External Random Perturbations Research Articles

Robust MPC-based trajectory tracking of autonomous underwater vehicles with model uncertainty

A robust model predictive control (MPC) method with dual closed-loops is presented to handle trajectory tracking of autonomous underwater vehicle (AUV) with uncertain model parameters and random external perturbations. First, constraint conditions are set for the motion state and control input of the underwater vehicle based on its motion characteristics. The position controller takes the velocity increment as input, thus providing a smoothly varying desired velocity for the velocity controller. The velocity controller comprises nominal MPC and a nonlinear auxiliary control law to overcome the effect of random perturbations on AUV tracking control. Then, a finite-time extended state observer (FTESO) is designed to compensate for dynamic model uncertainty. Furthermore, Lyapunov stability theory is employed to analyse the stability of the controller and FTESO. Ultimately, through comparative simulation experiments, the proposed control framework's effectiveness and robustness are verified, proving it to be a feasible AUV trajectory tracking control method.

Reduction of the optimal tracking problem in the presence of noise

In this paper, the decomposition method based on the theory of fast and slow integral manifolds is used to analyze the optimal tracking problem. We consider a singularly perturbed optimal tracking problem with a given reference trajectory in the case of incomplete information about the state vector in the presence of random external perturbations.

Optimal sparse control of interval networks: Voltage source converter based DC grid study

Decentralized optimal control of interval state space systems involves significant complications due to the required sparsity, robustness, and convergence rate. By adding an l1 term to the standard linear quadratic optimization, the obtained composite index, accommodating the sparsity, contains both differentiable and non-differentiable terms. Knowing that the choice of optimization techniques are problem-dependent, in this paper, several smart provisions such as “Active set”, “Coordinate descent”, and separately managing the differentiable part of the cost function are put together to form a relatively fast algorithm. In addition, a rule is introduced to adjust automatically the degree of sparsity and a constraint to confine the interval closed-loop system eigenvalues to the desired s plane region. As a result, a robust sparse decentralized control (RSDC) approach for interval networks is established. The RSDC method is utilized for the control of a multi-terminal VSC (Voltage Source Converter ) -based DC (Direct Current) grid with parametric uncertainty under various external random perturbations. The test results show that the proposed method with just 20 feedback links (out of available 100) performs superiorly to the alternative ones in terms of sparsity, convergence rate, and time-domain performances, verified through extensive simulations.

Aging and Failure of a Polymer Chain under Tension.

The rupture of a polymer chain maintained at temperature T under fixed tension is prototypical to a wide array of systems failing under constant external stress and random perturbations. Past research focused on analytic and numerical studies of the mean rate of collapse of such a chain. Surprisingly, an analytic calculation of the probability distribution function (PDF) of collapse rates appears to be lacking. Since rare events of rapid collapse can be important and even catastrophic, we present here a theory of this distribution, with a stress on its tail of fast rates. We show that the tail of the PDF is a power law with a universal exponent that is theoretically determined. Extensive numerics validate the offered theory. Lessons pertaining to other problems of the same type are drawn.

Thermodynamic optimization subsumed in stability phenomena

In the present paper the possibility of an energetic self-optimization as a consequence of thermodynamic stability is addressed. This feature is analyzed in a low dissipation refrigerator working in an optimized trade-off regime (the so-called Omega function). The relaxation after a perturbation around the stable point indicates that stability is linked to trajectories in which the thermodynamic performance is improved. Furthermore, a limited control over the system is analyzed through consecutive external random perturbations. The statistics over many cycles corroborates the preference for a better thermodynamic performance. Endoreversible and irreversible behaviors play a relevant role in the relaxation trajectories (as well as in the statistical performance of many cycles experiencing random perturbations). A multi-objective optimization reveals that the well-known endoreversible limit works as an attractor of the system evolution coinciding with the Pareto front, which represents the best energetic compromise among efficiency, entropy generation, cooling power, input power and the Omega function. Meanwhile, near the stable state, performance and stability are dominated by an irreversible behavior.

Necessary and Sufficient Conditions of Stability in the Quadratic Mean of Linear Stochastic Partial Differential-Difference Equations Subject to External Perturbations of the Type of Random Variables

We obtain the necessary and sufficient conditions for the stability in the quadratic mean of strong solutions to stochastic partial differential-difference equations with pairwise independent external random perturbations of the type of random variables.

Stochastic network Price identity

Through the introduction of stochastic operators, the following work is an extension of previous works on robustness and resilience of compartmentalized closed-loop input-output systems. Indeed, those can be subject to the onset of external random perturbations which compromise the functioning of the input-output processing. The stochastic version of the network Price identity shows that the amplified expected dismantlement of the network structure comes from an increased expectation of external disturbers. Nevertheless, resilience can lead to a partial or full offset of threats. Furthermore, by studying the eigenvalues of the Laplacian, we provide a quantified value of connectivity to the between-subnetwork coupling. The value turns out to be greater in resilient networked structures than in the robust ones.

Design of an Adaptive Sliding Mode Control for a Micro-AUV Subject to Water Currents and Parametric Uncertainties

This paper addresses the design of an adaptive sliding mode control for an autonomous underwater vehicle with the objective to reject bounded internal and external perturbations. The proposed control is used to achieve velocity regulation and autonomous path-following using waypoints. Each task is successfully performed in the presence of parametric uncertainties and irrotational water currents. Due to complex dynamics and random external perturbations, underwater vehicles need robust control. The closed-loop stability and finite-time convergence of the system are demonstrated using the Lyapunov direct method. To provide a detailed and realistic testing environment for the proposed adaptive controller, a dynamic model of the vehicle using the Lagrange method is derived where all underwater effects are included. On that basis, the proposed adaptive sliding mode controller is compared to its non-adaptive equivalent and PD (Proportional Derivative) computed torque control. The simulation results demonstrate that the proposed adaptive control has better robustness and precision for this particular type of vehicle.

Про існування розв’язку задачі Коші одного класу стохастичних диференціально-різницевих рівнянь в частинних похідних із зовнішними випадковими збуреннями

Про існування розв’язку задачі Коші одного класу стохастичних диференціально-різницевих рівнянь в частинних похідних із зовнішними випадковими збуреннями

Comparing forest governance models against invasive biological threats

In order to take account of the negative effects of invasive species and pathogens on networked forest areas, we study the dynamics of stochastic closed-loop input-output systems faced with the risk of external random perturbations. The extension of previous works on robustness is carried out by introducing a negative feedback mechanism, such that the output from an element contained in the system behaves as a negative input toward elements to which it is connected. Through the study of an overall network divided into compartments barely connected to one another, we first consider the pathway pertaining to monofunctional zoning. By looking at a single aggregated structure, we then move our focus to the pathway proper to multifunctionality. Our results show that, at significant time scales, the monofunctional-zoning mode of forest governance, generally applied in Australasia, performs robustly against invasive biological threats at all levels of outbreak probability. The multifunctional mode of forest governance, further practiced in Western Europe, is mainly sturdy when the probability of invasion verges into certainty. Should this not be the case, robustness is ensured would disturbers and perturbations be uncorrelated. Accordingly, the monofunctional pathway can afford adopting control strategies for outbreak avoidance, which is only acceptable in case the expected invasion can be halted. For the sake of maintaining low likelihood of invasion, the multifunctional pathway is compelled to applying preventive strategies.

On existence of solution of the Cauchy problem for nonlinear diffusion stochastic partial differential-difference equations of neutral type with random external perturbations

The question related to the existence of the Cauchy problem solution in the class of nonlinear diffusion stochastic partial differential-difference equations of a neutral type with random external disturbances which are independent from the Wiener process is considered. Sufficient conditions are obtained for the diffusion coefficients of nonlinear stochastic differential-difference equations of a neutral type (NDSDRRNT) that guarantee the existence of the solution with the probability of 1. The method of the proof is based on the results of O.M. Stanzhitsky and A.O. Tsukanova on the existence and uniqueness of the Cauchy problem solution for the stochastic differential reaction-diffusion equation of a neutral type. In this paper, we prove the existence of a "mild solution" of NDSDRRNT. In some cases, such equations are mathematical models of real processes, the consideration of which is planned in the future work.

Performance Analysis and Experimental Validation of 2-DOF Fractional-Order Controller for Underactuated Rotary Inverted Pendulum

Several numbers of controllers are developed and implemented to enhance the performance of rotary single inverted pendulum (RSIP). This paper addresses a new two-degree-of-freedom (2-DOF) fractional control strategy for RSIP, which is a composition of feedback and feed-forward paths. Primary controller relates the perturbation attenuation, while the secondary controller is accountable for set point tracking. The pole placement technique is used for the design of 2-DOF proportional integral derivative (2-DOF PID) controller. In order to intensify the potentiality of 2-DOF PID controller, it is supplemented with fractional calculus. The tuning of fractional parameters is done by frequency domain analysis using the Nyquist plot. The proposed 2-DOF fractional-order PID controller is materialized on RSIP system which out turns the outstanding experimental results for both stabilization and trajectory tracking tasks. The system is investigated for stability, sensitivity and robustness, which confirms the ability of the proposed controller to reject the external random perturbations.

A novel 2-DOF fractional-order [formula omitted] controller with inherent anti-windup capability for a magnetic levitation system

The facility of an extra degree-of-freedom (DOF) to reshape the transient response of unstable systems arises to the concept of 2-DOF controller. Integration of fractional calculus strengthens the performance of it. In this paper, a novel methodology for the design of a 2-DOF PIλ-Dμ controller for a class of open-loop unstable systems is proposed and is applied in a magnetic levitation system (MLS). The restructuring of PIλ controller dematerializes the requirement of a dedicated anti-wind scheme for removing the actuator saturation problem. A new graphical tuning approach is suggested to tune the fractional order parameters of the controller and the integer order gain parameters are decided by employing the pole-placement technique. Stability of the proposed controller scheme employed to MLS is analyzed on the basis of Riemann sheets concept in w-plane. Experimental demonstration of proposed scheme on MLS confirms the ability of the controller to reject the external random perturbations as well as actuator saturation.

Anti-windup Fractional Order $$\textit{PI}^\lambda -\textit{PD}^\mu $$ PI λ - PD μ Controller Design for Unstable Process: A Magnetic Levitation Study Case Under Actuator Saturation

Many studies have been conducted by researchers globally in the recent past on the control scheme to stabilize the levitated object of magnetic levitation system (MLS) at the unstable equilibrium point though very small amount of work has been reported regarding the design and tuning of fractional order controller for unstable process, especially in the presence of actuator saturation. In this paper, a novel methodology of fractional order \(PI^\lambda -PD^\mu \) controller for MLS is proposed for both stabilizing the system and removing the actuator saturation. Fractional order control facilitates an extra degree of freedom to change the order of integrator, arise a new concept to diminish the error windup during actuator saturation. The tuning of gain parameter of PID controller is done using the conventional pole placement technique, while a simple tuning method is proposed here to tune fractional parameter using stability margin and sensitivity function. Stability of the proposed controller scheme employed to MLS is analyzed on the basis of Riemann sheets concept in w-plane. To compensate for saturation due to integral term, back-calculation anti-windup scheme is used here. Experimental demonstration of proposed scheme on magnetic levitation confirms the ability of the controller to reject the external random perturbations as well as its robustness against the variation of system parameters.

Modeling of the external disturbances of the ground surface during military tracking vehicles movement

This article is dedicated to the study of the simulation modeling of random external perturbation influence on the military tracked vehicles movement, including accidental changes of the ground surface characteristics. Despite the significant amount of work which has been done in the field of simulation modeling regarding the perturbed motion of the tracked vehicles, the modeling of the ground surface characteristics changes needs additional consideration. The purpose of this work is to construct a simulation of random changes of the ground surface characteristics during the military tracked vehicles movement. Based on the inverse-transform method has been proposed an algorithm to obtain an array of random coefficients of resistance to the linear motion and rotation. The obtained random data has been used in the mathematical model of tracked vehicles to specify torque parameters on the driving wheels of right and left side of tracked vehicles, which are required to move on a defined path. Used as a random variables the empirical coefficients of the linear motion and rotation resistance also take into account the microprofile of ground surface that helps to adjust and at the same time to reduce the simulation complexity of tracked vehicles perturbed motion. Distribution functions of random values for the ground surface characteristics are simpler compared to the functions that describe a random change of only the ground surface microprofile. The results show that the algorithm can improve the accuracy of the simulation of tracked military vehicles perturbed motion and could be useful for studies aimed at improving the transmission elements and power units of military tracked vehicles

A Mechanistic, Stochastic Model Helps Understand Multiple Sclerosis Course and Pathogenesis

Heritable and nonheritable factors play a role in multiple sclerosis, but their effect size appears too small, explaining relatively little about disease etiology. Assuming that the factors that trigger the onset of the disease are, to some extent, also those that generate its remissions and relapses, we attempted to model the erratic behaviour of the disease course as observed on a dataset containing the time series of relapses and remissions of 70 patients free of disease-modifying therapies. We show that relapses and remissions follow exponential decaying distributions, excluding periodic recurrences and confirming that relapses manifest randomly in time. It is found that a mechanistic model with a random forcing describes in a satisfactory manner the occurrence of relapses and remissions, and the differences in the length of time spent in each one of the two states. This model may describe how interactions between “soft” etiologic factors occasionally reach the disease threshold thanks to comparably small external random perturbations. The model offers a new context to rethink key problems such as “missing heritability” and “hidden environmental structure” in the etiology of complex traits.

Large Deviations for a Mean Field Model of Systemic Risk

We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the strength of the intrinsic stabilization, the strength of the external random perturbations, and the degree of cooperation or interaction between them. The latter is the rate of mean reversion of each component to the empirical mean of the system. We interpret this model in the context of systemic risk and analyze in detail the effect of cooperation between the components, that is, the rate of mean reversion. We show that in a certain regime of parameters increasing cooperation tends to increase the stability of the individual agents but it also increases the overall or systemic risk. We use the theory of large deviations of diffusions interacting through their mean field.

Optimal Control of Pantograph-Catenary System Based on Parametric Identification

This article continues research on the pantograph- catenary system started in the previous papers (1), (2). The main purpose of the study is to use a computer of high- speed train to optimize the pantograph-catenary system by reducing power consumption when basic parameters of pantograph and catenary (contact network) change over time randomly. A linear model of pantograph-catenary system is considered where the upper and lower blocks of pantograph and catenary are modelled using lumped masses, springs and shock absorbers. The input and output system signals are measured when the train moves. These signals are processed by parametric identification algorithms to determine current values of system matrices. State matrices are used in Riccati equation to calculate controller coefficients. Adaptive controller provides dynamic stability of the system when its parameters change over time, and the system is subject to random external perturbations.

Dynamical properties of an harmonic oscillator impacting a vibrating wall

The dynamics of a spring-mass system under repeated impact with a vibrating wall is investigated using the static wall approximation. The evolution of the harmonic oscillator is described by two coupled difference equations. These equations are solved numerically, and in some cases exact analytical expressions have also been found. For a periodically vibrating wall, Fermi acceleration is only found at resonance. There, the average rebounding velocity increases linearly with the number of collisions. Near resonance, the average rebounding velocity grows initially with the number of collisions and eventually reaches a plateau. In the vicinity of resonance, the motion of the oscillator exhibits scaling properties over a range of frequency ratios. The presence of dissipation at resonance destroys the Fermi-acceleration process and induces scaling behavior similar to that at near resonance. For a moving wall with a random amplitude at collisions, Fermi acceleration is observed independently of the ratio between the wall and oscillator frequencies. In this case the average rebounding velocity grows with the square root of the number of collisions with the wall. Also, in this latter case, dissipation suppresses the Fermi-acceleration mechanism and induces a scaling behavior with the same universality class as that of the dissipative bouncing ball model with random external perturbations.

Collective behavior of multi-agent network dynamic systems under internal and external random perturbations

In this work, by formulating stochastic model for multi-agent network dynamic systems, the qualitative and quantitative properties of these dynamic models are investigated. In particular the cohesiveness, convergence, stability and invariant sets are addressed.