Control Of Stochastic Systems Research Articles

A maximum principle for mean-field stochastic control system with noisy observation

This paper is concerned with an optimal control problem driven by mean-field stochastic differential equation, where the state is partially observed via a noisy process. A new feature of the control problem is that the drift coefficient of observation equation is allowed to be a linear growth function, which immediately causes a difficulty in studying the control problem. A backward separation method with a dominated growth rate idea is used to overcome the difficulty. A maximum principle for optimality of the control problem is derived by an approximate technique. An asset–liability management problem for an insurance firm is studied. An optimal premium strategy in a feedback form is explicitly obtained.

A general maximum principle for progressive optimal stochastic control problems with Markov regime-switching

In this paper, we give a general maximum principle for optimal controls of stochastic systems driven by Markov chains. The control is allowed to enter both diffusion and jump terms and the control domain is not necessarily convex. We apply a new spike variation and the stochastic integral of progressive processes to obtain the main result.

Adaptive Asymptotic Control of Stochastic Systems With State Delay and Unknown Control Directions

For a class of stochastic nonlinear systems (SNSs) with state delay and unknown control directions (UCDs), the global asymptotic regulation problem is investigated in this brief. Based on the key Lyapunov-Krasovskii functional (KLF), a dynamic feedback control strategy is designed to solve the time delay and UCDs problems. The proposed dynamic compensator guarantees the global asymptotic convergence of the systems state in probability at the origin and the global boundedness of the closed-loop system (TCLS) in probability. Finally, an example is given to verify the effectiveness of the developed scheme.

Global asymptotic stability in mean for stochastic complex networked control systems

In this paper, global asymptotic stability in mean (GASM) for stochastic complex networked control systems (SCNCS) is studied. A fresh and suitable global Lyapunov function for SCNCS is constructed based on Kirchhoff’s matrix tree theorem in graph theory. Some sufficient criteria guaranteeing GASM for SCNCS are given, by applying Lyapunov method and stochastic analysis skills. These criteria are closely related to topological structure and coupling form functions of SCNCS. Furthermore, an application to a class of stochastic Lurie coupled control systems on networks (SLCCSN) is provided. Ultimately, a numerical test and its simulation process are presented to explain the validity of our theories.

Relative controllability of a stochastic system using fractional delayed sine and cosine matrices

In this paper, we study the relative controllability of a fractional stochastic system with pure delay in finite dimensional stochastic spaces. A set of sufficient conditions is obtained for relative exact controllability using fixed point theory, fractional calculus (including fractional delayed linear operators and Grammian matrices) and local assumptions on nonlinear terms. Finally, an example is given to illustrate our theory.

Wavelet Modeling of Control Stochastic Systems at Complex Shock Disturbances

This article is devoted to the development of methodological supports and experimental software tools for accuracy analysis and information processing in control stochastic systems (CStS) with complex shock disturbances (ShD) by means of wavelet Haar–Galerkin technologies. Basic new results include methods and algorithms of stochastic covariance analysis and modeling on the basis of the Galerkin method and wavelet expansion for linear, linear with parametric noises, and quasilinear CStS with ShD. Results are illustrated by an information-control system at ShD. New stochastic effects accumulation for systematic and random errors are detected and investigated.

Persuasion-Based Robust Sensor Design Against Attackers With Unknown Control Objectives

We introduce a robust sensor design framework to provide “persuasion-based” defense in stochastic control systems against an unknown type attacker with a control objective exclusive to its type. We design a robust “linear-plus-noise” signaling strategy in order to persuade the attacker to take actions that lead to minimum damage with respect to the system's objective. The specific model we adopt is a Gauss–Markov process driven by a controller with a (partially) “unknown” malicious/benign control objective. We seek to defend against the worst possible distribution over control objectives in a robust way under the solution concept of Stackelberg equilibrium, where the sensor is the leader. We show that a necessary and sufficient condition on the covariance matrix of the posterior belief is a certain linear matrix inequality. This enables us to formulate an equivalent tractable problem, indeed a semidefinite program, to compute the robust sensor design strategies “globally” even though the original optimization problem is nonconvex and highly nonlinear. We also extend this result to scenarios where the sensor makes noisy or partial measurements.

Control of stochastic networked control systems with time‐varying delays: The event‐triggered sampling case

AbstractIn this article, we aim to study the robust stabilization problem for a class of stochastic networked control delay systems with time‐varying delays and unknown parameters. By developing an event‐triggered strategy, the robustly exponential stability in mean‐square of the suggested system with an performance is obtained. Furthermore, the robustly exponential stabilization problem in mean‐square is also solved by designing an controller. Compared with many published results in the literature for discrete‐time stochastic systems, our work mainly focuses on the case of continuous‐time stochastic systems. In particular, time‐varying delays and unknown parameters are also considered. Finally, the applications of the theoretical results are illustrated by two numerical examples.

Resilient adaptive event-triggered H∞ control for networked stochastic control systems under denial-of-service attacks

This paper addresses the problem of resilient adaptive event-triggered control (AETC) for networked stochastic control systems (NSCSs) in the presence of the external disturbance and the energy-constrained, nonperiodic denial-of-service (DoS) attacks. A novel adaptive event-triggered scheme (AETS) that considers the effect of the energy-constrained, nonperiodic DoS attacks on the communication network is proposed to reduce the usage of system resources and adapt the variation of the plant state, and the model of closed-loop control system is established in the framework of time-delay systems and switched systems. Then, based on the Lyapunov stability theory, the stability criterion and the co-design algorithm are derived, which are used to ensure that the closed-loop control system is stochastically exponentially stable (SES) with an [Formula: see text] disturbance attenuation performance and to implement the co-design of state-feedback controller and proposed AETS, respectively. Unlike the network-based [Formula: see text] control approach for NSCSs in the existing literature, the resilient adaptive event-triggered network-based [Formula: see text] control approach proposed in this paper not only can considerably save the usage of system resources, but also can be resilient towards the energy-constrained, nonperiodic DoS attacks. Finally, a resilient AETC for the F16 aircraft system shows the effectiveness and superiority of proposed strategy.

Event-triggered fault detection for nonlinear descriptor networked control systems

This paper investigates the problem of filter-based fault detection (FD) for stochastic nonlinear descriptor networked control systems (NCSs). Based on the T-S fuzzy dynamic modeling technique, the nonlinear descriptor NCS is transformed into a combination of local linear models. Then, to save the network resources, a new adaptive event-triggered mechanism is presented to determine whether the sampled data is to be transmitted. Considering network-induced delay, data packet dropout, and asynchronous premise variables, a time-delay augmented system is established to improve the detection performance. The additional item caused by data packet dropout is regarded as a disturbance, and the effect of this part is attenuated by using the H∞ method. A sufficient condition is proposed to guarantee the admissibility of the augmented system, meanwhile, the desired filter parameters are obtained. Finally, simulation results are provided to demonstrate the feasibility of the proposed strategy.

Asymmetric information control for stochastic systems with different intermittent observations

This paper will investigate the linear quadratic (LQ) control problem for a stochastic system with different intermittent observations. Different from traditional LQ control problems, two controllers with different information structures are considered to minimize a quadratic performance index. Specifically, the information sets available to two controllers are different and mutually exclusive (i.e., either of both is not the subset of the other one). The problem under consideration in this paper is an asymmetric information control problem. It is highlighted that previous literature on asymmetric information control mainly focused on the case when the information set is a subset of the other one. However, the case of the information sets being mutually exclusive remains less investigated to the best of our knowledge, which brings essential difficulties in finding the optimal control strategies: the structures and forms of two controllers are not clear; seeking for the solvability conditions of the optimal control problem is challenging. We summarize the contributions of this paper as follows: Firstly, by adopting the convex variational method, the necessary and sufficient solvability conditions are derived under some basic assumptions, which are relied on the forward and backward difference equations (FBSDEs); Secondly, by decoupling the FBSDEs, the control strategies are derived; Finally, the results are extended to investigate the general multiple controllers case.

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

AbstractComplex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non‐Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data‐driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision‐making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.

Preface

After successfully held for two consecutive years, the 2021 3rd International Conference on Electronic Engineering and Informatics (EEI 2021) was successfully held in Dali, China during June 18-20, 2021. EEI 2021 is to bring together innovative academics and industrial experts in the field of Electronic Engineering and Informatics to a common forum. The primary goal of the conference is to promote research and developmental activities in Electronic Engineering and Informatics, and another goal is to promote scientific information interchange between researchers, developers, engineers, students, and practitioners working all around the world. The conference will be held every year to make it an ideal platform for people to share views and experiences in Electronic Engineering and Informatics and related areas.The conference model was divided into two sessions, including oral presentations and keynote speeches. In the first part, some scholars, whose submissions were selected as the excellent papers, were given 15 minutes to perform their oral presentations one by one. Then in the second part, keynote speakers were each allocated 30-45 minutes to hold their speeches. In this conference, we have invited Prof. Quanxin Zhu, from Hunan Normal University, China and Assoc. Prof. GHAMGEEN IZAT RASHED, from Wuhan University-School of Electrical Engineering and Automation to serve as our Conference Chairmen. And we were honored to invite 6 sophisticated keynote speakers to deliver keynote speeches during the conference. Prof. Yue Yang, from Nankai University, College of Electronic Information and Optical Engineering. He is engaged in basic and applied research in the fields of intelligent photonics, optical communication systems and networks, optical interconnection, detection and imaging display technologies, integrated photonics, optical fiber and free space optics. The next keynote speakers, Prof. Quanxin Zhu, from Hunan Normal University, China. His main research interests include Markov process, stability and control of stochastic systems. Prof. Philip T Moore, from School of Information Science and Engineering, Lanzhou University, China. The other keynote speakers as follow: Prof. Hiroshi Watanabe, from National Yang-Ming Chiao-Tung University/Dept. Electrical and Computer Engineering; Assoc.Prof. Kai-Sheng Chen, from National Central University, Taoyuan, Taiwan; Assoc. Prof. Anwar Ali, from Politecnico di Torino, Italy.We are glad to share with you that we received lots of submissions from the conference and we selected a bunch of high-quality papers and compiled them into the proceedings after rigorously reviewed them. These papers feature following topics but are not limited to: Electronic Technology, Information and Communication. All the papers have been through rigorous review and process to meet the requirements of international publication standard.We would like to thank the organization staff, the members of the program committees and reviewers. They have worked very hard in reviewing papers and making valuable suggestions for the authors to improve their work. We also would like to express our gratitude to the external reviewers, for providing extra help in the review process, and the authors for contributing their research result to the conference.Lastly, we would like to warmly thank all the authors who, with their presentations and papers, generously contributed to the lively exchange of scientific information that is so vital to the endurance of scientific conferences of this kind.The Committee of EEI 2021List of Committee members are available in this pdf.

Revealing the regularities related to the professional activities of the air traffic controller of airport traffic control tower

The object of research is the professional activity of an air traffic controller of the airport traffic control tower (henceforth Tower controller). The subject of research is the regularities revealing in this specialist activity in the performance of its work responsibility for the trainee reference model formation in the intelligent training system «ATC of Tower». One of the most problematic areas is the lack of training systems that would allow for independent training of these aviation specialists, whose knowledge assessment would be automatic and objective. The study used methods of analysis, combined timing, synthesis, statistical analysis and probabilistic modelling. The approach to data collection and analysis proposed as part of study made it possible to obtain an information flows circulation model at the Tower controller workplace and formalize the time characteristics of technological operations performed by it during the aircraft landing procedure. This is fundamentally important for the development of the trainee reference model of the intellectual training system, as well as for the implementation of the training mode and automatic objective assessment of the student’s knowledge and skills. The approbation obtained results of this approach of data collection and analysis make it possible to consider it an effective tool for obtaining objective information about the subject area of the Tower controller’s professional activity, which is a complex continuous-discrete stochastic dynamic control system with a mixed structure. In contrast to the formation of reference models existing approaches, the approach to collecting and analysing data proposed in the work makes it possible to develop a trainee reference model that more fully describes the Tower controller’s activities. Also, the proposed model reflects the order of actions, and when interacting with the trainee current model, it allows to implement objective (without an instructor) automatic assessment.

Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation

This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.

Robust Dynamic Programming for Temporal Logic Control of Stochastic Systems

Discrete-time stochastic systems are an essential modeling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification and synthesis of control strategies are computationally hard and generally rely on the use of approximate abstractions. Building on approximate abstractions, we compute control strategies with lower- and upper-bounds for satisfying unbounded temporal logic specifications. First, robust dynamic programming mappings over the abstract system are introduced to solve the control synthesis and verification problem. These mappings yield a control strategy and a unique lower bound on the satisfaction probability for temporal logic specifications that is robust to the incurred approximation errors. Second, upper-bounds on the satisfaction probability are quantified, and properties of the mappings are analyzed and discussed. Finally, we show the implications of these results to continuous state space of linear stochastic dynamic systems. This abstraction-based synthesis framework is shown to be able to handle infinite-horizon properties. Approximation errors expressed as deviations in the outputs of the models and as deviations in the probabilistic transitions are allowed and are quantified using approximate stochastic simulation relations.

Adaptive quantile control for stochastic system

Adaptive control has been successfully developed in deriving control law for stochastic systems with unknown parameters. The generation of reasonable control law depends on accurate parameter estimation. Recursive least square is widely used to estimate unknown parameters for stochastic systems; however, this approach only fits systems with Gaussian noises. In this paper, the adaptive quantile control is first proposed to cover the case where stochastic system noise follows sharp and thick tail distribution rather than Gaussian distribution. In the proposed approach, the system noise is modeled by the Asymmetric Laplace Distribution, and the unknown parameter is online estimated by our developed Bayesian quantile sum estimator, which combines recursive quantile estimations weighted by Bayesian posterior probabilities. With the real-time estimated parameter, the adaptive quantile control law is constructed based on the certainty equivalence principle. Our proposed estimator and controller are not computationally consuming and can be easily conducted in the Micro Controller Unit to fit practical applications. The comparison with some dominant controllers for the unknown stochastic system is conducted to verify the effectiveness of the adaptive quantile control.

An Investigation into Accuracy, Computation, and Robustness of Stochastic Linearization of Systems with Saturation Nonlinearities

Quasilinear Control (QLC) is a theory with a set of tools that can be used for the analysis and design of stochastic feedback control systems with nonlinear actuators and sensors. It is based on Stochastic Linearization (SL), a method of linearization that approximates a nonlinearity with an equivalent gain and a bias using statistical properties of its input. While the QLC literature has studied many problems in controls (e.g., performance analysis and controller design), important issues such as accuracy, robustness, and computation of SL have not been fully investigated. This paper fills this gap, with a special focus on feedback systems with saturating actuators, which are commonly encountered in feedback control systems and the QLC literature. Specifically, the accuracy of SL in approximating the saturated response is investigated. A mathematical relationship is established between the saturation authority and the worst-case open-loop accuracy, and the implications on closed-loop accuracy are described. To study the robustness of SL in practical situations, the sensitivities of the equivalent SL gain and bias to system parameters are investigated. Finally, several root-finding algorithms are compared in terms of their computational speed in solving the SL equations, and a novel change of coordinates is presented to improve the performance. The results provide valuable insights into and methods for addressing the computational aspects of SL that are critical for proper design and analysis of nonlinear stochastic feedback control systems.

Time optimal control to a partial stochastic differential system with pseudo almost periodic coefficients

In this paper, we study the time optimal control of a class of partial stochastic impulsive functional differential systems with pseudo almost periodic coefficients in the α-norm functional spaces. Firstly, the existence of p-mean piecewise pseudo almost periodic mild solutions for the impulsive stochastic control systems is investigated by utilising stochastic analysis, analytic semigroup, the fixed-point techniques with fractional power arguments. Secondly, the existence of time optimal pairs of a system governed by partial stochastic impulsive functional differential equations is also obtained. Finally, two examples are provided to illustrate the time optimal control problems of parabolic control system with pseudo almost periodic coefficients and impulses.

Reliability of nonlinear stochastic controlled systems considering the dynamics of sensors and actuators

A closed-loop controlled system usually consists of the main structure, sensors, and actuators. The dynamics of sensors and actuators may influence the motion of the main structure. This article presents an analytical study on the first-passage reliability of a nonlinear stochastic controlled system under the consideration of the dynamics of sensors and actuators. The coupled dynamic equations of the controlled systems with sensors and actuators are first given, which are further integrated into a controlled, randomly excited, dissipated Hamiltonian system. By applying the stochastic averaging method for quasi-Hamiltonian systems, a one-dimensional averaged differential equation for the Hamiltonian function is obtained. The backward Kolmogorov equation associated with the averaged equation is then derived for the first-passage reliability analysis, from which the approximate reliability function and probability density of first-passage time are obtained. The accuracy of the proposed procedure is demonstrated by an example. A comparative analysis of the reliability of the system with/without sensors and actuators is carried out, which indicates that ignoring sensors and actuators will make underestimation of the reliability of the closed-loop system with small time. However, when time increases, there appears the opposite trend. Our findings provide a reference for control strategy design.