Robust Stability Properties Research Articles

Higher-order implicit-explicit multi-domain compressible Navier-Stokes solvers

This paper presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional multi-domains. Building up on the recent single-domain ADI-based high-order Navier-Stokes solvers (Bruno and Cubillos (2016) [11]) this article presents multi-domain implicit-explicit methods of high-order of temporal accuracy. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of high-order backward differentiation formulae (BDF) and an alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Nearly dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. As demonstrated via a variety of numerical experiments in two and three dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, robust stability properties, limited dispersion, and high parallel efficiency.

Two‐Layer Terminal Sliding Mode Attitude Control of Satellites Equipped with Reaction Wheels

AbstractThis paper addresses the global stability and robust attitude tracking problem of a near polar orbit satellite subject to unknown disturbances and uncertainties. It is assumed that the satellite is fully actuated by a set of reaction wheels (RW) as control actuators because of their relative simplicity, versatility and high accuracy. The terminal sliding mode control (TSMC) approach is utilized in a two‐level architecture to achieve control objectives. In the lower layer a detumbling‐like controller is designed which guarantees the finite‐time detumbling and tracking of the desired angular velocities and based on this result a robust attitude tracking controller is designed in the upper layer to achieve 3‐axis attitude tracking in the presence of unknown disturbances and bounded uncertainties. Robust stability and tracking properties of designed controllers are proved using the Lyapunov theory. Finally, a set of numerical simulation results are provided to illustrate the effectiveness and performance of the proposed control method.

Robust nonlinear controller design for uncertain hypersonic vehicles

The problem of robust velocity and height control is dealt with for hypersonic vehicles subject to high nonlinearity and uncertainties. Robust linear controller design for nonlinear systems suffers from the problem of conservation because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve dynamic decoupling of the velocity and height channels. Robust controllers are then designed for each channel to achieve the desired tracking and restrain the effects of parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be accurately counteracted by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system. Moreover, the conservation of the robust controller design can be reduced because the nonlinear information of the dynamic system is used. Simulation results are given to show the advantages of the proposed robust nonlinear control method compared with its linear counterpart.

Robust mechanical stability, electronic structure, magnetism and thermoelectric properties of CoFeMnSb quaternary Heusler alloy: A first principle study

Mechanical, structural, electronic, magnetic and thermoelectric properties of multi functional CoFeMnSb quaternary Heusler alloy have been studied using spin polarized Density Functional and semiclassical Boltzmann transport theory. Ab-initio study reveals halfmetallic ferromagnetic characteristics of the alloy leading to high spin polarization. The calculated value of total magnetic moment (mt = 4.99 μB) almost follow the Slater-Pauling rule which is another prerequisite of halfmetallicity. Study of hydrostatic pressure shows a significant effect on the electronic structure of the alloy however, along with the robust mechanical stability there is no magnetic phase transition seen as such in the whole range of pressure. Due to the occurrence of flat bands near the Fermi level(EF) in the minority spin channel, thermoelectric properties are also studied for both the spin polarized channel using BoltzTraP code under constant relaxation time approximation of the charge carriers. Halfmetallic properties, robust mechanical stability and significantly high value of Seebeck coefficient (∼800μV/K for p-type and ∼−900μV/K for n-type) makes the material promising for spintronic as well as thermoelectric applications.

Robust Global Adaptive Exponential Stabilization of Discrete-Time Systems With Application to Freeway Traffic Control

This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust global exponential convergence to the desired equilibrium point of the system. The proposed control scheme consists of a nominal feedback law, which achieves robust global exponential stability properties when the vector of the parameters is known, in conjunction with a nonlinear dead-beat observer. The proposed adaptive control scheme depends on certain parameter observability assumptions. The obtained results are applicable to highly nonlinear uncertain discrete-time systems with unknown constant parameters. The successful applicability of the obtained results to real control problems is demonstrated by the rigorous application of the proposed adaptive control scheme to uncertain freeway models. A provided example demonstrates the efficiency of the approach.

High-Performance Porous Molybdenum Oxynitride Based Fiber Supercapacitors.

Scalable manufacturing of flexible, fiber-shaped energy-storage devices has enabled great technological advances in wearable and portable technology. Replacing inefficient oxides with inexpensive and high-performance oxynitrides with more favorable three-dimensional (3D) structures is critical if the practical applications of these technologies are to be realized. Here, we developed a facile and controllable approach for the synthesis of 3D porous micropillars of molybdenum oxynitride (MON), which exhibit high conductivity, robust stability, and excellent energy-storage properties. Our fiber electrode, containing a 3D hierarchical MON-based anode, yields remarkable linear and areal specific capacitances of 64.8 mF cm-1 and 736.6 mF cm-2, respectively, at a scan rate of 10 mV s-1. Moreover, a wearable asymmetric supercapacitor based on TiN/MON//TiN/MnO2 demonstrates good cycling stability with a linear capacitance of 12.7 mF cm-1 at a scan rate of 10 mV s-1. These remarkable electrochemical properties are mainly attributed to the synergistic effect between the chemical composition of oxynitride and the robust 3D porous structure composed of interconnected nanocrystalline morphology. The presented strategy for the controllable design and synthesis of novel-oxide-derived functional materials offers prospects in developing portable and wearable electronic devices. We also demonstrate that these fiber supercapacitors can be combined with an organic solar cell to construct a self-powered system for broader applications.

A robust suboptimal control system design of chaotic PMSMs

Chaotic phenomenon of power electronic systems and electric motor drives were introduced a few decades ago and has been followed with numerous of published work. However, chaos of permanent magnet synchronous motors (PMSMs), in particular, did not receive enough deserved interest. Considering this fact, this paper introduces a robust suboptimal control system for chaotic PMSMs. The proposed control system includes a suboptimal speed controller and a suboptimal load torque observer. The stability analysis and robustness properties of the proposed control system are presented in detail in this paper. Thanks to its robustness properties, the proposed suboptimal control system can not only eliminate the chaos but also provide better performances than conventional methods. Extensive simulations results under various scenarios prove the superiority of the proposed control technique over conventional controllers for chaotic PMSMs even under the condition of parameter uncertainties and variations of load torque disturbance.

Interaction of open and closed loop control in MPC

We present a novel MPC algorithm without terminal constraints and/or costs, for which the prediction horizon is reduced in comparison to standard MPC while asymptotic stability and inherent robustness properties are maintained. To this end, we derive simplified stability conditions and investigate the interplay of open and closed loop control in MPC. The insight gained from this analysis allows to close the control loop more often while keeping the computational complexity of basic MPC. Our findings are verified by numerical simulations.

Qualitative equivalences of ISS and [formula omitted]-gain stability properties for discrete-time nonlinear systems

Input-to-state stability (ISS) and input–output L2-gain are two important robust stability concepts in analyzing the interconnections of nonlinear dynamical systems. In this paper, we demonstrate several qualitative equivalences between different ISS related properties and lp-gain properties for discrete-time systems via nonlinear changes of coordinates. Prior to that, certain summation-to-summation estimates are shown to be equivalent to the standard definitions of ISS and integral ISS (iISS) which lead to sufficient Lyapunov function conditions to verify lp-gain properties. Combined with known results on the equivalence of 0-input global asymptotic stability and iISS, and a superposition principle, we subsequently outline interesting implicative relationships between various discrete-time robust stability properties.

An <i>H</i><sub>∞</sub> Design Approach for a PID Automatic Flight Control System of a Launch Vehicle

The paper presents a design methodology for the automatic flight control of a launch vehicle. In the proposed approach the controller has a PID (Proportional-Integral-Derivative) structure but its gains are determined solving an H∞ norm minimization problem of the mapping from the atmospheric disturbances to the control amplitude and to the angle of attack of the launcher. The design methodology is illustrated by numerical examples in which both time responses and stability robustness properties of the optimal PID controller are analyzed.

Aerodynamic Moment Model Calibration from Distributed Pressure Arrays

In recent years, studies on the role of distributed airflow mechanosensors in bird, bat, and insect flight behaviors have sparked a growing interest in integrating flow sensors, such as pressure or hair sensors, into flight control feedback systems of small unmanned aircraft. It is anticipated that a flight controller based on real-time distributed flow information feedback is more capable of rapidly responding to sudden airflow changes and may exhibit greater stability robustness properties than purely inertial feedback-based flight control laws. However, considering the uncertainty of state-of-the-art microflow sensor technologies, there is an urgent need for model calibration if flow information is to be used to calculate aerodynamic moments and/or forces for controlling aircraft motion. In this paper, a constrained least-squares estimator is developed to calculate the bias of distributed flow information to calibrate an aerodynamic moment model. Simulation and wind-tunnel experiment results demonstrate a significant improvement on the accuracy of the aerodynamic moment calculation after calibration.

Robust stability of dynamic predictor based control laws for input and state delay systems

The robust stability properties of the dynamic predictor scheme for state and input delay systems are analyzed in the frequency domain. Robust stability bounds are presented for the cases of uncertainty of the matrix parameters, of the state or input delay, and of the combination of both. An example illustrates the results.

SHG10 keratinolytic alkaline protease from Bacillus licheniformis SHG10 DSM 28096: Robust stability and unusual non-cumbersome purification.

Present study underlines an unusual non-cumbersome-powerful strategy for purification of SHG10 keratinolytic alkaline protease from Bacillus licheniformis SHG10 DSM 28096 with robust stability properties. The enzyme was impressively purified to homogeneity with specific activity, purification fold, and yield of 613.82 U mg-1 , 58.91 and 99%, respectively, via a sequential two-step purification strategy: precipitation with 65% (NH4 )2 SO4 and flow through fractions of DEAE-cellulose DE 53 column. SDS-PAGE conferred a monomeric enzyme with a molecular mass of 30.4 kDa. The enzyme demonstrated optimal activity at pH (10.0-11.0) and at 65 °C. It exhibited full stability at pH (6.0-11.0) over 38 h at 4 °C and at 65 °C for 15 min. Remarkable enhanced enzyme activity (130.15 and 126.37%) was retained in presence of commercial laundry detergents Oxi and Ariel after 1 h, respectively. Organic solvent stability of the enzyme was verified in butanol, ether, acetonitrile, isopropanol, and chloroform. Imposingly, full storage stability (100%) of the enzyme along 1 year in -20 °C was confirmed. Km -Vmax was 0.00174 mM-534.2 mM Sub · min-1 · mg protein-1 and 1.266 mg-28.89 mg Sub · h-1 · mg protein-1 on N-Suc-Ala-Ala-Pro-Phe-pNA and keratin azure, respectively. Robust stability properties of SHG10 keratinolytic alkaline protease along with rapid-efficient purification underpin its potential commercialization for industrial exploitation.

Linear Closed-Loop Control of Fluid Instabilities and Noise-Induced Perturbations: A Review of Approaches and Tools1

This review article is concerned with the design of linear reduced-order models and control laws for closed-loop control of instabilities in transitional flows. For oscillator flows, such as open-cavity flows, we suggest the use of optimal control techniques with Galerkin models based on unstable global modes and balanced modes. Particular attention has to be paid to stability–robustness properties of the control law. Specifically, we show that large delays and strong amplification between the control input and the estimation sensor may be detrimental both to performance and robustness. For amplifier flows, such as backward-facing step flow, the requirement to account for the upstream disturbance environment rules out Galerkin models. In this case, an upstream sensor is introduced to detect incoming perturbations, and identification methods are used to fit a model structure to available input–output data. Control laws, obtained by direct inversion of the input–output relations, are found to be robust when applied to the large-scale numerical simulation. All the concepts are presented in a step-by-step manner, and numerical codes are provided for the interested reader.

Input-to-State Stability, Integral Input-to-State Stability, and <inline-formula> <tex-math notation="LaTeX">${\cal L}_{2} $</tex-math></inline-formula>-Gain Properties: Qualitative Equivalences and Interconnected Systems

Input-to-state stability (ISS) and ${\cal L}_{2} $ -gain are well-known robust stability properties that continue to find wide application in the analysis and control of nonlinear dynamical systems and their interconnections. We investigate the relationship between ISS-type and ${\cal L}_{2} $ -gain properties, demonstrating several qualitative equivalences between these two properties via coordinate transformations. In particular, we investigate and clearly specify the relationship between ISS and linear ${\cal L}_{2}$ -gain, and between integral ISS and nonlinear ${\cal L}_{2} $ -gain. This latter relationship raises an interesting question as it is known that cascade and feedback interconnections of integral ISS systems are not generally well-behaved, whereas we demonstrate that such interconnections for systems with nonlinear ${\cal L}_{2} $ -gain are well-behaved. We subsequently present several new sufficient conditions for the stability of interconnected systems derived by exploiting the derived qualitative equivalences.

Proximal Markov chain Monte Carlo algorithms

This paper presents a new Metropolis-adjusted Langevin algorithm (MALA) that uses convex analysis to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in modern high-dimensional statistics and data analysis. The method is based on a new first-order approximation for Langevin diffusions that exploits log-concavity to construct Markov chains with favourable convergence properties. This approximation is closely related to Moreau---Yoshida regularisations for convex functions and uses proximity mappings instead of gradient mappings to approximate the continuous-time process. The proposed method complements existing MALA methods in two ways. First, the method is shown to have very robust stability properties and to converge geometrically for many target densities for which other MALA are not geometric, or only if the step size is sufficiently small. Second, the method can be applied to high-dimensional target densities that are not continuously differentiable, a class of distributions that is increasingly used in image processing and machine learning and that is beyond the scope of existing MALA and HMC algorithms. To use this method it is necessary to compute or to approximate efficiently the proximity mappings of the logarithm of the target density. For several popular models, including many Bayesian models used in modern signal and image processing and machine learning, this can be achieved with convex optimisation algorithms and with approximations based on proximal splitting techniques, which can be implemented in parallel. The proposed method is demonstrated on two challenging high-dimensional and non-differentiable models related to image resolution enhancement and low-rank matrix estimation that are not well addressed by existing MCMC methodology.

Disturbance observer-based sliding mode backstepping control for a re-entry vehicle with input constraint and external disturbance

An attitude controller is designed for a reusable launch vehicle (RLV) during the re-entry phase with input constraint, model uncertainty and external disturbance. A control-oriented model with matched and unmatched uncertainty is first derived for the control design. To proceed, the control scheme is designed taking advantage of the robust stability property of sliding mode control, the compensation ability of the non-linear disturbance observer (DOB) technique and the systematic design procedure of the backstepping technique. An additional system, the states of which are used for controller design and stability analysis, is constructed to handle the input constraint. The time derivative of the virtual control input is considered as an uncertainty to eliminate the ‘explosion of terms’ problem inherent in backstepping control. Moreover, the proposed method alleviates the chattering problem of the traditional sliding mode backstepping control scheme. Stability analysis of the composite control scheme consisting of the designed controller and the DOB is performed via Lyapunov theory. Finally, simulation results are compared to show that the proposed method is able to achieve better tracking performance and tackles input constraints more effectively than an adaptive filter backstepping control scheme.

An H∞ modified robust disturbance observer design for mechanical-positioning systems

This article presents a modified robust disturbance observer-RIC for a mechanicalpositioning system. The proposed RIC structure ensures a higher level of stability margin and offers transparent selection of the controller’s structure and feedback dynamic. The modified RIC controller design is divided into two main stages, where the first stage provides a design for the internal robust controller and the second a design for the external performance controller. The controller structure ensures a robust stability and performances property and good capability of low-frequency input and output disturbances suppression. The controller synthesis based on a pole-placement technique using optimization of the robust criteria based on even polynomials, and positive conditions. The solution to the problem is based on a multi-criterion optimization algorithm with a fixed order controller structure.

New Algorithm Based on Sign Decomposition to Verify the Robust Stability Property for a Class of Linear Time-Delay Systems

The main focus of this paper is to analyze the robust stability property for a class of time-delay systems when parametric polynomic uncertainty is considered. The analysis is made by replacing the time-delay part with an auxiliary equation and then using the sign definite decomposition to deal with the polynomic parametric uncertainty. Also, it is shown that it is possible to verify the robust stability property by first obtaining the Hurwitz matrix from the characteristic equation for this class of systems and then checking the leading principal minors positivity using the sign definite decomposition. Finally, an algorithm codified in MATLAB is used to evaluate and graphically show the robust stability property. This is shown by a series of points that were calculated using the sign definite decomposition.

Equivalences of Stability Properties for Discrete-Time Nonlinear Systems

Several qualitative equivalences are demonstrated between various robust stability properties for discrete-time nonlinear systems. In particular, two different summation-to-summation estimates are shown to be equivalent to the standard definitions of Input-to-State Stability (ISS) and integral ISS (iISS), respectively. Furthermore, ISS and iISS are shown to be qualitatively equivalent, via a nonlinear change of coordinates, to linear and nonlinear l2-gain properties, respectively. These equivalences, together with a previous result on the equivalence of 0-input global asymptotic stability and iISS provide interesting relationships between discrete-time robust stability properties that do not hold in continuous-time.