Composite hierarchical antidisturbance control for a class of discrete‐time stochastic systems

In this paper, antidisturbance control and estimation problem are discussed for a class of discrete‐time stochastic systems with nonlinearity and multiple disturbances, which include the disturbance with partially known information and a sequence of random vectors. A disturbance observer is constructed to estimate the disturbance with partially known information. A composite hierarchical antidisturbance control scheme is proposed by combining disturbance observer and H_∞ control. It is proved that the 2 different disturbances can be rejected and attenuated, and the corresponding desired performances can be guaranteed for discrete‐time stochastic systems with known and unknown nonlinear dynamics, respectively. Simulation examples are given to demonstrate the effectiveness of the proposed scheme.     

Composite hierarchical anti‐disturbance control for nonlinear systems with DOBC and fuzzy control

Anti‐disturbance control and estimation problem is introduced for a class of nonlinear system subject to disturbances. The adaptive disturbance observers are constructed separately from the controller design to estimate the disturbance with partial known information. By integrating disturbance‐observer‐based control with fuzzy control, a novel type of composite hierarchical anti‐disturbance control scheme is presented for a class of nonlinear system with unknown nonlinear dynamics. Simulations for a flight control system are given to demonstrate the effectiveness of the results compared with the previous schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Composite DOBC with fuzzy fault‐tolerant control for stochastic systems with unknown nonlinear dynamics

A class of stochastic nonlinear systems with fault and multisource disturbances is concerned. The fault is a general bounded actuator fault, and the multiple disturbances include partial‐known information disturbance and white noise. A stochastic adaptive disturbance observer is constructed to estimate the partial‐known information disturbance, based on which the partial‐known information disturbance can be compensated in the feed‐foreword channel immediately. Also, the multiplicative white noise can be attenuated by the designed feedback controller. To make the composite system is satisfactory, a composite disturbance based‐observer control with fuzzy fault‐tolerant control is proposed. The pole placement and LMI method is applied to attenuate and reject the disturbance. Furthermore, the fault can be compensated simultaneously. To verify the feasibility and availability of the designed control scheme, a simulation example is shown finally.     

Finite‐Time Fault‐Tolerant Control for a Class of Non‐Affine Nonlinear System Using Sliding Mode Disturbance Observer

This study investigates a finite‐time fault‐tolerant control scheme for a class of non‐affine nonlinear system with actuator faults and unknown disturbances. A global approximation method is applied to non‐affine nonlinear system to convert it into an affine‐like expression with accuracy. An adaptive terminal sliding mode disturbance observer is proposed to estimate unknown compound disturbances in finite time, including external disturbances and system uncertainties, which enhances system robustness. Controllers based on finite‐time Lyapunov theory are designed to force tracking errors to zero in finite time. Simulation results demonstrate the effectiveness of proposed method.     

Model‐free adaptive formation control for unknown multiinput‐multioutput nonlinear heterogeneous discrete‐time multiagent systems with bounded disturbance

Based on the model‐free adaptive control, the distributed formation control problem is investigated for a class of unknown heterogeneous nonlinear discrete‐time multiagent systems with bounded disturbance. Two equivalent data models to the unknown multiagent systems are established through the dynamic linearization technique considering the circumstances with measurable and unmeasurable disturbances. Based on the obtained data models, two distributed controllers are designed with only using the input/output and disturbance data of the neighbor agents system. The tracking error of the closed‐loop system driven by the proposed controllers is shown to be bounded by the contraction mapping principle and inductive methods. An example illustrates the effectiveness of the proposed two distributed controllers.     

Elegant antidisturbance fault‐tolerant control for stochastic systems with multiple heterogeneous disturbances

In this article, the elegant antidisturbance fault‐tolerant control (EADFTC) problem is studied for a class of stochastic systems in the simultaneous presence of multiple heterogeneous disturbances and time‐varying faults. The multiple heterogeneous disturbances include white noise, norm bounded uncertain disturbances and uncertain modeled disturbances with multiple nonlinearities and unknown amplitudes, frequencies, and phases. The time‐varying fault signals are caused by lose efficacy of actuator. To online estimate uncertain modeled disturbances and time‐varying faults, a novel composite observer structure consisting of the adaptive nonlinear disturbance observer and the fault diagnosis observer is constructed. The novel EADFTC strategy is proposed by integrating composite observer structure with adaptive disturbance observer‐based control theory and H_∞ technology. It is proved that all the signals of closed‐loop system are asymptotically bounded in mean square under the circumstances of multiple heterogeneous disturbances and time‐varying faults occur simultaneously. Finally, the effectiveness and availability of proposed strategy are demonstrated by means of the numerical simulation and a doubly fed induction generators system simulation, respectively.     

Design of UDE‐based controllers from their two‐degree‐of‐freedom nature

The control algorithm based on the uncertainty and disturbance estimator (UDE) is a robust control strategy and has received wide attention in recent years. In this paper, the two‐degree‐of‐freedom nature of UDE‐based controllers is revealed. The set‐point tracking response is determined by the reference model, whereas the disturbance response and robustness are determined by the error feedback gain and the filter introduced to estimate the uncertainty and disturbances. It is also revealed that the error dynamics of the system is determined by two filters, of which one is determined by the error feedback gain and the other is determined by the filter introduced to estimate the uncertainty and disturbances. The design of these two filters are decoupled in the frequency domain. Moreover, after introducing the UDE‐based control, the Laplace transform can be applied to some time‐varying systems for analysis and design because all the time‐varying parts are lumped into a signal. It has been shown that, in addition to the known advantages over the time‐delay control, the UDE‐based control also brings better performance than the time‐delay control under the same conditions. Design examples and simulation results are given to demonstrate the findings. Copyright © 2010 John Wiley & Sons, Ltd.     

Iterative Learning Control for Linear Discrete‐Time Systems with Unknown High‐Order Internal Models: A Time‐Frequency Analysis Approach

This work focuses on the iterative learning control (ILC) for linear discrete‐time systems with unknown initial state and disturbances. First, multiple high‐order internal models (HOIMs) are introduced for the reference, initial state, and disturbances. Both the initial state and disturbance consist of two components, one strictly satisfies HOIM and the other is random bounded. Then, an ILC scheme is constructed according to an augmented HOIM that is the aggregation of all HOIMs. For all known HOIMs, an ILC design criterion is introduced to achieve satisfactory tracking performance based on the 2‐D theory. Next, the case with unknown HOIMs is discussed, where a time‐frequency‐analysis (TFA)‐based ILC algorithm is proposed. In this situation, it is shown that the tracking error inherits the unknown augmented HOIM that is an aggregation of all unknown HOIMs. Then, a TFA‐based method, e.g., the short‐time Fourier transformation (STFT), is employed to identify the unknown augmented HOIM, where the STFT could ignore the effect of the random bounded initial state and disturbances. A new ILC law is designed for the identified unknown augmented HOIM, which has the ability to reject the unknown the initial state and disturbances that strictly satisfy HOIMs. Finally, a gantry robot system with iteration‐invariant or slowly‐varying frequencies is given to illustrate the efficiency of the proposed TFA‐based ILC algorithm.     

Stochastic Optimal Design for Unknown Linear Discrete‐Time System Zero‐Sum Games in Input‐Output form Under Communication Constraints

In this paper, stochastic optimal strategy for unknown linear discrete‐time system quadratic zero‐sum games in input‐output form with communication imperfections such as network‐induced delays and packet losses, otherwise referred to as networked control system (NCS) zero‐sum games, relating to the H_∞ optimal control problem is solved in a forward‐in‐time manner. First, the linear discrete‐time zero sum state space representation is transformed into a linear NCS in the state space form after incorporating random delays and packet losses and then into the input‐output form. Subsequently, the stochastic optimal approach, referred to as adaptive dynamic programming (ADP), is introduced which estimates the cost or value function to solve the infinite horizon optimal regulation of unknown linear NCS quadratic zero‐sum games in the presence of communication imperfections. The optimal control and worst case disturbance inputs are derived based on the estimated value function in the absence of state measurements. An update law for tuning the unknown parameters of the value function estimator is derived and Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control and disturbance signals converge to optimal control and worst case disturbances, respectively. Simulation results are included to verify the theoretical claims.     

Finite‐time tracking control for a class of nonlinear systems with multiple mismatched disturbances

This article investigates the finite‐time output tracking problem for a class of nonlinear systems with multiple mismatched disturbances. To efficiently estimate the disturbances and their derivatives, a continuous finite‐time disturbance observer (CFTDO) design method is developed. Based on the modified adding a power integrator method and CFTDO technique, a composite tracking controller is constructed such that the system output can track the desired reference signal in finite time. Simulation results demonstrate the effectiveness of the proposed control approach.     

Robust control of nonlinear semi‐strict feedback systems using finite‐time disturbance observers

The output tracking controller design problem is dealt with for a class of nonlinear semi‐strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances, and uncertain nonlinear virtual control coefficients of the subsystems. The controller is designed in a backstepping manner, and to avoid the shortcoming of ‘explosion of terms’, the dynamic surface control technique that employs a group of first‐order low‐pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input‐to‐state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite‐time disturbance observer that estimates the disturbance term in a finite‐time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Composite antidisturbance control for nonlinear systems via nonlinear disturbance observer and dissipative control

This paper investigates the design problem of composite antidisturbance control for a class of nonlinear systems with multiple disturbances. First, a novel nonlinear disturbance observer‐based control scheme is constructed to estimate and compensate the disturbance modeled by the nonlinear exosystem. Then, by combining the dissipative control theory, a linear matrix inequality‐based design method of composite antidisturbance control is developed such that the augmented system is exponentially stable in the absence of unmodeled disturbances, and is dissipative in the presence of unmodeled disturbances. In this case, the original closed‐loop system is exponentially stable in the presence of modeled disturbances. Subsequently, two special cases of composite antidisturbance control are derived with H_∞ performance and passivity, respectively. Finally, the proposed method is applied to control A4D aircraft to show its effectiveness.     

Adaptive Robust Output Tracking Control of Uncertain Nonlinear Cascade Systems with Disturbance and Multiple Unknown Time‐Varying Delays

In this paper, an adaptive robust controller is designed for a class of uncertain nonlinear cascade systems with multiple time‐varying delays under external disturbance. It is assumed that multiple time‐varying delays are not exactly known and, therefore, the delayed terms must not appear in the adaptation and control laws. Accordingly, by using a Lyapunov‐Krasovskii function, delays are deleted from the adaptation and control laws. A controller based on an adaptive backstepping approach is designed to assure the global asymptotic tracking of the desired output and boundedness of the other states. The proposed controller is proved to be robust against unknown time‐varying delays and external disturbances applying to the system. Simulation results are provided to show the effectiveness of the proposed approach.     

Consensus of second‐order multi‐agent systems with exogenous disturbances

In this paper, the consensus of second‐order multi‐agent dynamical systems with exogenous disturbances is studied. A pinning control strategy is designed for a part of agents of the multi‐agent systems without disturbances, and this pinning control can bring multiple agents' states to reaching an expected consensus track. Under the influence of the disturbances, disturbance observers‐based control (DOBC) is developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi‐agent systems with disturbances under the composite controller can be achieved for fixed and switching topologies. Finally, by applying an example of multi‐agent systems with switching topologies and exogenous disturbances, the consensus of multi‐agent systems is reached under the DOBC with the designed parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

Novel sliding mode control for multi‐input–multi‐output discrete‐time system with disturbance

This paper investigates sliding mode control for multi‐input–multi‐output discrete‐time system with disturbances. First of all, a novel nonlinear sliding surface, named as hyperbolic hybrid switching sliding surface, is proposed. Two different types of hyperbolic functions are introduced into the proposed sliding surface. Due to the changing of values of the hyperbolic functions, sliding surface switching occurs during the control process, which ensures that both settling time and overshoot can be decreased. The sliding mode controller is obtained based on a novel nonlinear reaching law. The nonlinear reaching law contains several parameters, and by properly designing these parameters, we can decrease the bounds of the sliding variables to small values. The stability analysis of the sliding motion is carried out from singular system viewpoint. Finally, simulation examples and comparison examples are presented to illustrate that the system performance is improved obviously by proposed novel sliding mode control, and the system is robust to the disturbances.     

Robust control approach for input–output linearizable nonlinear systems using high‐gain disturbance observer

This paper addresses a robust control approach for a class of input–output linearizable nonlinear systems with uncertainties and modeling errors considered as unknown inputs. As known, the exact feedback linearization method can be applied to control input–output linearizable nonlinear systems, if all the states are available and modeling errors are negligible. The mentioned two prerequisites denote important problems in the field of classical nonlinear control. The solution approach developed in this contribution is using disturbance rejection by applying feedback of the uncertainties and modeling errors estimated by a specific high‐gain disturbance observer as unknown inputs. At the same time, the nonmeasured states can be calculated from the estimation of the transformed system states. The feasibility and conditions for the application of the approach on mechanical systems are discussed. A nonlinear multi‐input multi‐output mechanical system is taken as a simulation example to illustrate the application. The results show the robustness of the control design and plausible estimations of full‐rank disturbances.Copyright © 2012 John Wiley & Sons, Ltd.     

Robust Repetitive Control and Disturbance Rejection Based on Two‐Dimensional Model and Equivalent‐Input‐Disturbance Approach

A new configuration of a modified repetitive‐control system has been devised for a class of strictly proper plants that suppresses exogenous disturbances and uncertainties in the dynamics of the plant. It extends the applicability of the control system. The system consists of four parts: a two‐dimensional augmented model of the plant, which takes into account the difference in characteristics between continuous control and discrete learning in repetitive control; an equivalent‐input‐disturbance estimator; a state observer; and a state‐feedback controller. A robust‐stability condition expressed in terms of a linear matrix equality is used to determine the gains of the observer and the controller. Finally, a comparison of our method with repetitive control based on linear active disturbance rejection control (LADRC) shows how effective our method is and that it is superior to LADRC‐based repetitive control.