Showing papers on "Stochastic process published in 2021"
TL;DR: A survey of recent developments in the rapidly expanding field of asymptotic distribution theory, with a special emphasis on the problems of time dependence and heterogeneity, can be found in this article.
Abstract: This is a survey of the recent developments in the rapidly expanding field of asymptotic distribution theory, with a special emphasis on the problems of time dependence and heterogeneity. The book is designed to be useful on two levels. First as a textbook and reference work, giving definitions of the relevant mathematical concepts, statements, and proofs of the important results from the probability literature, and numerous examples; and second, as an account of recent work in the field of particular interest to econometricians, including a number of important new results. It is virtually self-contained, with all but the most basic technical prerequisites being explained in their context; mathematical topics include measure theory, integration, metric spaces, and topology, with applications to random variables, and an extended treatment of conditional probability. Other subjects treated include: stochastic processes, mixing processes, martingales, mixingales, and near-epoch dependence; the weak and strong laws of large numbers; weak convergence; and central limit theorems for nonstationary and dependent processes. The functional central limit theorem and its ramifications are covered in detail, including an account of the theoretical underpinnings (the weak convergence of measures on metric spaces), Brownian motion, the multivariate invariance principle, and convergence to stochastic integrals. This material is of special relevance to the theory of cointegration.
314 citations
TL;DR: It is proved that the designed method can guarantee that all the signals in the closed-loop systems are bounded in probability, and the distributed consensus tracking errors can converge to a small neighborhood of the origin via the Lyapunov stability theory.
Abstract: This article studies the distributed observer-based event-triggered bipartite tracking control problem for stochastic nonlinear multiagent systems with input saturation. First, different from conventional observers, we construct a novel distributed reduced-order observer to estimate unknown states for the stochastic nonlinear systems. Then, an event-triggered mechanism with relative threshold is introduced to reduce the burden of communication. In addition, the bipartite tracking controller is proposed for stochastic multiagent systems by using fuzzy logic systems and the backstepping approach. Meanwhile, it is proved that the designed method can guarantee that all the signals in the closed-loop systems are bounded in probability, and the distributed consensus tracking errors can converge to a small neighborhood of the origin via the Lyapunov stability theory. Finally, a simulation example is given to prove the effectiveness of the designed scheme.
255 citations
TL;DR: The aim of this work is to design an appropriate SMC law based on an adaptive event-triggered communication scheme such that the resulting closed-loop system could realize stochastic stability and reduce communication burden.
Abstract: In this article, the sliding mode control (SMC) design is studied for a class of stochastic switching systems subject to semi-Markov process via an adaptive event-triggered mechanism. Network-induced communication constraints, semi-Markov switching parameters, and uncertain parameters are considered in a unified framework for the SMC design. Due to the constraint of measuring transducers, the system states always appear with unmeasurable characteristic. Compared with the traditional event-triggered mechanism, the adaptive event-triggered mechanism can effectively reduce the number of triggering than the static event-triggered mechanism. During the data transmission of network communication systems, network-induced delays are characterized from the event trigger to the zero-order holder. The aim of this work is to design an appropriate SMC law based on an adaptive event-triggered communication scheme such that the resulting closed-loop system could realize stochastic stability and reduce communication burden. By introducing the stochastic semi-Markov Lyapunov functional, sojourn-time-dependent sufficient conditions are established for stochastic stability. Then, a suitable SMC law is designed such that the system state can be driven onto the specified sliding surface in a finite-time region. Finally, the simulation study on boost converter circuit model (BCCM) illustrates the effectiveness of the theoretical findings.
237 citations
TL;DR: A definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Lyapunov theorem is established and proved and used to demonstrate the effectiveness of the proposed schemes.
Abstract: In this article, the adaptive finite-time tracking control is studied for state constrained stochastic nonlinear systems with parametric uncertainties and input saturation. To this end, a definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Lyapunov theorem is established and proved. To alleviate the serious uncertainties and state constraints, the adaptive backstepping control and barrier Lyapunov function are combined in a unified framework. Then, by applying a function approximation method and the auxiliary system method to deal with input saturation respectively, two adaptive state-feedback controllers are constructed. Based on the proposed stochastic Lyapunov theorem, each constructed controller can guarantee the closed-loop system achieves SGFSP, the system states remain in the defined compact sets and the output tracks the reference signal very well. Finally, a stochastic single-link robot system is established and used to demonstrate the effectiveness of the proposed schemes.
127 citations
TL;DR: An observer-based adaptive control strategy for nonlinear stochastic Markovian jump systems with uncertain time-varying delay is proposed, and an interesting result reveals that the stability for the dynamics with type of uncertain transition rates may cover the completely known type.
Abstract: In this article, the issue of sliding mode control for nonlinear stochastic Markovian jump systems with uncertain time-varying delay is investigated. Considering the system state measurements and the state-dependent disturbances are not available for feedback purposes, an observer-based adaptive control strategy is proposed. Based on the decomposition of the input matrices, the state-space representation of the system is turned into a regular form with the aid of T–S fuzzy models first. Then, a fuzzy observer system is constructed, which could be transformed into two lower order subsystems. By choosing a common linear switching surface, on which it also obtains linear sliding mode dynamics in a simple form. Further, an adaptive controller is synthesized relying on the bounded system delay information to ensure the estimated states driven on the predefined sliding surface and remain the sliding motion. Also, the stochastic stability analysis of the sliding mode dynamics is undertaken with two types of transition rates, and an interesting result reveals that the stability for the dynamics with type of uncertain transition rates may cover the completely known type. Finally, a single-link robot arm model is provided to verify the validity of the proposed method.
112 citations
TL;DR: In this article, the authors propose the use of so-called control barrier certificates to solve simpler reachability tasks along with computing the corresponding controllers and probability bounds, and combine those controllers to obtain a hybrid control policy solving the considered problem.
Abstract: This article focuses on synthesizing control policies for discrete-time stochastic control systems together with a lower bound on the probability that the systems satisfy the complex temporal properties. The desired properties of the system are expressed as linear temporal logic specifications over finite traces. In particular, our approach decomposes the given specification into simpler reachability tasks based on its automata representation. We, then, propose the use of so-called control barrier certificate to solve those simpler reachability tasks along with computing the corresponding controllers and probability bounds. Finally, we combine those controllers to obtain a hybrid control policy solving the considered problem. Under some assumptions, we also provide two systematic approaches for uncountable and finite input sets to search for control barrier certificates. We demonstrate the effectiveness of the proposed approach on a room temperature control and lane keeping of a vehicle modeled as a four-dimensional single-track kinematic model. We compare our results with the discretization-based methods in the literature.
68 citations
TL;DR: Stochastic process theory, general stochastic process, Markov process and normal process are respectively used to simulate the risk-accident process in this paper, and the results provide useful reference for the prediction and management of construction accidents.
Abstract: There are many factors leading to construction safety accident. The rule presented under the influence of these factors should be a statistical random rule. To reveal those random rules and study the probability prediction method of construction safety accident, according to stochastic process theory, general stochastic process, Markov process and normal process are respectively used to simulate the risk-accident process in this paper. First, in the general-random-process-based analysis the probability of accidents in a period of time is calculated. Then, the Markov property of the construction safety risk evolution process is illustrated, and the analytical expression of probability density function of first-passage time of Markov-based risk-accident process is derived to calculate the construction safety probability. In the normal-process-based analysis, the construction safety probability formulas in cases of stationary normal risk process and non-stationary normal risk process with zero mean value are derived respectively. Finally, the number of accidents that may occur on construction site in a period is studied macroscopically based on Poisson process, and the probability distribution of time interval between adjacent accidents and the time of the nth accident are calculated respectively. The results provide useful reference for the prediction and management of construction accidents.
59 citations
TL;DR: By suitably selecting the estimator parameters, it is proved that the proposed least-squares estimators are convergent, as well as strongly consistent in some special cases.
Abstract: For stochastic strict-feedback nonlinear systems with unknown parameters in the drift terms or the diffusion terms, we develop new least-squares identification schemes without regressor filtering. A key new ingredient in the proposed estimator design is a weighted term with design parameters, which is introduced to deal with the nonlinear terms and stochastic noise. With such an estimator, new adaptive controllers are designed to guarantee that the equilibrium at the origin of the closed-loop system is globally stable in probability, and the states are regulated to zero almost surely. Besides, by suitably selecting the estimator parameters, we prove that the proposed least-squares estimators are convergent, as well as strongly consistent in some special cases. Finally, two simulation examples are given to illustrate the least-squares identification and the adaptive control design.
55 citations
TL;DR: The largest Lyapunov index is used to reveal the maximum prediction range of RUL, and the prediction results of the comparative case show that the prediction performance of the GC degradation model is better than Brownianmotion, fractional Brownian motion, and long short-term memory neural network.
54 citations
TL;DR: Results show the new PRGP model can outperform the previous compatible methods, such as calibrated pure physical models and pure machine learning methods, in estimation precision and input robustness.
Abstract: Despite the wide implementation of machine learning (ML) technique in traffic flow modeling recently, those data-driven approaches often fall short of accuracy in the cases with a small or noisy training dataset. To address this issue, this study presents a new modeling framework, named physics regularized machine learning (PRML), to encode classical traffic flow models (referred as physics models) into the ML architecture and to regularize the ML training process. More specifically, leveraging the Gaussian process (GP) as the base model, a stochastic physics regularized Gaussian process (PRGP) model is developed and a Bayesian inference algorithm is used to estimate the mean and kernel of the PRGP. A physics regularizer, based on macroscopic traffic flow models, is also developed to augment the estimation via a shadow GP and an enhanced latent force model is used to encode physical knowledge into the stochastic process. Based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is then developed to maximize the evidence lowerbound of the system likelihood. For model evaluations, this paper conducts empirical studies on a real-world dataset which is collected from a stretch of I-15 freeway, Utah. Results show the new PRGP model can outperform the previous compatible methods, such as calibrated traffic flow models and pure machine learning methods, in estimation precision and is more robust to the noisy training dataset.
53 citations
TL;DR: It is proved that the closed-loop stochastic nonlinear system is semiglobally uniformly ultimately bounded in probability, and the output tracking error converges to a small neighborhood of zero.
Abstract: This article investigates the event-triggered adaptive tracking control for a class of pure-feedback stochastic nonlinear systems with full state constraints and input saturation. The saturated input is expressed as a smooth nonlinear function with bounded disturbance. The pure-feedback structure is transformed into strict-feedback case via mean value theorem, and a novel event-triggered adaptive fuzzy tracking control scheme with relative threshold is then proposed. The barrier Lyapunov function is introduced to analyze the system stability, and the state constraints are, thus, guaranteed. It is proved that the closed-loop stochastic nonlinear system is semiglobally uniformly ultimately bounded in probability, and the output tracking error converges to a small neighborhood of zero. Finally, the effectiveness of the proposed method is verified via simulation studies.
TL;DR: A new Stochastically Corrected Stochastic Compositional gradient method (SCSC) is presented, and the exhibited rate of convergence matches that of the original Adam on non-compositional stochastic optimization.
Abstract: Stochastic compositional optimization generalizes classic (non-compositional) stochastic optimization to the minimization of compositions of functions. Each composition may introduce an additional expectation. The series of expectations may be nested. Stochastic compositional optimization is gaining popularity in applications such as reinforcement learning and meta learning. This paper presents a new S tochastically C orrected S tochastic C ompositional gradient method ( SCSC ). SCSC runs in a single-time scale with a single loop, uses a fixed batch size, and guarantees to converge at the same rate as the stochastic gradient descent (SGD) method for non-compositional stochastic optimization. This is achieved by making a careful improvement to a popular stochastic compositional gradient method. It is easy to apply SGD-improvement techniques to accelerate SCSC. This helps SCSC achieve state-of-the-art performance for stochastic compositional optimization. In particular, we apply Adam to SCSC, and the exhibited rate of convergence matches that of the original Adam on non-compositional stochastic optimization. We test SCSC using the model-agnostic meta-learning tasks.
TL;DR: A novel Halanay-type inequality is established to handle periodically intermittent control and two main theorems are shown, whose conditions indicate how the control duration, the control gain, and the coupling strength affect the realization of the stability of highly nonlinear stochastic coupled systems.
Abstract: This article considers the stabilization of highly nonlinear stochastic coupled systems (HNSCSs) with time delay via periodically intermittent control. This article is motivated by that known differential inequalities to deal with periodically intermittent control do not work for HNSCSs, since the coefficients of the system do not satisfy the linear growth condition. In order to cope with this problem, a novel Halanay-type inequality is established to handle periodically intermittent control, which generalizes previous results. Then, based on this differential inequality, the graph theory, and the Lyapunov method, two main theorems are shown, whose conditions indicate how the control duration, the control gain, and the coupling strength affect the realization of the stability. Then, the theoretical results are applied to the modified van der Pol–Duffing oscillators. Finally, corresponding simulation results are presented to illustrate the effectiveness of the theoretical results.
TL;DR: The purpose of the problem addressed is to design a recursive filter, such that in the simultaneous presence of the stochastic noises, the channel fading and the data coding–decoding mechanism, an upper bound of the filtering error variance is obtained and then minimized at each time step.
Abstract: In this article, the recursive filtering problem is studied for a class of discrete-time nonlinear stochastic systems subject to fading measurements. In order to facilitate the data transmission in a resource-constrained communication network, the multiple description coding scheme is adopted to encode the fading measurements into two descriptions with the identical importance. Two independent Bernoulli distributed random variables are introduced to govern the occurrences of the packet dropouts in two channels from the encoders to the decoders. The channel fading phenomenon is characterized by the $M$ th-order Rice fading model whose coefficients are mutually independent random variables obeying certain probability distributions. The purpose of the problem addressed is to design a recursive filter, such that in the simultaneous presence of the stochastic noises, the channel fading and the data coding–decoding mechanism, an upper bound of the filtering error variance is obtained and then minimized at each time step. In virtue of the Riccati difference equation technique and the stochastic analysis approach, the explicit form of the desired filter parameters is derived by solving a sequence of coupled algebraic Riccati-like difference equations. Finally, a simulation experiment is provided to show the applicability of the developed filtering scheme.
TL;DR: A distributionally robust model for three-phase unbalanced DNR is proposed to obtain the optimal configuration under the worst-case PD of DG outputs and loads within the ambiguity set and inherits the advantages of stochastic optimization and robust optimization.
Abstract: Distributed generator (DG) volatility has a great impact on system operation, which should be considered beforehand due to the slow time scale of distribution network reconfiguration (DNR). However, it is difficult to derive accurate probability distributions (PDs) for DG outputs and loads analytically. To remove the assumptions on accurate PD knowledge, a deep neural network is first devised to learn the reference joint PD from historical data in an adaptive way. The reference PD along with the forecast errors are enveloped by a distributional ambiguity set using Kullback-Leibler divergence. Then a distributionally robust model for three-phase unbalanced DNR is proposed to obtain the optimal configuration under the worst-case PD of DG outputs and loads within the ambiguity set. The result inherits the advantages of stochastic optimization and robust optimization. Finally, a modified column-and-constraint generation method with efficient scenario decomposition is investigated to solve this model. Numerical tests are carried out using an IEEE unbalanced benchmark and a practical-scale system in Shandong, China. Comparison with the deterministic, stochastic and robust DNR methods validates the effectiveness of the proposed method.
TL;DR: It is shown that neglecting either the effects of dynamic environments or the correlation among component lifetimes would underestimate the reliability of series systems and overestimateThe reliability of parallel systems.
Abstract: The working conditions of multicomponent systems are usually dynamic and stochastic. Reliability evaluation of such systems is challenging, since the components are generally positively correlated. Based on the cumulative exposure principle, we model the effects of the dynamic environments on the component lifetimes by a common stochastic time scale, and exponential dispersion process is utilized to describe the stochastic time scale. Then, the component lifetimes are shown to be positively quadrant dependent, and the joint survival function of the component lifetimes is derived, which includes the results of [1] as special cases. In this article, we show that neglecting either the effects of dynamic environments or the correlation among component lifetimes would underestimate the reliability of series systems and overestimate the reliability of parallel systems. We also investigate the problem of parameter redundancy of the model, and give some suggestions for data analysis. Simulation studies show that the unified model is flexible and useful for suggesting an optimal model given observed data.
TL;DR: This short note considers time-varying stochastic functional differential systems with distributed-delay dependent impulsive effects, and some stability criteria for such systems are established by developing some inequality techniques and using Lyapunov approach.
Abstract: In this short note, we consider time-varying stochastic functional differential systems with distributed-delay dependent impulsive effects Such systems arise from a large number of applications, such as financial markets and population dynamics By developing some inequality techniques and then combining stochastic analysis theory, Lyapunov approach, some stability criteria for such systems are established The feature of the criteria shows that derivatives of the Razumikhin functions are allowed to be indefinite, and the restrictions with respect to the system parameters is very loose Finally, we carry out two numerical experiments to show the usefulness and significance of the criteria
TL;DR: This article investigates the adaptive fuzzy fault-tolerant control problem for a class of strict-feedback stochastic nonlinear systems with quantized input signal and uses the Lyapunov stability theory to guarantee that all the signals of the closed-loop system are bounded in probability in the presence of quantizedinput and actuator faults.
Abstract: This article investigates the adaptive fuzzy fault-tolerant control problem for a class of strict-feedback stochastic nonlinear systems with quantized input signal. A hysteretic quantizer is utilized to avoid chattering caused by quantized input signals. The fuzzy-logic systems are utilized to approximate the unknown nonlinear functions and also to construct the fuzzy state observer, which is used to estimate the immeasurable state vector. The actuator faults considered in this article are loss of effectiveness and lock-in-place faults. By using the Lyapunov stability theory, the closed-loop stochastic nonlinear system is guaranteed to be stable in probability, and all the signals of the closed-loop system are bounded in probability in the presence of quantized input and actuator faults. Finally, a simulation example is given to verify the validity of the proposed control strategy.
TL;DR: The main purpose of this paper is to construct an appropriate state estimation scheme under which the corresponding state estimation error dynamics is finite-time bounded in the mean square.
Abstract: The finite-time state estimation issue is addressed in this paper for discrete time-delayed neural networks (NNs). More than one communication channel is utilized to improve the communication performance. The transmission delays of each channel are modeled by a family of stochastic variables which are independent and identically distributed. The main purpose of this paper is to construct an appropriate state estimation scheme under which the corresponding state estimation error dynamics is finite-time bounded in the mean square. By employing the stochastic analysis approach and introducing a special Lyapunov-like functional, we have developed certain sufficient conditions to achieve the prescribed estimation performance. Furthermore, the exact expressions of the achieved estimator parameters are given by solving a special minimization problem subject to certain inequality constraints. Finally, we propose an illustrative simulation to examine the correctness, as well as the effectiveness, of our proposed state estimation method.
TL;DR: In this article, the authors present ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito stochastic nonlinear systems and Lagrangian systems.
Abstract: This article presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is nonconvex, its equivalent convex formulation is proposed utilizing SDC parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with ${\bf \mathcal {L}_2}$ -robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, $\mathcal {H}_\infty$ , and baseline nonlinear controllers for spacecraft attitude control and synchronization problems.
TL;DR: In this paper, the authors propose a motivation for a mixed local/nonlocal problem with a new type of Neumann condition, which is based on formal expansions and approximations.
Abstract: We propose here a motivation for a mixed local/nonlocal problem with a new type of Neumann condition. Our description is based on formal expansions and approximations. In a nutshell, a biological species is supposed to diffuse either by a random walk or by a jump process, according to prescribed probabilities. If the process makes an individual exit the niche, it must come to the niche right away, by selecting the return point according to the underlying stochastic process. More precisely, if the random particle exits the domain, it is forced to immediately reenter the domain, and the new point in the domain is chosen randomly by following a bouncing process with the same distribution as the original one. By a suitable definition outside the niche, the density of the population ends up solving a mixed local/nonlocal equation, in which the dispersion is given by the superposition of the classical and the fractional Laplacian. This density function satisfies two types of Neumann conditions, namely the classical Neumann condition on the boundary of the niche, and a nonlocal Neumann condition in the exterior of the niche.
TL;DR: Finite-horizon state estimation for time-varying coupled stochastic networks through the round-robin scheduling protocol is presented and the corresponding recursive estimator design algorithm is presented that is suitable for online application.
Abstract: This article is concerned with the problem of finite-horizon $H_{\infty }$ state estimation for time-varying coupled stochastic networks through the round-robin scheduling protocol. The inner coupling strengths of the considered coupled networks are governed by a random sequence with known expectations and variances. For the sake of mitigating the occurrence probability of the network-induced phenomena, the communication network is equipped with the round-robin protocol that schedules the signal transmissions of the sensors’ measurement outputs. By using some dedicated approximation techniques, an uncertain auxiliary system with stochastic parameters is established where the multiplicative noises enter the coefficient matrix of the augmented disturbances. With the established auxiliary system, the desired finite-horizon $H_{\infty }$ state estimator is acquired by solving coupled backward Riccati equations, and the corresponding recursive estimator design algorithm is presented that is suitable for online application. The effectiveness of the proposed estimator design method is validated via a numerical example.
23 Mar 2021
TL;DR: The authors derived a thermodynamic uncertainty relation for stochastic processes with unidirectional transitions and applied it on a random walk with stochastically resetting, and on the Michaelis-Menten model of enzymatic catalysis.
Abstract: The authors derive a thermodynamic uncertainty relation for stochastic processes with unidirectional transitions and apply it on a random walk with stochastic resetting, and on the Michaelis-Menten model of enzymatic catalysis.
TL;DR: In this study, three numerical analysis examples and one engineering design example are presented to demonstrate the effectiveness of the proposed Kriging-assisted time-variant reliability analysis method based upon stochastic process discretization.
TL;DR: In this article, it was shown that if a sequence of piecewise affine linear processes converges with a positive rate to a stochastic process that is strongly Holder continuous in time, then this sequence converges in the strong sense even with respect to much stronger Holder norms and the convergence rate is essentially reduced by the Holder exponent.
Abstract: We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process that is strongly Holder continuous in time, then this sequence converges in the strong sense even with respect to much stronger Holder norms and the convergence rate is essentially reduced by the Holder exponent. Our first application hereof establishes pathwise convergence rates for spectral Galerkin approximations of stochastic partial differential equations. Our second application derives strong convergence rates of multilevel Monte Carlo approximations of expectations of Banach-space-valued stochastic processes.
TL;DR: Some sufficient conditions are presented such that the considered closed-loop interconnected system is stochastically finite-time bounded with a prescribed disturbance attenuation level, and the gain matrices of fuzzy observer and fuzzy controller can be found by solving an optimization algorithm with linear matrix inequalities constraints.
Abstract: This article investigates the observer-based finite-time $H_\infty$ control problem for interconnected fuzzy systems with quantization and random network attacks, where two types of network attacks including denial-of-service (DoS) and fault data injection (FDI) attacks are considered. In order to achieve the occupancy reduction of network resources, the measured outputs of interconnected systems are quantized through a logarithmic quantizer before being transmitted by the communication channel. Combining the effects of quantization and random network attacks, an observer-based control model is first constructed. Then, based on Lyapunov functional approach and stochastic analysis technique, some sufficient conditions are presented such that the considered closed-loop interconnected system is stochastically finite-time bounded with a prescribed disturbance attenuation level, and the gain matrices of fuzzy observer and fuzzy controller can be found by solving an optimization algorithm with linear matrix inequalities constraints. Finally, two simulation examples are given to illustrate the validity of the proposed approach.
TL;DR: In this article, the authors studied discrete space and time first-passage processes under discrete time resetting in a general setup without specifying their forms and sketch out the steps to compute the moments and probability density function which is often intractable in the continuous time restarted process.
Abstract: First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under restart mechanism. Emanating from the canonical diffusion problem by Evans and Majumdar, restart has been shown to outperform the completion of many first-passage processes which otherwise would take longer time to finish. However, most of the studies so far assumed continuous time underlying first-passage time processes and moreover considered continuous time resetting restricting out restart processes broken up into synchronized time steps. To bridge this gap, in this paper, we study discrete space and time first-passage processes under discrete time resetting in a general setup without specifying their forms. We sketch out the steps to compute the moments and the probability density function which is often intractable in the continuous time restarted process. A criterion that dictates when restart remains beneficial is then derived. We apply our results to a symmetric and a biased random walker in one-dimensional lattice confined within two absorbing boundaries. Numerical simulations are found to be in excellent agreement with the theoretical results. Our method can be useful to understand the effect of restart on the spatiotemporal dynamics of confined lattice random walks in arbitrary dimensions.
TL;DR: It can be rigorously proved that the designed controller can not only make the system states finite-time converge to the origin in probability but also ensure that the constraint on system output is not violated.
Abstract: This article addresses the problem of finite-time stabilization for a class of high-order nonlinear stochastic systems with asymmetric output constraints. A novel barrier Lyapunov function (BLF) is first presented to handle such asymmetric constraints. Further, based on the proposed BLF and the adding a power integrator technique, a controller design approach is developed by the backstepping method. It can be rigorously proved that the designed controller can not only make the system states finite-time converge to the origin in probability but also ensure that the constraint on system output is not violated. Another novelty of this approach is that it is a unified tool owing to its simultaneous application to the systems without output constraints. Finally, the validity of the proposed scheme can be verified by a simulation example.
TL;DR: In this article, the authors proposed a new computationally efficient analytical framework of voltage sensitivity analysis that allows for stochastic analysis of voltage change due to random changes in PV generation, and derived an analytical approximation for voltage change at any node of the network due to a change in power at other nodes in an unbalanced distribution network.
Abstract: From an operational and planning perspective, it is important to quantify the impact of increasing penetration of photovoltaics on the distribution system voltage. Most existing impact assessment studies are scenario-based where derived results are scenario specific and not generalizable. Moreover, stochasticity in temporal behavior of multiple spatially distributed PVs requires a large number of scenarios to be simulated that increases with the size of the network and the level of penetration. Therefore, we propose a new computationally efficient analytical framework of voltage sensitivity analysis that allows for stochastic analysis of voltage change due to random changes in PV generation. We derive an analytical approximation for voltage change at any node of the network due to a change in power at other nodes in an unbalanced distribution network. Then, we derive the probability distribution of voltage change at a certain node due to random changes in power injections/consumptions at multiple locations of the network. The accuracy of the proposed method is illustrated using a modified version of IEEE 37 bus and IEEE 123 bus test systems. The proposed framework can serve as a powerful tool for proactive monitoring/control of voltage, and ease the computational burden associated with perturbation based cybersecurity mechanisms.
01 Nov 2021
TL;DR: In this paper, a neural stochastic contraction metric (NSCM) is constructed using a deep neural network to construct a contraction metric and its differential Lyapunov function, sampled via simplified convex optimization.
Abstract: We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable learning-based control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct a contraction metric and its differential Lyapunov function, sampled via simplified convex optimization in the stochastic setting. Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, thereby ensuring exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances. The trained NSCM model allows autonomous systems to approximate optimal stable control and estimation policies in real-time, and outperforms existing nonlinear control and estimation techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the deterministic NCM, as shown in simulation results.