Stochastic Robustness Research Articles

Stochastic robustness analysis of wing-aileron flutter suppression systems

In this work a stochastic robustness analysis approach is used to compare the performances of two non-linear flutter suppression systems designed for stabilization of a wing-aileron lifting structure. A reduced order modelling approach based on an alternative aeroelastic beam finite element is presented and used for the flutter suppression systems design, which are driven by a simple adaptive controller and a sliding mode controller, respectively. A heuristic algorithm is used to determine the simple adaptive controller invariant parameters at the design point while a simple parametric study is performed to tune the sliding mode controller. The performances of each closed loop system are evaluated taking into account mass, stiffnesses, and aerodynamics uncertainties of the aeroelastic plant also considering the presence of discrete gust disturbances.

The Stochastic Robustness of Nominal and Stochastic Model Predictive Control

In this work, we establish and compare the stochastic and deterministic robustness properties achieved by nominal model predictive control (MPC), stochastic MPC (SMPC), and a proposed constraint-tightened MPC (CMPC) formulation, which represents an idealized version of tube-based MPC. We consider three definitions of robustness for nonlinear systems and bounded disturbances: robust asymptotic stability (RAS), robust asymptotic stability in expectation (RASiE), and RASiE w.r.t. the stage cost <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell (\cdot)$</tex-math></inline-formula> used in these MPC formulations ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula> -RASiE). Via input-to-state stability (ISS) and stochastic ISS (SISS) Lyapunov functions, we establish that MPC, subject to sufficiently small disturbances, and CMPC ensure all three definitions of robustness without a stochastic objective function. While SMPC also ensures RASiE and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula> -RASiE, SMPC does not guarantee RAS for nonlinear systems. Through a few simple examples, we illustrate the implications of these results and demonstrate that, depending on the definition of robustness considered, SMPC is not necessarily more robust than nominal MPC even if the disturbance model is exact.

Resilient Vector Consensus Over Random Dynamic Networks Under Mobile Malicious Attacks

Abstract This paper investigates the problem of resilient vector consensus for a group of dynamic agents against mobile malicious attacks. As real networks often operate under random environment and noises, we approach this problem by considering general random dynamic networks with weighted directed topologies. We propose three types of mobile attack models, which differ in the timing of moving of attackers and the capability of detecting such moving. By employing distributed discrete-time algorithms, the Lyapunov theory and martingale convergence theorem, resilient vector consensus is shown to be reached for all three models when the underlying network satisfies certain stochastic robustness conditions.

Learning Stochastic Graph Neural Networks With Constrained Variance

Stochastic graph neural networks (SGNNs) are information processing architectures that learn representations from data over random graphs. SGNNs are trained with respect to the expected performance, which comes with no guarantee about deviations of particular output realizations around the optimal expectation. To overcome this issue, we propose a variance-constrained optimization problem for SGNNs, balancing the expected performance and the stochastic deviation. An alternating primal-dual learning procedure is undertaken that solves the problem by updating the SGNN parameters with gradient descent and the dual variable with gradient ascent. To characterize the explicit effect of the variance-constrained learning, we analyze theoretically the variance of the SGNN output and identify a trade-off between the stochastic robustness and the discrimination power. We further analyze the duality gap of the variance-constrained optimization problem and the converging behavior of the primal-dual learning procedure. The former indicates the optimality loss induced by the dual transformation and the latter characterizes the limiting error of the iterative algorithm, both of which guarantee the performance of the variance-constrained learning. Through numerical simulations, we corroborate our theoretical findings and observe a strong expected performance with a controllable variance.

Stochastic aeroservoelastic analysis of a flapped airfoil

In order to increase the operability range of wings in terms of speed, the suppression of aeroelastic vibrations due to flutter phenomena using a trailing edge flap is analyzed. The aeroelastic modelling of a three degrees of freedom 3DOF airfoil in unsteady incompressible flow with pitch and control surface stiffness non-linearities is studied and an augmented state space representation is used for the time domain analysis of the problem. A V-stack piezoelectric actuator is used to move the trailing edge flap and its dynamic behavior is included in the analyses by means of a finite element model; the actuator input voltage saturation is also taken into account. A heuristic method, named Population Decline Swarm Optimization, is used for the tuning of the filtered PID controller parameters for different velocity values. The optimization algorithm is also used for the tuning of the Simple Adaptive Controller SAC invariant gains. A general uncertain state space modelling of the aero-servo-elastic plant is provided and used first for the open loop stochastic flutter analysis. Then, the stochastic robustness analysis is carried out to verify the robustness to structural, aerodynamic, and actuator parameters uncertainties of the proposed flutter suppression systems and to compare the gain scheduled PID approach with the SAC scheme.

Inherent Stochastic Robustness of Model Predictive Control to Large and Infrequent Disturbances

We introduce a new class of large, infrequent disturbances to complement the small, persistent disturbances typically considered in robustness analysis. This new class of disturbances includes discrete disturbances that become pertinent when considering discrete actuators and production scheduling in control problems. To properly account for the infrequent nature of these disturbances, we define a stochastic form of robustness. Under suitable assumptions, we prove that certain closed-loop systems subject to large, infrequent disturbances admit an SISS-Lyapunov function and are robust in this stochastic context. We apply these results to economic model predictive control (MPC) with a strictly dissipative nominal system and stage cost, which includes tracking MPC as a special case, and prove that economic MPC is robust to large, infrequent disturbances. Without dissipativity assumptions, we define and establish robust asymptotic performance for economic MPC. We present a simple tracking problem to illustrate the results of this work, and a production scheduling (economic MPC) problem, to demonstrate the relevance of this analysis to practical applications.

Stochastic Robustness of Delayed Discrete Noises for Delay Differential Equations

Stochastic robustness of discrete noises has already been proposed and studied in the previous work. Nevertheless, the significant phenomenon of delays is left in the basket both in the deterministic and the stochastic parts of the considered equation by the existing work. Stimulated by the above, this paper is devoted to studying the stochastic robustness issue of delayed discrete noises for delay differential equations, including the issues of robust stability and robust boundedness.

On the stochastic robustness of complete clustering predictability for a first‐order consensus model

AbstractWe study stochastic noise response on the complete cluster predictability of a first‐order stochastic consensus model on the real line with an odd, bounded, Lipschitz, and monotone coupling function. Emergence of multiclusters is one of the novel dynamical features of the deterministic consensus model, and it has been extensively studied in collective dynamics community. Recently, the second author and his collaborators proposed a complete cluster predictability of the first‐order nonlinear consensus model that can be derived from the Cucker–Smale flocking model on the real line, and they verified that the proposed clustering algorithm explicitly determines the number of asymptotic clusters and their cluster velocities only in terms of the initial data, coupling strength and supremum of coupling function. In this work, we show that the same cluster algorithm does work for the complete clustering predictability problem when the deterministic consensus model is stochastically perturbed in a multiplicative way.

A multi-criteria and stochastic robustness analysis approach to compare nations sustainability

Clustering nations using sustainability indexes has been proposed as a means to support decision-making in politics, academia and business. This starts by computing indexes that describe the social, economic and environmental progress of countries, and continues by ranking and clustering countries that face similar sustainability challenges. Although multi-criteria methods exist to support this process, two main issues have not been addressed in an integrated approach: uncertainty in decision-making parameters and imprecise data sources. In this study, we propose a procedure in which the PROMETHEE II multi-criteria method is used for ranking countries and an iterative algorithm is applied to find ordered clusters. A stochastic robustness analysis procedure helps to identify groups with robust sustainability paths. The approach is applied to the Human Development Index and the Sustainable Development Goals Index. By analyzing the ambiguous assignments of nations to clusters three groups of countries can be identified. First, countries that have very good arguments to be considered in a given cluster. Second, countries which have some merits to be considered in a cluster and where focusing resources would allow them to improve in their current group or jumping into a better one. Third, nations that have very ambiguous arguments to be considered in any cluster such that the support to improve their performance would have to be analyzed in depth on multiple fronts. Thus, policy decision-making could be enhanced with this approach, providing new and helpful visualizations of nations in HDI and SDG. Finally, limitations of this proposal and future research are discussed.

On the dynamics and robustness of the chemostat with multiplicative noise

Abstract The stochastic dynamics of a two-state bioreactor model with random feed flow fluctuations and non-monotonic specific growth rate is analyzed. Using the Fokker-Planck equation approach for describing the probability density function (PDF) evolution the lack of stochastic robustness due to deterministic bifurcation phenomena for the open-loop reactor operating under optimal (maximum production) operation condition is established, and the associated stochastic stabilization problem is addressed. Inherent differences between the presence of multiplicative noise, due to the feed flow fluctuations, and additive background noise are analytically established. Numerical simulation results illustrate these inherent differences, the stochastic fragility of the open-loop operation yielding a stochastic extinction phenomenon, as well as the stochastic PDF stabilization with a proportional feedback control.

Modeling and Flight Experiments for Swarms of High Dynamic UAVs: A Stochastic Configuration Control System with Multiplicative Noises.

UAV Swarm with high dynamic configuration at a large scale requires a high-precision mathematical model to fully exploit its boundary performance. In order to instruct the engineering application with high confidence, uncertainties induced from either systematic measurement or the environment cannot be ignored. This paper investigates the stochastic model of the UAV Swarm system with multiplicative noises. By combining the cooperative kinematic model with a simplified individual dynamic model of fixed-wing-aircraft for the first time, the configuration control model is derived. Considering the uncertainties in actual flight, multiplicative noises are introduced to complete the stochastic model. Following that, the estimator and controller are designed to control the formation. The mean-square uniform boundedness condition of the proposed stochastic system is presented for the closed-loop system. In the simulation, the stochastic robustness analysis and design (SRAD) method is used to optimize the properties of the formation. More importantly, the effectiveness of the proposed model is also verified using real data of five unmanned aircrafts collected in outfield formation flight experiments.

Bayesian analysis of semiparametric Bernstein polynomial regression models for data with sample selection

ABSTRACTIn regression analysis, a sample selection scheme often applies to the response variable, which results in missing not at random observations on the variable. In this case, a regression analysis using only the selected cases would lead to biased results. This paper proposes a Bayesian methodology to correct this bias based on a semiparametric Bernstein polynomial regression model that incorporates the sample selection scheme into a stochastic monotone trend constraint, variable selection, and robustness against departures from the normality assumption. We present the basic theoretical properties of the proposed model that include its stochastic representation, sample selection bias quantification, and hierarchical model specification to deal with the stochastic monotone trend constraint in the nonparametric component, simple bias corrected estimation, and variable selection for the linear components. We then develop computationally feasible Markov chain Monte Carlo methods for semiparametric Bernstein polynomial functions with stochastically constrained parameter estimation and variable selection procedures. We demonstrate the finite-sample performance of the proposed model compared to existing methods using simulation studies and illustrate its use based on two real data applications.

False Data Injection Attacks in Electricity Markets by Limited Adversaries: Stochastic Robustness

Deregulated electricity markets rely on a two-settlement system consisting of day-ahead and real-time (RT) markets, across which electricity price is generally volatile. In electricity markets, locational marginal pricing is widely adopted to set electricity prices and manage transmission congestion. Such locational marginal prices (LMPs) strongly hinge on the reliability and accuracy of the state estimation routines, which are designed to provide RT information about the state of the power grid based on meter measurements. However, state estimation is vulnerable to false data injection attacks (FDIAs), which aim to compromise the readings of measurement meters in order to distort state estimates and, subsequently, mislead the computation of RT LMPs, and thus carry out financial misconduct. Existing studies show that if the adversaries are omniscient , i.e., have full and instantaneous access to grid topology and state, they can design profitable attack strategies without being detected by the residue-based bad data detectors. This paper focuses on a more realistic FDIA setting, in which the attackers have only partial and imperfect information due to their limited resources and restricted physical access to the grid. Specifically, the attackers are assumed to have uncertainties about the state of the grid, and the uncertainties are modeled stochastically. Based on this model, this paper offers a framework for characterizing the optimal stochastic guarantees for the effectiveness of the attacks and the associated economic impacts. Designing such attacks is investigated analytically, and is examined in the standard IEEE 14-bus and 118-bus systems.

Improved Hybrid Fireworks Algorithm-Based Parameter Optimization in High-Order Sliding Mode Control of Hypersonic Vehicles

With respect to the nonlinear hypersonic vehicle (HV) dynamics, achieving a satisfactory tracking control performance under uncertainties is always a challenge. The high-order sliding mode control (HOSMC) method with strong robustness has been applied to HVs. However, there are few methods for determining suitable HOSMC parameters for an efficacious control of HV, given that the uncertainties are randomly distributed. In this study, we introduce a hybrid fireworks algorithm- (FWA-) based parameter optimization into HV control design to satisfy the design requirements with high probability. First, the complex relation between design parameters and the cost function that evaluates the likelihood of system instability and violation of design requirements is modeled via stochastic robustness analysis. Subsequently, we propose an efficient hybrid FWA to solve the complex optimization problem concerning the uncertainties. The efficiency of the proposed hybrid FWA-based optimization method is demonstrated in the search of the optimal HV controller, in which the proposed method exhibits a better performance when compared with other algorithms.

Flight control for air-breathing hypersonic vehicles using linear quadratic regulator design based on stochastic robustness analysis

The flight dynamics model of air-breathing hypersonic vehicles (AHVs) is highly nonlinear and multivariable coupling, and includes inertial uncertainties and external disturbances that require strong, robust, and high-accuracy controllers. In this paper, we propose a linear-quadratic regulator (LQR) design method based on stochastic robustness analysis for the longitudinal dynamics of AHVs. First, input/output feedback linearization is used to design LQRs. Second, subject to various system parameter uncertainties, system robustness is characterized by the probability of stability and desired performance. Then, the mapping relationship between system robustness and LQR parameters is established. Particularly, to maximize system robustness, a novel hybrid particle swarm optimization algorithm is proposed to search for the optimal LQR parameters. During the search iteration, a Chernoff bound algorithm is applied to determine the finite sample size of Monte Carlo evaluation with the given probability levels. Finally, simulation results show that the optimization algorithm can effectively find the optimal solution to the LQR parameters.

Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments

ABSTRACTImproving the robustness, vis-à-vis matched input disturbances of interconnection and damping assignment, passivity based control (IDA-PBC) for a class of underactuated mechanical systems is addressed in this paper. The characterised class of systems is described by a Port Controlled Hamiltonian (PCH) model which represents another alternative to the classical Euler–Lagrange models for which IDA–PBC yields a smooth stabilising controller. Our main contribution consists of combining the so-called IDA-PBC controller with an adaptive control technique. Some sufficient stability conditions on matched input disturbances are given. In order to estimate the stability and performance robustness of both controllers, a stochastic robustness analysis was used. Indeed, we used the Monte Carlo simulation (MCS) based on uncertainties to analyse the behaviour of the closed-loop system. The comparison of the stability robustness between the classical IDA-PBC controller and the proposed one is then provided. As an illustration, we proposed to revisit the application of IDA-PBC controller to the inertia wheel inverted pendulum in the presence of matched disturbances. Simulation and real-time experimental results mirror the theoretical results and prove the efficiency of the proposed controller.

Robust attitude control for reusable launch vehicles based on fractional calculus and pigeon-inspired optimization

In this paper, a robust attitude control system based on fractional order sliding mode control and dynamic inversion approach is presented for the reusable launch vehicle U+0028 RLV U+0029 during the reentry phase. By introducing the fractional order sliding surface to replace the integer order one, we design robust outer loop controller to compensate the error introduced by inner loop controller designed by dynamic inversion approach. To take the uncertainties of aerodynamic parameters into account, stochastic robustness design approach based on the Monte Carlo simulation and Pigeon-inspired optimization is established to increase the robustness of the controller. Some simulation results are given out which indicate the reliability and effectiveness of the attitude control system.

A practical parameter determination strategy based on improved hybrid PSO algorithm for higher-order sliding mode control of air-breathing hypersonic vehicles

A hybrid particle swarm optimization (PSO) algorithm for longitudinal dynamic models of air-breathing hypersonic flight vehicles (HFV) is proposed and applied to determine design parameters for a higher-order sliding model controller (HOSMC) while considering the effects of parameter uncertainty on trajectory tracking control. The input and output linearization of air-breathing HFV longitudinal dynamic models were achieved using the feedback linearization approach. Also, an HOSMC was designed for air-breathing HFV trajectory tracking control, and the design parameters were determined based on stochastic robustness analysis and hybrid PSO algorithm. Simulations revealed that the HOSMC design parameters can be optimized effectively and easily using the parameter determination strategy based on an improved hybrid PSO algorithm. The proposed HOSMC was used to stabilized the trajectory tracking of air-breathing HFV and the controller proposed exhibited great robustness.

Stochastic-based robust dynamic resource allocation for independent tasks in a heterogeneous computing system

Heterogeneous parallel and distributed computing systems frequently must operate in environments where there is uncertainty in system parameters. Robustness can be defined as the degree to which a system can function correctly in the presence of parameter values different from those assumed. In such an environment, the execution time of any given task may fluctuate substantially due to factors such as the content of data to be processed. Determining a resource allocation that is robust against this uncertainty is an important area of research. In this study, we define a stochastic robustness measure to facilitate resource allocation decisions in a dynamic environment where tasks are subject to individual hard deadlines and each task requires some input data to start execution. In this environment, the tasks that cannot meet their deadlines are dropped (i.e., discarded). We define methods to determine the stochastic completion times of tasks in the presence of the task dropping. The stochastic task completion time is used in the definition of the stochastic robustness measure. Based on this stochastic robustness measure, we design novel resource allocation techniques that work in immediate and batch modes, with the goal of maximizing the number of tasks that meet their individual deadlines. We compare the performance of our technique against several well-known approaches taken from the literature and adapted to our environment. Simulation results of this study demonstrate the suitability of our new technique in a dynamic heterogeneous computing system.

Stochastic Mesocortical Dynamics and Robustness of Working Memory during Delay-Period.

The role of prefronto-mesoprefrontal system in the dopaminergic modulation of working memory during delayed response tasks is well-known. Recently, a dynamical model of the closed-loop mesocortical circuit has been proposed which employs a deterministic framework to elucidate the system’s behavior in a qualitative manner. Under natural conditions, noise emanating from various sources affects the circuit’s functioning to a great extent. Accordingly in the present study, we reformulate the model into a stochastic framework and investigate its steady state properties in the presence of constant background noise during delay-period. From the steady state distribution, global potential landscape and signal-to-noise ratio are obtained which help in defining robustness of the circuit dynamics. This provides insight into the robustness of working memory during delay-period against its disruption due to background noise. The findings reveal that the global profile of circuit’s robustness is predominantly governed by the level of D1 receptor activity and high D1 receptor stimulation favors the working memory-associated sustained-firing state over the spontaneous-activity state of the system. Moreover, the circuit’s robustness is further fine-tuned by the levels of excitatory and inhibitory activities in a way such that the robustness of sustained-firing state exhibits an inverted-U shaped profile with respect to D1 receptor stimulation. It is predicted that the most robust working memory is formed possibly at a subtle ratio of the excitatory and inhibitory activities achieved at a critical level of D1 receptor stimulation. The study also paves a way to understand various cognitive deficits observed in old-age, acute stress and schizophrenia and suggests possible mechanistic routes to the working memory impairments based on the circuit’s robustness profile.