Closed-loop Stochastic System Research Articles

H∞ Controller Design for Networked Systems With Two-Channel Packet Dropouts and FDI Attacks.

In this article, the stochastic analysis and H∞ controller design problems of networked systems with packet dropouts and false data injection attacks are investigated. Different from the existing literature, we focus on the linear networked systems with external disturbances and both sensor-controller channel and controller-actuator channel are studied. First, we present a discrete-time modeling framework that leads to a stochastic closed-loop system with randomly varying parameters. To facilitate the analysis and H∞ control of resulting discrete-time stochastic closed-loop system, an equivalent yet analyzable stochastic augmented model is further constructed by matrix exponential computation. Based on this model, a stability condition is derived in the form of linear matrix inequality (LMI) with the aid of a reduced-order confluent Vandermonde matrix, Kronecker product operation, and law of total expectation. Specifically, the dimension of the LMI obtained in this article does not increase as the upper bound of consecutive packet dropouts does, which is also different from the existing literature. Subsequently, a desired H∞ controller is obtained such that the original discrete-time stochastic closed-loop system is exponentially mean-square stable with a prescribed H∞ performance. Finally, a numerical example and a direct current motor system are exploited to substantiate the effectiveness and practicability of the designed strategy.

Command-Filtered Neuroadaptive Output-Feedback Control for Stochastic Nonlinear Systems With Input Constraint.

In this article, an adaptive neural-network (NN) command-filtered output-feedback control strategy is proposed for a class of stochastic nonlinear systems (SNSs) with the actuator constraint. The problem of "explosion of complexity" existing in the conventional backstepping design procedure for SNSs is successfully resolved based on the command filter technique, and the error compensation mechanism is introduced to remove effectively the influence of filtered error. By using the NNs to identify the unknown nonlinear functions, a neural-network-based state observer is designed to estimate the unmeasurable states of the SNSs. Based on the quartic Lyapunov function, the stability of stochastic closed-loop systems is analyzed. It is proved that all signals of the closed-loop systems are bounded in probability, and the tracking error approaches a small neighborhood of the origin in probability. Finally, the effectiveness of the developed control algorithm in this article is verified by a comparison example.

Scheme of Operation for Multi-Robot Systems with Decision-Making Based on Markov Chains for Manipulation by Caged Objects

This paper presents the design of a new control scheme for a group of omnidirectional robots in a multi-robot system operating in an environment with obstacles. The control scheme uses a decision agent based on discrete-time Markov chains and takes into account the state of the system, obstacle positions, and geometries to manipulate targets, providing robustness against measurement uncertainties. The decision process is dynamic, with state information updating at each time step and tasks being executed based on the hierarchy determined by quadratic hierarchical programming. The system’s stability in the mean-square sense is analyzed through the study of a closed-loop stochastic system, and the effectiveness of the proposed control scheme is demonstrated through numerical simulations, including a comparative analysis with a finite-state machine decision agent.

Stabilization of Networked Control Systems Subject to Consecutive Packet Dropouts: The Random Clock Offsets Case

In this article, the stabilization problem is investigated for a class of networked control systems with random clock offsets and consecutive packet dropouts. Different from the existing literature, the consecutive packet dropouts occurring in communication networks are subject to clock offsets, and the clock offsets between the sensor and the controller are described by a random variable with a certain probability distribution. First, we construct a closed-loop discrete-time stochastic system by considering the random clock offsets and the consecutive packet dropouts in a unified framework. To render the discrete-time system suitable for analysis, an equivalent yet tractable stochastic augmented model is then established, where the system matrix is characterized by high nonlinearity and dual randomness, which poses substantial difficulties for the expectation operation in the controller design process. In order to deal with the difficulties, the law of total expectation, confluent Vandermonde matrix, and Kronecker product operation are introduced and then a stability condition in the form of linear matrix inequality is obtained. Based on this, a desired controller is designed, such that the closed-loop stochastic system is stochastically stable. Finally, a numerical example with two cases and an example using batch reactor are provided to demonstrate the effectiveness of the proposed design approach.

A new design method to global asymptotic stabilization of strict-feedforward stochastic nonlinear time delay systems

The stabilization problems of stochastic nonlinear systems remain challenging because many new obstacles will be encountered and need to be cautiously handled. This paper discusses the global asymptotic stabilization problem of stochastic nonlinear systems which possess strict-feedforward structure and multiple time delays. In the first place, we are trying to transform the considered system into an equivalent one by constructing the novel parameter-dependent state feedback controller and the suitable coordinate transformation. And then, through using the stochastic time delay system stability criterion and introducing the proper Lyapunov–Krasovskii functional, the global asymptotic stability of stochastic closed-loop system is proved. Finally, simulation results show the effectiveness of the parameter-dependent state feedback controller.

Mean square bounded attitude coordination control of spacecraft formation with stochastic uncertainties

This paper addresses the attitude coordination control problem of spacecraft formation on SO(3) with attitude constraints and stochastic uncertainties. To achieve the control objective, the attitude coordination control law is designed based on the behavioral formation approach and the modified super-twisting control techniques. The sufficient conditions are given for the closed-loop stochastic SFF system to reach the mean square bounded attitude coordination without breaking the attitude constraints. These conditions clearly indicate the way to select the control law parameters, which is convenient in practice. Under these conditions, upper bounds of the system state errors are explicitly estimated, which depends on the stochastic uncertainties, the behavior weights, and the control law parameters. Simulation results verify the applicability and effectiveness of the proposed control law.

Memoryless parameter-dependent control strategy of stochastic strict-feedback time delay systems

For a class of stochastic strict-feedback nonlinear systems subject to different time delay states, this paper mainly concerns the problem of global asymptotic stabilization. Two new control strategies that the memoryless parameter-dependent state feedback control and the memoryless parameter-dependent output feedback control are taken into consideration, respectively. By skillfully constructing the Lyapunov-Krasovskii (L-K) functional, taking the proper determined parameter and employing the stochastic nonlinear time delay system (SNTDS) stability theory, the global asymptotic stability of the stochastic closed-loop system can be achieved. The proposed output feedback control scheme is finally utilized for the control design of the one-link manipulator system and two-stage chemical reactor system, which can verify the availability of the control approach.

Stabilization of networked systems with communication constraints: The random sampling periods case

In this paper, the stabilization problem of networked systems with communication constraints is studied, where the random sampling periods, deception attacks and packet losses are considered simultaneously. Different from the existing literature, the actual sampling periods are subject to undesirable physical constraints and fluctuate around an ideal sampling period with certain probability distribution. First, a closed-loop discrete-time stochastic system is constructed by considering the random sampling periods, deception attacks and packet losses in a unified framework. Second, an equivalent yet tractable stochastic model is established with the aid of matrix exponential computation. By reduced-order confluent Vandermonde matrix approach, law of total expectation, convolution formula and Kronecker product operation, a controller is designed such that the exponential stability in the mean-square sense of closed-loop stochastic system is guaranteed. Subsequently, a special model is discussed where no deception attack occurs and then the corresponding controller is designed. Finally, an illustrative example is given to show the effectiveness of the designed approach.

Protocol-Based Stability Analysis of Stochastic Hybrid Systems Under DoS Attacks

The stability issue of stochastic hybrid systems against energy-constrained denial-of-service (DoS) attacks is investigated in this article. A sampled-data-based Round-Robin protocol, which sends measurement data cyclically according to the predetermined transmission sequence, is introduced to avoid communication network congestion. Additionally, a new switched time-delay stochastic closed-loop system with an unstable subsystem is established by discussing the effect of DoS attacks. Then, the stability of the closed-loop system is discussed in light of the piecewise Lyapunov–Krasovskii functional method and stochastic analysis technique. Finally, two examples are included to illustrate the correctness and applicability of the proposed method.

Finite-time guaranteed cost control for uncertain delayed switched nonlinear stochastic systems

This paper studies the finite-time guaranteed cost control problem for switched nonlinear stochastic systems with parameter uncertainties and time-varying delays. By choosing a model-dependent and delay-dependent Lyapunov-Krasovskii functional, applying the average dwell time approach and the Gronwall inequality, some novel sufficient conditions are derived to ensure that the switched nonlinear stochastic closed-loop system is finite-time stochastically stable and an upper bound is given on the performance index. The obtained nonlinear matrix is transformed into a linear matrix form, and then the feedback controller gains of the switched nonlinear stochastic systems with time-varying delay are obtained. Finally, two simulation examples are designed to verify the effectiveness of the suggested approach.

Necessary and Sufficient Conditions for Fault Diagnosability of Linear Open- and Closed-Loop Stochastic Systems Under Sensor and Actuator Faults

In this article, the diagnosability problem is investigated for open-loop and closed-loop stochastic systems under sensor and actuator faults. A novel quantitative fault diagnosability analysis method is developed to characterize the detectability and isolability for a given system without any predetermined fault diagnosis algorithm. By exploiting the Bhattacharyya distance, some novel indices are proposed to evaluate the difficulty degree of fault detectability and isolability. Necessary and sufficient conditions are established for the diagnosability of both open- and closed-loop stochastic systems undergoing sensor and actuator faults. In addition, the relationship between the fault detectability of open-loop systems and that of closed-loop ones is discussed.

Real-Time Reachable Set Control for Singular Markov Jump Networked Cascade Systems

This study is concerned with the problem of real-time reachable set (RS) control for a class of singular Markov jump (SMJ) networked cascade systems with time-delay, disturbance and non-zero initial conditions. Aiming at the shortcoming that the output of the controlled object is non-zero disturbance in single loop feedback control, an SMJ networked cascade control system model is proposed. By utilizing the Lyapunov stability theory, the linear matrix inequality technique and the free-weighting matrix method, the sufficient stability conditions and the real-time RS boundary for the closed-loop stochastic systems are obtained. Then, the gains of the cascade controller are represented by a reasonable matrix decoupling method. Finally, a simulation example is given to illustrate the effectiveness of the proposed design method.

A Probability Theory Approach to Stability Analysis of Networked Sampled-Data Systems With Consecutive Packet Dropouts

In this brief note, a probability theory approach is proposed to investigate the stability analysis issue for a class of networked sampled-data systems with packet dropouts. The continuous-time linear system under consideration is first transformed into a discrete-time system, where the system matrix of the discrete-time system is characterized by stochastic characteristic. Then, by the matrix exponential computation, an equivalent discrete-time stochastic system is established. Based on this, a controller is designed by the law of total expectation, which guarantees the stochastic stability of the closed-loop stochastic system. Finally, a numerical example and an example using power grid with IEEE 4-bus line are used to verify the effectiveness and applicability of the proposed design algorithm.

Output feedback domain stabilization in probability in fixed time for nonlinear stochastic systems

This work is concerned with the domain stabilization in probability in fixed time for stochastic nonlinear systems with outputs. The purpose of stabilization is to find a suitable output feedback controller such that the trajectory of the resulting closed-loop stochastic system, starting from an initial value outside a given target domain D, could arrive at the target domain in fixed time T with a minimum probability p. A separation result is shown under Lyapunov-based assumptions, which decomposes the control design into a state feedback problem and a filtering problem. Accordingly, the design of the output feedback controller is proposed with the help of the separation result under certain conditions. Furthermore, design procedures are given to accomplish the purpose of domain stabilization in probability in fixed time for a class of nonlinear stochastic systems. The ARE-based method is applied to solve the state feedback problem, whereas high-gain observers and saturation control techniques are used for the filtering problem. An example is provided for demonstration.

Parameter-dependent controller design of stochastic strict feedforward nonlinear systems

In this paper, the exponentially stable problem is discussed for a class of stochastic strict feedforward nonlinear systems. Firstly, by employing the proper coordinate transformation and the novel parameter-dependent controller, the initial stochastic strict feedforward nonlinear system is converted to an equivalent system. After that, the implementable parameter-dependent controller, which is adopted to handle the nonlinearities, can be achieved by reasonably selecting the designed parameter. Finally, by means of stochastic Lyapunov stability theory, it is rigorously verified that the proposed parameter-dependent state-feedback controller and parameter-dependent output-feedback controller can guarantee that the stochastic closed-loop system is the fourth moment exponentially stable. Simulation results demonstrate the efficiency of the proposed parameter-dependent controller.

Dynamic Event-Triggered Adaptive Tracking Control for a Class of Unknown Stochastic Nonlinear Strict-Feedback Systems

In this paper, the dynamic event-triggered tracking control issue is studied for a class of unknown stochastic nonlinear systems with strict-feedback form. At first, neural networks (NNs) are used to approximate the unknown nonlinear functions. Then, a dynamic event-triggered controller (DETC) is designed through the adaptive backstepping method. Especially, the triggered threshold is dynamically adjusted. Compared with its corresponding static event-triggered mechanism (SETM), the dynamic event-triggered mechanism (DETM) can generate a larger execution interval and further save resources. Moreover, it is verified by two simulation examples that show that the closed-loop stochastic system signals are ultimately fourth moment semi-globally uniformly bounded (SGUUB).

H∞ Constrained Pareto Suboptimal Strategy for Stochastic LPV Time-Delay Systems

Not only in control problems, but also in dynamic games, several sources of performance degradation, such as model variation, deterministic and stochastic uncertainties and state delays, need to be considered. In this paper, we present an [Formula: see text] constrained Pareto suboptimal strategy for stochastic linear parameter-varying (LPV) time-delay systems involving multiple decision makers. The goal of developing the [Formula: see text] constrained Pareto suboptimal strategy set is to construct a memoryless state feedback strategy set, so that the closed-loop stochastic LPV system is stochastically mean-square stable. In the paper, the existence condition of the extended bounded real lemma is first established via linear matrix inequalities (LMIs). Then, a quadratic cost bound for cost performance is derived. Based on these preliminary results, sufficient conditions for the existence of such a strategy set under the [Formula: see text] constraint are derived by using cross-coupled bilinear matrix inequalities (BMIs). To determine the strategy set, a viscosity iterative scheme based on the LMIs is established to avoid the processing of BMIs. Finally, two numerical examples are presented to demonstrate the reliability and usefulness of the proposed method.

Minimum Variance Pole Placement in Uncertain Linear Control Systems

The pole-placement issue for linear multi-input multi-output (MIMO) dynamic systems with uncertain parameters has been addressed in this article. A static feedback matrix has been designed for minimizing variances of closed-loop poles (CLPs) and for assigning poles to the nominal system at the desired places. It is assumed that the joint probability density function (PDF) of uncertain parameters is known and the system has more than one input. A new unknown vector is used like an eigenvector for a stochastic closed-loop system matrix to state the problem. The variances of poles are considered as cost functions, and the means of poles are termed constraints. This form of the problem statement has helped us to simply find a solution. In the first step, the optimization problem with constraints was handled by solving the equality constraint, and then, the problem was converted to a classic extended eigenvalue optimization problem. Later, the eigenvalue optimization problem was solved by the Rayleigh quotient and the feedback matrix was accomplished. Finally, this approach was simulated and validated using the MATLAB simulations, and the results were compared with a robust pole-placement method, which MATLAB control toolbox uses. The Monte Carlo simulations showed lower covariance for CLPs around the mean poles as compared to the robust pole-placement method.

Full State Constrained Stochastic Adaptive Integrated Guidance and Control for STT Missiles with Non-Affine Aerodynamic Characteristics

Considering a class of skid-to-turn (STT) missiles with stochastic disturbances, non-affine aerodynamic characteristics and full state constraints, a novel full state constrained stochastic adaptive integrated guidance and control (IGC) scheme is proposed in this paper. By introducing several four-order Barrier Lyapunov functions (BLFs), the required state constraints of the stochastic closed-loop system are guaranteed to be never violated. With the aid of mean value theorem and neural network approximation, the non-affine aerodynamic characteristics can be handled. Moreover, by using several hyperbolic tangent functions and estimating the upper bounds of the uncertainties, the adverse effects caused by stochastic disturbances and unknown target maneuvers can be eliminated. The stochastic stability of the closed-loop system is proven based on Lyapunov theory. Numerical simulations results show the effectiveness and the advantages of the proposed algorithm.

Event-Triggered Adaptive Fuzzy Tracking Control for Pure-Feedback Stochastic Nonlinear Systems With Multiple Constraints

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.