Ramesh K. Agarwal

Beyond Navier–Stokes: Burnett equations for flows in the continuum–transition regime

In hypersonic flows about space vehicles in low earth orbits or flows in microchannels of microelectromechanical devices, the local Knudsen number lies in the continuum–transition regime. Navier–Stokes equations are not adequate to model these flows since they are based on small deviation from local thermodynamic equilibrium. To model these flows, a number of extended hydrodynamics or generalized hydrodynamics models have been proposed over the past fifty years, along with the direct simulation Monte Carlo (DSMC) approach. One of these models is the Burnett equations which are obtained from the Chapman–Enskog expansion of the Boltzmann equation [with Knudsen number (Kn) as a small parameter] to O(Kn2). With the currently available computing power, it has been possible in recent years to numerically solve the Burnett equations. However, attempts at solving the Burnett equations have uncovered many physical and numerical difficulties with the Burnett model. As a result, several improvements to the conventio...

Mixed H-Infinity and Passive Filtering for Discrete Fuzzy Neural Networks With Stochastic Jumps and Time Delays

In this brief, the problems of the mixed H-infinity and passivity performance analysis and design are investigated for discrete time-delay neural networks with Markovian jump parameters represented by Takagi-Sugeno fuzzy model. The main purpose of this brief is to design a filter to guarantee that the augmented Markovian jump fuzzy neural networks are stable in mean-square sense and satisfy a prescribed passivity performance index by employing the Lyapunov method and the stochastic analysis technique. Applying the matrix decomposition techniques, sufficient conditions are provided for the solvability of the problems, which can be formulated in terms of linear matrix inequalities. A numerical example is also presented to illustrate the effectiveness of the proposed techniques.

Stochastic finite-time state estimation for discrete time-delay neural networks with Markovian jumps

Abstract This paper investigates the problem of stochastic finite-time state estimation for a class of uncertain discrete-time Markovian jump neural networks with time-varying delays. A state estimator is designed to estimate the network states through available output measurements such that the resulted error dynamics is stochastically finite-time stable. By stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are derived for the error dynamics to be stochastic finite-time stable. The desired state estimator is designed via linear matrix inequality technique. Simulation examples are provided to illustrate the effectiveness of the obtained results.

Optimal guaranteed cost control of uncertain discrete time-delay systems

This paper considers the problem of robust guaranteed cost control of linear discrete time-delay systems with parametric uncertainties. By matrix inequality approach, the robust quadratic stability of the system is studied. A control design method is developed such that the closed-loop system with a cost function has a upper bound irrespective of all admissible parameter uncertainties and unknown time delays. Furthermore, the upper bound (cost) can be optimized by incorporating with a minimization problem. A numerical example is given to show the potential of the proposed techniques.

Automatic Landing System Design Using Fuzzy Logic

A fuzzy logic system is developed for automatic landing control of a transport aircraft. A linear longitudinal aircraft model, with landing gear and flaps deployed at the sea level, is employed for fuzzy logic controller design of automatic landing system including the two landing phases - the glide-path capture and the flare maneuver. In addition, the fuzzy control system is tested using different values of fuzzy controller scaling factors on a six degree of. freedom nonlinear aircraft model. It is shown that the simple tuning fuzzy controller with altered scaling factors is well suited for controlling the trajectory of the aircraft in the landing phase which requires simultaneous control of engine thrust for the velocity and elevator for the pitch attitude in order to change altitude with a constant airspeed.

Design of Automatic Landing Systems Using Mixed H/H Control

Mixed H2/HX control technique is employed to develop controllers for auto-landing systems for a commercial airplane. A linear model of the aircraft in longitudinal motion is established using the appropriate aerodynamic coefficients. With the control actuator, tracking errors, and altitude motion, the aircraft is shown to be governed by an augmentation system along with its filter model. Two kinds of optimal and robust control requirements are designed, which need to be satisfied simultaneously. One of requirements is with respect to an optimal trajectory selection for landing routes. The H2 method is used to minimize a cost function such that the optimal gain for trajectory optimization can be obtained. The other requirement is with respect to the disturbance attenuation. The Hm technique is employed to obtain the necessary formulation for the robust control gain to minimize the affection of the disturbance to the performance output. An algorithm is developed based on the convex theory for the mixed H2I Hn control and filter gains, which provides a suboptimal solution. A large commercial aircraft (Boeing 747-200) is employed to illustrate the potential of the proposed method. It is shown that the glide slope capture motion and flare maneuver of the aircraft are accomplished quite well, and the amplitudes of all maneuver are within FAA requirements. L INTRODUCTION Control of aircraft under difficult maneuvers is a problem of both theoretical and practical interest. Control under one of these difficult maneuvers, that of landing, is discussed and addressed in this paper. Design of automatic landing systems has been achieved using both robust and optimal control methods [1-3]. Reference [1] employed the #„ synthesis to design an automatic landing controller for an F-14 aircraft. Design of landing systems encountering windshear is given in

Fault detection for networked control systems with quantization and Markovian packet dropouts

In this paper, the problem of fault detection is investigated for networked control systems with signal quantization and random packet dropouts. In the study, the packet dropouts are modeled by a time-homogeneous Markov process. A residual generator is constructed, and the corresponding fault detection problem is converted into an H ∞ filtering problem. A sufficient condition for the design of fault detection is derived, which makes the resulting residual system to be stochastically stable with a prescribed H ∞ performance level. Finally, a numerical example is given to illustrate the effectiveness and efficiency of the proposed design method. HighlightsWe presented a new approach on H-infinity fault detection problem for network control system with quantization and packet dropouts.A two state Markov chain is used to characterize the packet dropout phenomenon of the network.A residual generator is constructed and the corresponding fault detection problem is formulated as an H-infinity filtering problem.A numerical example shows the effectiveness of the obtained design techniques.

Robust finite-time fuzzy H∞ control for uncertain time-delay systems with stochastic jumps

Abstract This paper investigates the problem of robust finite-time H ∞ control for a class of uncertain discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi–Sugeno (T–S) model. Initially, the concepts of stochastic finite-time boundedness and stochastic finite-time H ∞ stabilization are presented. Then, by using stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastically finite-time bounded and satisfies a prescribed H ∞ disturbance attenuation level in a given finite-time interval. Furthermore, sufficient criteria on stochastic finite-time H ∞ stabilization using a fuzzy state-feedback controller are provided, and the controller is designed by solving an optimization problem in terms of linear matrix inequalities. Finally, two numerical examples are exploited to show the validity of the proposed design techniques.

Robust Hinfinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty

This paper studies, via a linear matrix inequality approach, the problem of Hinfinity control for discrete time-delay linear systems with parametric uncertainty. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and time delay in the state. First, the problem of robust stability of the underlying system is investigated. Next, we address the problem of robust Hinfinity state feedback control in which both robust stability and a prescribed Hinfinity performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a linear matrix inequality has a symmetric positive definite solution.

Factors affecting the accuracy of pressure measurements in vascular stenoses from phase-contrast MRI

In this work the effects of noise, resolution, and velocity (flow) on the measurement of intravascular pressure from phase‐contrast (PC) MRI are discussed. To elucidate these effects, we employed an axisymmetric geometry that enabled us to calculate pressures in <2 min on a Sun Ultra SPARC 10 workstation. To determine the effects of vascular stenoses, we fabricated several stenotic phantom geometries (with 50%, 75%, and 90% area stenoses), and performed both MRI and computational fluid dynamics (CFD) simulations for various flow rates for these phantom geometries. Noise with Gaussian statistics was added to the velocity field obtained from the CFD simulations. The pressure maps obtained directly from CFD simulations for our phantom geometries were compared with pressure maps derived by our algorithm when 1) the input was noise‐corrupted velocity data from CFD, and 2) the input was PC‐MRI data collected from the phantoms. The quantitative effects of noise, resolution, and flow rate on the accuracy of pressure measurements were determined. We found that for flow rates below the Reynolds number for turbulent flow, resolution is a more significant determinant of accuracy than SNR. Furthermore, if other parameters remain constant, increased flow rates may result in decreased accuracy. Magn Reson Med 52:300–309, 2004.