The Great Question of the State: Why a Country Is Resilient Even With the Most Incompetent Governance

Stochastic disturbance with finite-time chaos stabilization and synchronization for a fractional-order nonautonomous hybrid nonlinear complex system via a sliding mode control

A distributed consensus control method is developed in this paper for second-order nonlinear multiagent systems with external stochastic disturbances. By utilizing the graph theory, the stochastic theory, the control technique, and the linear matrix inequality method, sufficient conditions are derived to guarantee the convergence to mean-square exponential consensus for strongly connected proximity networks and proximity networks with directed spanning trees, respectively. Particularly, using such a methodology, a detailed distributed consensus controller design procedure is provided for networked Euler–Lagrange systems, which are often used in mechanical engineering processes. Finally, the effectiveness of the proposed consensus control method is illustrated by numerical simulations on networked Euler–Lagrange systems.

Active disturbance rejection control approach to output-feedback stabilization of nonlinear system with Lévy noises

In this paper, the active disturbance rejection control (ADRC) approach is applied to output-feedback stabilization for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameters from their nominal values. The stochastic total disturbance is then compensated in the feedback loop. As a result, we prove theoretically the mean square practical stability for the closed-loop system with constant gain ESO. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.

SummaryIn this paper, we apply the active disturbance rejection control approach to output‐feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time‐varying gain are used in ESO design separately. The mean square practical stability for the closed‐loop system with constant gain ESO and the mean square asymptotic stability with time‐varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output‐feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd.

A scientific and applied problem was solved in the articles. It aimed to increase the efficiency of operation of the dynamic "crane-load" system of the tower crane slewing mechanism even when external stochastic disturbances (wind gusts) affect the load. The existing mathematical model of the movement of the dynamic "cart-load" system was used to conduct the research, which, based on the results of mathematical transformations, was simplified to a system of three linear differential equations. In the given optimal control problem, asymmetric constraints on optimal control were used, and the problem was reduced to the problem of unconstrained minimization of the integral-terminal criterion. Since the solution of the problem was found in the closed-loop form, a control function was developed. It included the phase coordinates function vector and vector of parameters K1...K4. The general solution of the optimization problem consisted in finding the values of acceleration duration T and components K1...K4. The modified RING-ROT-PSO optimization method was used to solve the problem. As a result of solving the optimization problem, the mode of movement of the dynamic "crane-load" system of the slewing mechanism was obtained, which eliminates the load's oscillations during acceleration to a steady velocity even when the system is affected by external stochastic disturbances. According to the results of the solution, the corresponding graphical dependencies characterizing the kinematic, dynamic and energy characteristics were built and their analysis was carried out.

We consider stochastic almost output synchronization for time-varying directed networks of nonidentical and non-introspective (i.e., agents have no access to their own states or outputs) agents under external stochastic disturbances. The network experiences switches at unknown moments in time without chattering. A purely decentralized (i.e., the additional communication channel among agents is dispensed) time-invariant protocol based on a low- and high-gain method is designed for each agent to achieve stochastic almost output synchronization, while reducing the impact of stochastic disturbances.Moreover, we extend the problem to the case where stochastic disturbances can have nonzero mean or other disturbances are present with known frequencies. Another purely decentralized protocol is designed to completely reject the impact of disturbances with known frequencies on the synchronization error.

The dynamics of many real-life control applications is influenced significantly by external stochastic disturbances. In the simplest case, these disturbances can be described by Gaussian probability distributions. In such cases, the corresponding continuous-time system models turn into systems of stochastic differential equations. Moreover, colored noise can be obtained by a suitable continuous-time filtering of white Gaussian noise. For that reason, it is often sufficient to limit the analysis and design of control systems with stochastic disturbances to the case in which the disturbance inputs can be described by a standard Brownian motion (standard Wiener process). Using suitable techniques for stability analysis of systems of stochastic differential equations, the robustness of linear and nonlinear control strategies can be evaluated and improved for many practical applications. In this paper, a stability and robustness analysis is performed for feedback linearizing controllers of crane systems in marine applications. In this scenario, external disturbances are mostly caused by the excitation of oscillations due to wind and waves. Representative simulation results and an investigation of different control procedures regarding their capability to stabilize the nonlinear closed-loop control system in the presence of stochastic disturbance inputs conclude this paper.

Distributed adaptive tracking-type games are investigated for a class of coupled stochastic linear multi-agent systems with uncertainties of unknown structure parameters, external stochastic disturbances, unmodeled dynamics, and unknown agents' interactions. The control goal is to make the states of all the agents converge to a desired function of the population state average (PSA). Due to the fact that only local information is available for each agent, the control is distributed. For the time-invariant parameter case, the extended least-squares algorithm, Nash certainty equivalence (NCE) principle, and certainty equivalence (CE) principle are used to estimate the unknown parameters and the PSA term, and to design adaptive control, respectively. Under some mild conditions, it is shown that the closed-loop system is almost surely uniformly stable with respect to the population number N; the estimate for the PSA term is strongly consistent; the adaptive control is almost surely an asymptotic Nash equilibrium. When the dynamics of each agent contains time-varying parameters and unmodeled dynamics, the projected least mean square (LMS) algorithm, NCE principle, and CE principle are adopted to estimate the unknown time-varying parameters, and the unknown PSA term, and to design robust adaptive control, respectively. In addition to stability of the closed-loop system and consistency of the PSA estimate, the control law is shown to be robust Nash equilibrium with respect to the unmodeled dynamics, the variation of the unknown parameters, and the external disturbances. Two numerical examples are given to illustrate the methods and results of this paper.

The exhaust gas recirculation (EGR) valve plays an important role in improving engine fuel economy and reducing emissions. In order to improve the positioning accuracy and robustness of the EGR valve under uncertain dynamics and external disturbances, this paper proposes a positioning servo system design for an electromotive (EM) EGR valve based on the Kalman filter. Taking a novel valve driven by a central winding limited angle torque motor (LATM) as the object, we have fully considered the influence of the motor rotor position and load current, as well as the magnetic field saturation and cogging effect, improved the existing LTAM model, and derived accurate torque expression. The parameter uncertainty of the above internal model and the external stochastic disturbance were unified as “total disturbance”, and a Kalman filter-based observer was designed for disturbance estimations and real-time feed-forward compensation. Furthermore, using non-contact magnetic angle measurements to obtain accurate valve position information, a position control model with real-time response and high accuracy was established. Numerous simulated and experimental data show that in the presence of ± 25% plant model parameter fluctuations and random shock-type disturbances, the servo system scheme proposed in this paper achieves a maximum position deviation of 0.3 mm, a repeatability of positioning accuracy after disturbances of 0.01 mm, and a disturbance recovery time of not more than 250 ms. In addition, the above performance is insensitive to the duration of the disturbance, which demonstrates the strong robustness, high accuracy, and excellent dynamic response capability of the proposed design.

This paper presents a control system synthesis technique for direct, computer-aided design of control system software with performance improvements in the areas of: sample time determination, control/structural interactions, noise effects (including gusts), dynamic response characteristics, and reduced sensor requirements. The design approach uses a newly developed set of control synthesis computer programs (known as DIGISYN). DIGISYN is based on stochastic control and estimation theory. Control requirements are specified as upper bounds for the state vector error and the desired vehicle response to either control commands or external disturbances. Using a system dynamics model that includes parasitic modes, DIGISYN collectively considers system and sensor noise and external stochastic disturbances (e.g., wind gusts) to determine the maximum permissible sample time, the optimal state estimator, and a set of feedback gains to yield the desired response characteristics. The unique feature of this approach is that sample time is determined by propagating the state covariance matrix until the specified error bounds are exceeded. The rationale for using this method to determine sampling time is that corrective action to reduce the system errors is only applied at the end of each sample period. This paper discusses an application of DIGISYN to pitch-plane control of the Grumman V/STOL Design 607A and verifies performance via a time history simulation. I. Introduction EVOLVING aircraft requirements include extended flight regimes for multimission aircraft and advanced control modes (e.g., automatic landing, speed command, load alleviation) to obtain improved performance. This increasing demand on flight control systems plus the trend toward increased use of computers in aircraft mandates an organized methodology for digital design. In this paper, autopilot is defined as the software link between flight control commands (generated manually or via an automatic guidance law), vehicle mo

Active-disturbance-rejection controlling method is proposed in this essay aiming at the problems of omnidirectional robots, such as complex model, strong coupling and controlling difficulty caused by internal and external stochastic disturbance. Taking eight-wheel omnidirectional robots as the example, the coupling method based on active-disturbance-rejection is designed by analysing the kinematic-dynamic model of the robot. Non-linear function is used as the state feedback of the components of the active-disturbance rejection controller, and extended state observe is adopted to estimate the internal and external stochastic disturbances and to provide active disturbance compensation. Through simulation experiment comparing with traditional PID controller, the decoupled active-disturbance-rejection controller can control omnidirectional robots better inhibit the unknown disturbance and improve the performance of the system.

ABSTRACTIn this paper, both linear extended state observer (ESO) and nonlinear ESO with homogeneous weighted functions are proposed for a class of multi-input multi-output (MIMO) nonlinear systems composed of coupled subsystems with large stochastic uncertainties. The stochastic uncertainties in each subsystem including internal coupled unmodelled dynamics and external stochastic disturbance without known statistical characteristics are lumped together as the stochastic total disturbance (extended state) of each subsystem. The linear ESO and nonlinear ESO are designed separately for real-time estimation of not only the unmeasured state but also the stochastic total disturbance of each subsystem. The practical mean square convergence of these two classes of ESOs are developed. Some numerical simulations are presented to demonstrate the effectiveness of the ESOs with the advantages of smaller peaking values and more accurate estimation by the nonlinear ESO.

In this paper, the active disturbance rejection control (ADRC) approach is applied to a class of multi-input multioutput (MIMO) uncertain stochastic nonlinear systems. An extended state observer (ESO) is first designed for estimation of both unmeasured states and stochastic total disturbance of each subsystem which represents the total effects of internal unmodeled stochastic dynamics and external stochastic disturbance with unknown statistical property. The ADRC controller based on the states of ESO is further designed to achieve the closed-loop system’s output regulation performance including practical mean square reference signals tracking, disturbance attenuation, and practical mean square stability when the reference signals are zero avoiding solving any partial differential equations in the conventional output regulation theory. Some numerical simulations are presented to demonstrate the effectiveness of the proposed ADRC approach.

Extended state observer (ESO) is the key part of active disturbance rejection control, a new control strategy motivated and developed highly from PID’s model-free feature. In this paper, both constant gain ESO and time-varying gain ESO are proposed for a class of multi-input multi-output uncertain stochastic nonlinear systems subject to vast stochastic uncertainties. The total stochastic uncertainties in each subsystem including unmodeled dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without known statistical characteristics, and uncertain nonlinear interactions between subsystems are regarded as the stochastic total disturbance (extended state) of each subsystem of the plant. The constant gain ESO and time-varying gain ESO are designed for the estimation of not only the unmeasured state but also the stochastic total disturbance of each subsystem in real time, and the corresponding mean square convergence of these two classes of ESOs are developed rigorously. Some numerical simulations are presented to demonstrate the effectiveness of estimation by ESO approach and the peaking value reduction by the time-varying gain ESO.