilot is constructed by augmenting the classical autopilot's fixed-gain controllers with a learning-based controller, which is recursively optimized using retrospective cost optimization. Numerical simulations show that online learning improves the tracking performance of the classical autopilot in both nominal and off-nominal interception scenarios.

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arXiv2025

Feedback Linearization-based Guidance Law for Guaranteed Interception

This paper presents an input-output feedback linearization (IOL)-based guidance law to ensure interception in a pursuer-evader engagement scenario. A point-mass dynamic model for both the pursuer and the evader is considered. An IOL guidance law is derived using range and line-of-sight (LOS) rate measurements. It is found that the range-based IOL guidance law exhibits a singularity under certain conditions. To address this issue, a fuzzy logic system is employed to smoothly blend the IOL guidance with the classical proportional guidance law, thereby avoiding the singularity. In contrast, the LOS-based IOL guidance law is free of singularities but suffers from divergence issues due to angle-related complications. To resolve this, a simple correction function is introduced to ensure consistent interception behavior. Results from Monte Carlo simulations indicate that both modifications of the IOL guidance laws cause interception with control limits applied.

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arXiv2025

An In-situ Solid Fuel Ramjet Thrust Monitoring and Regulation Framework Using Neural Networks and Adaptive Control

Controlling the complex combustion dynamics within solid fuel ramjets (SFRJs) remains a critical challenge limiting deployment at scale. This paper proposes the use of a neural network model to process in-situ measurements for monitoring and regulating SFRJ thrust with a learning-based adaptive controller. A neural network is trained to estimate thrust from synthetic data generated by a feed-forward quasi-one-dimensional SFRJ model with variable inlet control. An online learning controller based on retrospective cost optimization is integrated with the quasi-one-dimensional SFRJ model to regulate the thrust. Sensitivity studies are conducted on both the neural network and adaptive controller to identify optimal hyperparameters. Numerical simulation results indicate that the combined neural network and learning control framework can effectively regulate the thrust produced by the SFRJ model using limited in-situ data.

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arXiv2025

A Novel Neural Filter to Improve Accuracy of Neural Network Models of Dynamic Systems

The application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where the prediction error diverges over time, thus degrading their accuracy. This paper presents a neural filter to enhance the accuracy of long-term state predictions of neural network-based models of dynamic systems. Motivated by the extended Kalman filter, the neural filter combines the neural network state predictions with the measurements from the physical system to improve the estimated state's accuracy. The neural filter's improvements in prediction accuracy are demonstrated through applications to four nonlinear dynamical systems. Numerical experiments show that the neural filter significantly improves prediction accuracy and bounds the state estimate covariance, outperforming the neural network predictions. Furthermore, it is also shown that the accuracy of a poorly trained neural network model can be improved to the same level as that of an adequately trained neural network model, potentially decreasing the training cost and required data to train a neural network.

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arXiv2025

Single-Shot Learning of Multirotor Controller Gains: A Data-Driven Approach with Experimental Validation

This paper demonstrates the single-shot learning capabilities of retrospective cost optimization based data-driven control applied to learning multirotor controller gains for trajectory tracking. In particular, the proposed control approach is first used within a simple multirotor simulation environment to learn appropriate multirotor controller gains to follow a trajectory. Then, the gains resulting from a single simulation run are used in a more complex multirotor simulation environment based on Simulink for performance verification. Finally, the resulting gains are implemented in a physical quadrotor and the results for waypoint and trajectory tracking are reported in this paper. The proposed control approach is the continuous-time version of the widely used discrete-time retrospective control adaptive control algorithm, which is simpler to implement within continuous-time simulation environments and whose performance does not depend on appropriate sampling time choice.

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arXiv2025

Continuous-Time Output Feedback Adaptive Control for Stabilization and Tracking with Experimental Results

This paper presents a continuous-time output feedback adaptive control technique for stabilization and tracking control problems. The adaptive controller is motivated by the classical discrete-time retrospective cost adaptive control algorithm. The particle swarm optimization framework automates the adaptive algorithm's hyper-parameter tuning. The proposed controller is numerically validated in the tracking problems of a double integrator and a bicopter system and is experimentally validated in an attitude stabilization problem. Numerical and experimental results show that the proposed controller is an effective technique for model-free output feedback control.

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arXiv2025

Model-free Dynamic Mode Adaptive Control using Matrix RLS

This paper presents a novel, model-free, data-driven control synthesis technique known as dynamic mode adaptive control (DMAC) for synthesizing controllers for complex systems whose mathematical models are not suitable for classical control design. DMAC consists of a dynamics approximation module and a controller module. The dynamics approximation module is motivated by data-driven reduced-order modeling techniques and directly approximates the system's dynamics in state-space form using a matrix version of the recursive least squares algorithm. The controller module includes an output tracking controller that utilizes sparse measurements from the system to generate the control signal. The DMAC controller design technique is demonstrated through various dynamic systems commonly found in engineering applications. A systematic sensitivity study demonstrates the robustness of DMAC with respect to its own hyperparameters and the system's parameters.

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arXiv2025

Data-driven Fuzzy Control for Time-Optimal Aggressive Trajectory Following

Optimal trajectories that minimize a user-defined cost function in dynamic systems require the solution of a two-point boundary value problem. The optimization process yields an optimal control sequence that depends on the initial conditions and system parameters. However, the optimal sequence may result in undesirable behavior if the system's initial conditions and parameters are erroneous. This work presents a data-driven fuzzy controller synthesis framework that is guided by a time-optimal trajectory for multicopter tracking problems. In particular, we consider an aggressive maneuver consisting of a mid-air flip and generate a time-optimal trajectory by numerically solving the two-point boundary value problem. A fuzzy controller consisting of a stabilizing controller near hover conditions and an autoregressive moving average (ARMA) controller, trained to mimic the time-optimal aggressive trajectory, is constructed using the Takagi-Sugeno fuzzy framework.

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arXiv2025

Adaptive Control of Dual-Rotor Rotational System with Unknown Geometry and Unknown Inertia

This paper develops an input-output feedback linearization-based adaptive controller to stabilize and regulate a dual-rotor rotational system (DRRS), whose inertial properties as well as the geometric configuration of rotors are unknown. First, the equations of motion governing the dynamics of DRRS are derived using the Newton-Euler approach. Next, an input-output feedback linearization technique is used to linearize the dynamics from the rotor speeds to the angular position of the system. A finite-time convergent estimator, based on the portion of the DRRS dynamics, is used to update the required parameters in the controller. Finally, the proposed controller is validated in both step and harmonic command-following problems, and the robustness of the controller to the system's parameters is demonstrated.

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arXiv2025

Learning-based Attitude Estimation with Noisy Measurements and Unknown Gyro Bias

This paper introduces a learning-based, data-driven attitude estimator, called the retrospective cost attitude estimator (RCAE), for the SO(3) attitude representation. RCAE is motivated by the multiplicative extended Kalman filter (MEKF). However, unlike MEKF, which requires computing a Jacobian to compute the correction signal, RCAC uses retrospective cost optimization that depends only on the measured data. Moreover, due to the structure of the correction signal, RCAE does not require explicit estimation of gyro bias. The performance of RCAE is verified and compared with MEKF through both numerical simulations and physical experiments.

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arXiv2024

MPC-guided, Data-driven Fuzzy Controller Synthesis

Model predictive control (MPC) is a powerful control technique for online optimization using system model-based predictions over a finite time horizon. However, the computational cost MPC requires can be prohibitive in resource-constrained computer systems. This paper presents a fuzzy controller synthesis framework guided by MPC. In the proposed framework, training data is obtained from MPC closed-loop simulations and is used to optimize a low computational complexity controller to emulate the response of MPC. In particular, autoregressive moving average (ARMA) controllers are trained using data obtained from MPC closed-loop simulations, such that each ARMA controller emulates the response of the MPC controller under particular desired conditions. Using a Takagi-Sugeno (T-S) fuzzy system, the responses of all the trained ARMA controllers are then weighted depending on the measured system conditions, resulting in the Fuzzy-Autoregressive Moving Average (F-ARMA) controller. The effectiveness of the trained F-ARMA controllers is illustrated via numerical examples.

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arXiv2024

Singularity-free Backstepping-based Adaptive Control of a Bicopter with Unknown Mass and Inertia

The paper develops a singularity-free backstepping-based adaptive control for stabilizing and tracking the trajectory of a bicopter system. In the bicopter system, the inertial parameters parameterize the input map. Since the classical adaptive backstepping technique requires the inversion of the input map, which contains the estimate of parameter estimates, the stability of the closed-loop system cannot be guaranteed due to the inversion of parameter estimates. This paper proposes a novel technique to circumvent the inversion of parameter estimates in the control law. The resulting controller requires only the sign of the unknown parameters. The proposed controller is validated in simulation for a smooth and nonsmooth trajectory-tracking problem.

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arXiv2024

Adaptive Nonlinear Control of a Bicopter with Unknown Dynamics

This paper presents an adaptive, model-based, nonlinear controller for the bicopter trajectory-tracking problem. The nonlinear controller is constructed by dynamically extending the bicopter model, stabilizing the extended dynamics using input-output linearization, augmenting the controller with a finite-time convergent parameter estimator, and designing a linear tracking controller. Unlike control systems based on the time separation principle to separate the translational and rotational dynamics, the proposed technique is applied to design a controller for the full nonlinear dynamics of the system to obtain the desired transient performance. The proposed controller is validated in simulation for a smooth and nonsmooth trajectory-tracking problem.

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arXiv2024

Computing Invariant Zeros of a Linear System Using State-Space Realization

It is well known that zeros and poles of a single-input, single-output system in the transfer function form are the roots of the transfer function's numerator and the denominator polynomial, respectively. However, in the state-space form, where the poles are a subset of the eigenvalue of the dynamics matrix and thus can be computed by solving an eigenvalue problem, the computation of zeros is a non-trivial problem. This paper presents a realization of a linear system that allows the computation of invariant zeros by solving a simple eigenvalue problem. The result is valid for square multi-input, multi-output (MIMO) systems, is unaffected by lack of observability or controllability, and is easily extended to wide MIMO systems. Finally, the paper illuminates the connection between the zero-subspace form and the normal form to conclude that zeros are the poles of the system's zero dynamics

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arXiv2024

Adaptive Backstepping Control of a Bicopter in Pure Feedback Form with Dynamic Extension

This paper presents a model-based, adaptive, nonlinear controller for the bicopter stabilization and trajectory-tracking problem. The nonlinear controller is designed using the backstepping technique. Due to the non-invertibility of the input map, the bicopter system is first dynamically extended. However, the resulting dynamically extended system is in the pure feedback form with the uncertainty appearing in the input map. The adaptive backstepping technique is then extended and applied to design the controller. The proposed controller is validated in simulation for a smooth and nonsmooth trajectory-tracking problem.

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arXiv2024

Retrospective Cost-based Extremum Seeking Control with Vanishing Perturbation for Online Output Minimization

Extremum seeking control (ESC) constitutes a powerful technique for online optimization with theoretical guarantees for convergence to the neighborhood of the optimizer under well-understood conditions. However, ESC requires a nonconstant perturbation signal to provide persistent excitation to the target system to yield convergent results, which usually results in steady state oscillations. While certain techniques have been proposed to eliminate perturbations once the neighborhood of the minimizer is reached, system modifications and environmental perturbations can suddenly change the minimizer and nonconstant perturbations would once more be required to convergence to the new minimizer. Hence, this paper develops a retrospective cost-based ESC(RC/ESC) technique for online output minimization with a vanishing perturbation, that is, a perturbation that becomes zero as time increases independently from the state of the controller or the controlled system. The performance of the proposed algorithm is illustrated via numerical examples.

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arXiv2023

Circumventing Unstable Zero Dynamics in Input-Output Linearization of Longitudinal Flight Dynamics

In this paper, we consider the problem of input-output linearization of the longitudinal flight dynamics. In longitudinal flight dynamics, inputs are typically thrust and elevator deflection whereas the outputs are the velocity and the flight path angle. An input-output linearization-based controller can be designed to render the multi-input, multi-output system linear; however, the resulting zero dynamics turns out to be unstable. In this work, we remove the zero dynamics from the closed-loop dynamics by considering an additional output. Although the additional output makes the system tall, which, in general, means that the input-to-output dynamics can not be linearized, we show that in the case of longitudinal flight dynamics, linearization is possible due to special geometric properties of the nonlinear terms.

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