Dispersion Analysis in Hypersonic Flight During Planetary Entry Using Stochastic Liouville Equation

Halder, Abhishek; Bhattacharya, Raktim

doi:10.2514/1.51196

Cited by 90 publications

(53 citation statements)

References 25 publications

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“…Building on our earlier work [25,26], we show that stochastic initial condition and parametric uncertainties can be propagated through the closed-loop nonlinear dynamics in exact arithmetic. This is achieved by leveraging the fact that the transfer operator governing the evolution of joint densities is an infinite-dimensional linear operator, even though the underlying finite-dimensional closed-loop dynamics is nonlinear.…”

Section: Introductionmentioning

confidence: 80%

“…It can be shown [26] that the characteristic curves for Eq. (6) are the trajectories of the closed-loop ordinary differential equation (ODE) _ x f cl xt; p; t. If the nonlinear vector field f cl is Lipschitz, then the trajectories are unique, and hence the characteristic curves are nonintersecting.…”

Section: Characteristic Ordinary Differential Equation Computationmentioning

confidence: 99%

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Optimal Transport Approach for Probabilistic Robustness Analysis of F-16 Controllers

Halder

Lee

Bhattacharya

2015

Journal of Guidance, Control, and Dynamics

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This paper presents a new framework for controller robustness verification with respect to an F-16 aircraft's closed-loop performance in longitudinal flight. The state regulation performance of a linear quadratic regulator and a gain-scheduled linear quadratic regulator are compared, where both controllers are applied to nonlinear open-loop dynamics of an F-16, in the presence of stochastic initial condition and parametric uncertainties, as well as actuator disturbance. It is shown that, in the presence of initial condition uncertainties alone, both the linear quadratic regulator and gain-scheduled linear quadratic regulator have comparable immediate and asymptotic performances, but the gain-scheduled linear quadratic regulator exhibits better transient performance at intermediate times. This remains true in the presence of additional actuator disturbance. Also, the gain-scheduled linear quadratic regulator is shown to be more robust than the linear quadratic regulator against parametric uncertainties. The probabilistic framework proposed here leverages transfer-operator-based density computation in exact arithmetic and introduces optimal transport theoretic performance validation and verification for nonlinear dynamical systems. Numerical results from the proposed method are in unison with Monte Carlo simulations.

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Section: Introductionmentioning

confidence: 80%

Section: Characteristic Ordinary Differential Equation Computationmentioning

confidence: 99%

Optimal Transport Approach for Probabilistic Robustness Analysis of F-16 Controllers

Halder

Lee

Bhattacharya

2015

Journal of Guidance, Control, and Dynamics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The easiest, but more expensive in computational terms, is the classical Monte-Carlo method. Halder and Bhattacharya [11] classify those methods in two categories: parametric (in which one evolves the statistical moments) and non-parametric (in which the probability density function is evolved). In this work, a non-parametric method is applied, in which the wind probability density function (pdf) is evolved.…”

Section: Introductionmentioning

confidence: 99%

Stochastic analysis of fuel consumption in aircraft cruise subject to along-track wind uncertainty

Vázquez

Rivas

Franco

2017

Aerospace Science and Technology

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“…A framework based on the stochastic Liouville Equation (SLE) was provided for both three-state and six-state Vinh's equations for hypersonic entry in Mars atmosphere [4]. Wu et al [5] applied the stochastic small-gain theorem and backstepping design technique in the stochastic nonlinear systems with uncertain nonlinear functions and unmodeled dynamics.…”

Section: Introductionmentioning

confidence: 99%

Neural Networks Approximator Based Robust Adaptive Controller Design of Hypersonic Flight Vehicles Systems Coupled with Stochastic Disturbance and Dynamic Uncertainties

Zhu

Sun

Zhang

2017

Mathematical Problems in Engineering

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A neural network robust control is proposed for a class of generic hypersonic flight vehicles with uncertain dynamics and stochastic disturbance. Compared with the present schemes of dealing with dynamic uncertainties and stochastic disturbance, the outstanding feature of the proposed scheme is that only one parameter needs to be estimated at each design step, so that the computational burden can be greatly reduced and the designed controller is much simpler. Moreover, by introducing a performance function in controller design, the prespecified transient and performance of tracking error can be guaranteed. It is proved that all signals of closed-loop system are uniformly ultimately bounded. The simulation results are carried out to illustrate effectiveness of the proposed control algorithm.

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Dispersion Analysis in Hypersonic Flight During Planetary Entry Using Stochastic Liouville Equation

Cited by 90 publications

References 25 publications

Optimal Transport Approach for Probabilistic Robustness Analysis of F-16 Controllers

Optimal Transport Approach for Probabilistic Robustness Analysis of F-16 Controllers

Stochastic analysis of fuel consumption in aircraft cruise subject to along-track wind uncertainty

Neural Networks Approximator Based Robust Adaptive Controller Design of Hypersonic Flight Vehicles Systems Coupled with Stochastic Disturbance and Dynamic Uncertainties

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