Stochastic Interconnected Systems Research Articles

Dynamic event-triggered optimal control for stochastic interconnected nonlinear systems with matched disturbances via adaptive dynamic programming

This paper presents a dynamic event-triggered adaptive dynamic programming (DETADP) algorithm to study the optimal control issue of stochastic interconnected nonlinear systems with matched disturbances. By constructing an improved cost function related to the actuator faults for each auxiliary subsystem, the original control issue is converted into finding an array of decentralized optimal control policies. In order to eliminate the effect of matching perturbations, an integral sliding mode control strategy is developed using the DETADP algorithm to ensure optimal performance for general nonlinear dynamics. When the system trajectories converge to a sliding-mode surface, equivalent sliding mode dynamics are transformed into reformulated auxiliary systems with a modified cost function. Then, a DETADP algorithm is introduced under an identifier-critic network framework, where the identifier aims to determine the stochastic dynamic, the critic aims to acquire the solutions of Hamilton–Jacobi–Bellman(HJB) equations. Furthermore, a novel dynamic event-triggering condition is designed to determine the occurrence of an event by introducing a dynamic variable. By using the Lyapunov stability theory, all signals in the closed-loop system are proved to be uniformly ultimately bounded. Finally, practical simulation examples are conducted to validate the effectiveness of the designed method.

Decentralized Saturation-Tolerant Control for Stochastic Interconnected Systems with Preassigned Performance and Input Quantization

Decentralized Saturation-Tolerant Control for Stochastic Interconnected Systems with Preassigned Performance and Input Quantization

Event‐triggered control for stochastic interconnected nonlinear systems with unknown control directions

SummaryThis paper presents an event‐triggered control strategy for stochastic interconnected nonlinear systems with unknown control directions. Firstly, a new lemma is proposed for stochastic nonlinear systems with multiple time‐varying unknown control directions, which guarantees the boundedness of Nussbaum function parameter variables. Different from the existing results, each subsystem is allowed to have multiple time‐varying unknown control directions. Then, by using the backstepping method, a novel controller is proposed based on the relative threshold event‐triggered strategy. The controller not only reduces the communication burden but also eliminates the interference of unknown control directions. Based on Lyapunov stability theory, it is proved that the controller can make all signals in the closed‐loop system be bounded in probability and the system state variables converge to zero in probability. Finally, two simulation examples are presented to certify the effectiveness of the proposed control algorithm.

Event-triggered optimal decentralized control for stochastic interconnected nonlinear systems via adaptive dynamic programming

This paper presents an event-triggered adaptive dynamic programming (ETADP) algorithm to study the optimal decentralized control issue of interconnected nonlinear systems subject to stochastic dynamics. By developing a performance index function for augmented auxiliary subsystem, the primordial control issue is converted into deriving an array of optimal control policies sampling in an aperiodic pattern. Then, an ETADP algorithm is introduced under an identifier-actor-critic network framework, where the identifier aims to determine the stochastic dynamic, the critic aims to assess the system performance and the actor aims to implement the control action. A remarkable feature is that the actor-critic updating laws are constructed through the negative gradient method of a positive function, which is designed in the light of the partial derivative of a Hamilton–Jacobi-Bellman equation. Under the provided weight tuning rule, the traditional ADP algorithm can be significantly simplified. The stability of the close-loop system is verified through direct Lyapunov theory, and a numerical simulation is given to confirm the effectiveness of the optimal control scheme.

From Small-Gain Theory to Compositional Construction of Barrier Certificates for Large-Scale Stochastic Systems

This article is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against high-level logic properties. Our proposed methodology involves decomposition of interconnected systems into smaller subsystems and leverages the notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">control</i> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sub-barrier certificates</i> of subsystems, enabling one to construct control barrier certificates of interconnected systems by employing some <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\max$</tex-math></inline-formula> -type small-gain conditions. The main goal is to synthesize hybrid controllers enforcing complex logic properties, including the ones represented by the accepting language of deterministic finite automata, while providing probabilistic guarantees on the satisfaction of given specifications in bounded-time horizons. To do so, we propose a systematic approach to first decompose high-level specifications into simple reachability tasks by utilizing automata corresponding to the complement of specifications. We then construct control sub-barrier certificates and synthesize local controllers for those simpler tasks and combine them to obtain a hybrid controller that ensures satisfaction of the complex specification with some lower bound on the probability of satisfaction. We finally apply our proposed techniques to a fully-interconnected Kuramoto network composed of 100 nonlinear oscillators.

Sampled-Data Stabilization of Stochastic Interconnected Cyber-Physical Systems Under DoS Attacks

Cyber-physical systems (CPSs) can be accessed and controlled remotely, which increases their application prospects; however, these characteristics also make them more vulnerable to cyberattacks. In addition, an increasing number of resource-saving sampled-data control methods have attracted attention in the field of research. How to ensure the stability of the system that is attacked by cyberattacks and to reduce further the communication resources is a challenge. In this article, we study the security control problem of stochastic interconnected CPSs under two-channel denial-of-service attacks based on sampled-data output-feedback. First, the state observer and controller are designed with only the system output of the sampling points in the nonattack intervals. Next, the time intervals related to stable and unstable dynamics are distinguished. By analyzing the Lyapunov function in the intervals classified as previously mentioned respectively, the relationship between the sampling period and attack characteristics is derived to ensure that the system is globally mean-square uniformly ultimately bounded. The simulation results are presented to substantiate the analysis.

Improved Input-to-State Stability Analysis of Impulsive Stochastic Systems

This article is concerned with the input-to-state stability (ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic nonlinear systems. By constructing a general SISS-Lyapunov function, which takes the exponential SISS-Lyapunov function as a special case, the ISS criteria are obtained, respectively, for destabilizing and stabilizing impulses. It should be stressed that we impose the average dwell-time (ADT) condition for destabilizing impulses and reverse average dwell-time (RADT) condition for stabilizing impulses to restrain the occurrence of impulses, which extends the fixed dwell-time condition in recent literature. Moreover, the ADT and RADT conditions in this article correspond to the average impulsive interval method in most existing results under the exponential ISS-Lyapunov condition. As a subsequent result, the ISS and SISS of impulsive stochastic interconnected systems on networks are also studied by the Lyapunov method and graph-theoretic technique. Finally, several illustrative examples together with their numerical simulations are provided to demonstrate the theoretical results.

Compositional (In)Finite Abstractions for Large-Scale Interconnected Stochastic Systems

This article is concerned with a compositional approach for constructing both infinite (reduced-order models) and finite abstractions [a.k.a. finite Markov decision processes (MDPs)] of large-scale interconnected discrete-time stochastic systems. The proposed framework is based on the notion of stochastic simulation functions enabling us to employ an abstract system as a substitution of the original one in the controller design process with guaranteed error bounds. In the first part of this article, we derive sufficient small-gain-type conditions for the compositional quantification of the probabilistic distance between the interconnection of stochastic control subsystems and that of their infinite abstractions. We then construct infinite abstractions together with their corresponding stochastic simulation functions for a particular class of discrete-time nonlinear stochastic control systems. In the second part of this article, we leverage small-gain-type conditions for the compositional construction of finite abstractions. We propose an approach to construct finite MDPs as finite abstractions of concrete models or their reduced-order versions satisfying an incremental input-to-state stability property. We also show that for the particular class of nonlinear stochastic control systems, the aforementioned property can be readily checked by matrix inequalities. We demonstrate the effectiveness of the proposed results by applying our approaches to a fully interconnected network of 20 nonlinear subsystems (totally 100 dimensions). We construct finite MDPs from their reduced-order versions (together 20 dimensions) with guaranteed error bounds on their output trajectories. We also apply the proposed results to a temperature regulation in a circular building and construct compositionally a finite abstraction of a network containing 1000 rooms. We employ the constructed finite abstractions as substitutes to compositionally synthesize policies regulating the temperature in each room for a bounded time horizon.

Adaptive Decentralized Control Scheme for a Stochastic Interconnected System

This work investigates a decentralized state feedback scheme of neural network control for an interconnected system. The completely unknown associated terms are estimated directly by the neural structure. A modified approach is proposed to deal with the state feedback format. By combining the Lyapunov function and backstepping technology together, an adaptive decentralized controller is established, and we can construct the boundedness of all signals in the closed-loop structure through the controller, which can drive the formation of a given reference signal. In the end, the effectiveness of the presented strategy is referred to a simulation example.

Centralized Versus Decentralized Detection of Attacks in Stochastic Interconnected Systems

We consider a security problem for interconnected systems with linear, discrete, time-invariant, stochastic dynamics, where the objective is to detect exogenous attacks by processing measurements at different locations. We consider centralized and decentralized detectors, which differ primarily in their knowledge of the system model. In particular, a decentralized detector has a model of the dynamics of the isolated subsystems, but is unaware of the interconnection signals that are exchanged among subsystems. Instead, a centralized detector has a model of the entire dynamical system. We characterize the performance of the two detectors and show that, depending on the system and attack parameters, each of the detectors can outperform the other. Hence, it may be possible for the decentralized detector to outperform its centralized counterpart, despite having less information about the system dynamics, and this property is due to the nature of the considered attack detection problem (that is, a simple vs. composite hypothesis testing problem). Finally, we numerically validate our findings on a power system model.

Adaptive Robust Control for Stochastic Systems With Unknown Interconnections

This article considers the decentralized stabilization problem of stochastic interconnected systems. The considered stochastic systems simultaneously contain unknown interconnections, power integrator dynamics, and time-varying delays. First, both state and output feedback controllers are presented for the stochastic interconnected nonlinear systems. Novel barrier Lyapunov–Krasivskii functions are used for the stability analysis of the proposed method. Second, fuzzy systems are adopted to approximate the complex and unknown dynamics in the systems with guaranteed compact set conditions. Based on barrier functions and switching mechanism, it is strictly proved that all the states will always remain in a compact set. Third, an adaptive compensator is presented to handle the resulting errors from input quantization, which finally renders asymptotic stability of the whole interconnected systems. Simulations are conducted to verify the main results.

Adaptive Neural-Network-Based Dynamic Surface Control for Stochastic Interconnected Nonlinear Nonstrict-Feedback Systems With Dead Zone

In this paper, an adaptive neural-network-based dynamic surface control (DSC) method is proposed for a class of stochastic interconnected nonlinear nonstrict-feedback systems with unmeasurable states and dead zone input. First, an appropriate state observer is constructed to estimate the unmeasured state variables of the stochastic interconnected system. Then radial basis function neural networks combined with adaptive backstepping technique are applied to model the unknown nonlinear system functions of the stochastic interconnected system; and the DSC method is adopted to ensure the computation burden is greatly reduced. Furthermore, the proposed controllers guarantee that the closed-loop stochastic interconnected system is semi-globally bounded stable in probability. In the end, two simulation examples are provided to show the effectiveness and practicability of the proposed control scheme.

Compositional construction of infinite abstractions for networks of stochastic control systems

This paper is concerned with a compositional approach for constructing infinite abstractions of interconnected discrete-time stochastic control systems. The proposed approach uses the interconnection matrix and joint dissipativity-type properties of subsystems and their abstractions described by new notions of so-called stochastic storage functions. The interconnected abstraction framework is based on new notions of so-called stochastic simulation functions, constructed compositionally using stochastic storage functions of components. Using stochastic simulation functions, one can quantify the distance between original interconnected stochastic systems and interconnected abstractions in the probabilistic setting. Accordingly, one can leverage the proposed results to perform analysis and synthesis over abstract interconnected systems, and then carry the results back over concrete ones. In the first part of the paper, we derive dissipativity-type compositional reasoning for the quantification of the distance in probability between the interconnection of stochastic control subsystems and that of their abstractions. Moreover, we focus on a class of discrete-time nonlinear stochastic control systems with independent noises in the abstract and concrete subsystems, and propose a computational scheme to construct abstractions together with their corresponding stochastic storage functions. In the second part of the paper, we consider specifications expressed as syntactically co-safe linear temporal logic formulae and show how a synthesized policy for the abstract system can be refined to a policy for the original system while providing a guarantee on the probability of satisfaction. We demonstrate the effectiveness of the proposed results by constructing an abstraction (totally 3 dimensions) of the interconnection of three discrete-time nonlinear stochastic control subsystems (together 222 dimensions) in a compositional fashion such that the compositionality condition does not require any constraint on the number or gains of the subsystems. We also employ the constructed abstraction as a substitute to synthesize a controller enforcing a syntactically co-safe linear temporal logic specification.

Stochastic and adaptive optimal control of uncertain interconnected systems: A data-driven approach

This paper provides a novel non-model-based, data-driven stochastic H∞ control design for linear continuous-time stochastic interconnected systems with unknown dynamics. Our contributions are three-fold. First, we develop a tool to show how to assign an arbitrarily small input-to-output stochastic L2 gain of the closed-loop system, by combining the gain assignment technique with the zero-sum dynamic game-based H∞ control design. Second, robustness to dynamic uncertainties is tackled using the small-gain theory. Third, we develop a non-model-based stochastic robust adaptive dynamic programming (RADP) algorithm for adaptive optimal controller design. In sharp contrast to the existing methods, the obtained algorithm is based on value iteration (VI), and the knowledge of an initial stabilizing control policy is no longer needed. An example of a power electronic system is adopted to illustrate the obtained results.

Decentralized adaptive approximation-based fuzzy output-feedback control of uncertain switched stochastic interconnected nonlinear systems

In this paper, a decentralized adaptive approximation-based output feedback control scheme is developed for a class of uncertain switched stochastic nonlinear interconnected systems. Fuzzy logic systems (FLSs) combined with adaptive backstepping method are applied to model the unknown nonlinear functions of the switched system. The full-order observer is designed to estimate the immeasurable states and the dynamic surface control (DSC) technique is adopted to ensure the computation burden is greatly reduced. Moreover, the proposed controllers guarantee the semi-global bounded of the resulting closed-loop system under any switching laws. Simulation results show the effectiveness of the proposed control scheme.

A new decentralized implicit adaptive regulator for large-scale systems described by discrete-time state-space mathematical models

In this paper, we treat the problem of decentralized implicit adaptive regulation for large-scale stochastic systems composed into a set of interconnected systems that are described by discrete-time state-space mathematical models with unknown parameters. The key idea in the decentralized regulation method is to design local regulator using only local information such that the state of each interconnected system is regulated to a certain constant reference signal. The main contribution is the proposition of a decentralized implicit adaptive regulator based on state-feedback strategy that can be applied to stochastic interconnected systems with unknown parameters. Furthermore, the practical implementation of the proposed decentralized implicit adaptive regulator can be made easily (low-cost implementation of the electronic components, short computation of the decentralized control law, etc.). A theorem is established and proved which gives sufficient stability conditions of the resulting closed-loop interconnected systems by using the Lyapunov method. An example of numerical simulation is treated to test the performance of the proposed decentralized implicit adaptive regulator.

Decentralized risk-sensitive design for large-scale stochastic interconnected systems with time-varying delays

In this paper, the problem of risk-sensitivity for a class of large-scale interconnected stochastic nonlinear systems with unbounded time-varying delays is investigated. The design procedure is dedicated to designing a decentralized controller by using only local measurements in each subsystems, and the designed controller can guarantee any desired achievable level of long-term average cost for a given risk-sensitivity parameter μ. Under some suitable conditions, we prove the globally asymptotic stability in probability by applying the design procedure. Finally, two examples are presented to illustrate our results.

New results on stability analysis and stabilization of time-delay continuous Markovian jump systems with partially known rates matrix

Summary In this note, the problems of stability analysis and controller synthesis of Markovian jump systems with time-varying delay and partially known transition rates are investigated via an input–output approach. First, the system under consideration is transformed into an interconnected system, and new results on stochastic scaled small-gain condition for stochastic interconnected systems are established, which are crucial for the problems considered in this paper. Based on the system transformation and the stochastic scaled small-gain theorem, stochastic stability of the original system is examined via the stochastic version of the bounded realness of the transformed forward system. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a precise approximation of the time-varying delay and the new result on the stochastic scaled small-gain theorem. The proposed stability condition is demonstrated to be much less conservative than most existing results. Moreover, the problem of stabilization is further solved with an admissible controller designed via convex optimizations, whose effectiveness is also illustrated via numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

Decentralized Output Feedback Adaptive NN Tracking Control for Time-Delay Stochastic Nonlinear Systems With Prescribed Performance.

This paper studies the dynamic output feedback tracking control problem for stochastic interconnected time-delay systems with the prescribed performance. The subsystems are in the form of triangular structure. First, we design a reduced-order observer independent of time delay to estimate the unmeasured state variables online instead of the traditional full-order observer. Then, a new state transformation is proposed in consideration of the prescribed performance requirement. Using neural network to approximate the composite unknown nonlinear function, the corresponding decentralized output tracking controller is designed. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of uniformly ultimately boundedness and that both transient-state and steady-state performances are preserved. Finally, a simulation example is given, and the result shows the effectiveness of the proposed control design method.

Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

AbstractIn this paper, the interconnecting structure between a certain system and its lower order subsystems within the infinite‐dimension stochastic interconnected systems is analyzed. Assuming that the excitations are parametric white noises, the exponential string stability for a few classes of nonlinear stochastic interconnected systems is discussed. By using the vector Lyapunov function method, the sufficient conditions of exponential string stability are derived, expanding the scope of the parameters for systems stability. Moreover, some cases of exponential string stability for vehicle‐following systems in automated highway systems are specified. Finally, an example is shown to illustrate the proposed method.