Cluster synchronization of fractional-order complex networks via uncertainty and disturbance estimator-based modified repetitive control

The combined problems of cluster synchronization and disturbance rejection for a family of fractional-order complex networks subject to coupling delay, unknown uncertainty and disturbances (UDs) are examined in this study. In particular, the existence of coupling delay is taken into the account with both known and unknown cases. First, a new uncertainty and disturbance estimator (UDE)-based control protocol is formulated for the concerned system to estimate and compensate for the effects of UD. Although the UDE strategy has proven to be a viable tool to deal with slowly changing UDs in control design, the presence of rapidly changing UDs or sinusoidal disturbances is not an effective tool. A well-known modified iterative control (MRC) block is built internally in a closed feedback control loop to solve this problem. After implementing UDE and MRC blocks into the feedback loop, the resulting system becomes almost UD-free. Moreover, a set of sufficient linear matrix inequality constraints are established to ensure the cluster synchronization of the resulting system. Lastly, the benefits, feasibility and robustness of the established UDE-based MRC scheme are confirmed by two illustrative examples.     

Robust adaptive sliding mode control for uncertain discrete-time systems with time delay

This paper focuses on robust adaptive sliding mode control for discrete-time state-delay systems with mismatched uncertainties and external disturbances. The uncertainties and disturbances are assumed to be norm-bounded but the bound is not necessarily known. Sufficient conditions for the existence of linear sliding surfaces are derived within the linear matrix inequalities (LMIs) framework by employing the free weighting matrices proposed in He et al. (2008) [3], by which the corresponding adaptive controller is also designed to guarantee the state variables to converge into a residual set of the origin by estimating the unknown upper bound of the uncertainties and disturbances. Also, simulation results are presented to illustrate the effectiveness of the control strategy.     

Robust 2DoF PI tuning rules for integrating processes with dead time via frequency response model matching

The integrating characteristics are commonly found in composition control and level control of a distillation column in chemical processes. This paper presents a simple and intuitive robust tuning method of two-degree-of-freedom (2DoF) proportional-integral (PI) controller for integrating processes with dead time. The frequency response model matching approach is utilized with performance and robustness considerations for both regulatory and servo control issues. The regulatory control issue aims at matching the frequency response of the closed-loop system with that of the reference model for disturbance rejection, where the feedback controller parameters are calculated by solving a group of overdetermined algebraic equations subject to a robustness constraint evaluated by the maximum sensitivity. The target of the servo response is to follow a prescribed set-point reference trajectory, with the set-point weighting factor tuned to satisfy a defined tracking performance metric. A curve fitting procedure is utilized to generate analytical tuning rules in terms of the process model parameters and the desired robustness specification. It is shown that, apart from giving more exact achievement of the control system robustness, the tuning rules presented work well for a wider range of process dynamics than the existing methods. Illustrative examples are given to show the effectiveness of the proposed method.     

L1-gain analysis and control of impulsive positive systems with interval uncertainty and time delay

This paper investigates L₁-gain analysis and control of impulsive positive systems (IPSs) with interval uncertainty and time delay. For different types of impulsive effect, by means of the Razumikhin techniques and Lyapunov function theory, conditions are developed for guaranteeing the robust exponential stability with L₁-gain performance. Then the positive stabilization with L₁-gain performance is also addressed for IPSs with interval uncertainty and time delay through the state feedback control. In addition, the way to explore the minimum L₁-gain is discussed. All the obtained conditions can be easily inspected by the linear programming (LP) method when some parameters are preset. Finally, simulations are provided to demonstrate the validity of the theoretical results.     

Robust control for discrete-time singular large-scale systems with parameter uncertainty

This paper addresses the problem of robust stabilization for uncertain discrete-time singular large-scale systems with parameter uncertainties. The system under consideration is not necessarily regular. The parameter uncertainties are assumed to be time invariant, but norm-bounded. The purpose of the robust stabilization problem is to design state feedback controllers such that, for all admissible uncertainties, the closed-loop system is regular, causal and stable. In terms of strict LMIs, sufficient conditions for the solvability of the problem is presented, and the parameterization of desired state feedback controllers is also given. A numerical example is given to demonstrate the applicability of the proposed design approach.     

Distributed state estimator-based consensus tracking of multi-agent systems with exogenous disturbance

The consensus tacking problem for multi-agent systems with a leader of none control input and unknown control input is studied in this paper. By virtue of the relative state information of neighboring agents, state estimator and disturbance estimator are designed for each follower to estimate the system states and exogenous disturbance, respectively. Meanwhile, a novel control protocol based on two estimators is designed to make tracking error eventually converge to zero. Furthermore, the obtained results are further extended to the leader with unknown control input. A novel state estimator with adaptive time-varying gain is proposed such that consensus tracking condition is independent of the Laplacian matrix with regard to the communication topology. Finally, two examples are presented to verify the feasibility of the proposed control protocol.     

Direct synthesis-based controller design for integrating processes with time delay

Using the direct synthesis method, a PID controller in series with a lead/lag compensator is designed for control of open loop integrating processes with time delay. Set-point weighting is considered for reducing the undesirable overshoot. Guidelines are provided for selection of the desired closed loop tuning parameter in the direct synthesis method and set point weighting parameter. The method gives significant load disturbance rejection performances. Illustrative examples are considered to show the performances of the proposed method. Significant improvement is obtained when compared to recently reported methods.     

Analysis and tuning of reduced-order active disturbance rejection control

To reduce the phase lag introduced by extended state observer (ESO), an reduced-order active disturbance rejection control (RADRC) method is recommended. This paper investigates the structure and parameter tuning of RADRC. Firstly, it is shown that RADRC can serve as a general-purpose fixed-structure controller because any proper controller with integrator can be realized via an RADRC. Then the relationship between the parameters of an RADRC and those of a full-order linear active disturbance rejection control (LADRC) is analyzed. It is shown that an RADRC with the proper controller and observer gains can obtain similar disturbance-rejection performance as a full-order LADRC. Simulation results demonstrate that any plant that can be controlled by LADRC can also be controlled by an RADRC with a similar disturbance-rejection performance.     

Dynamic event-triggered control of networked control systems with uncertainty and transmission delay

This paper presents a method for designing dynamic event-triggered controller of networked control systems (NCSs) with uncertainty and time delays. Under the condition that the Lyapunov function of the system is allowed to increase at each jump point, the globally exponentially stable (GES) of the system can be achieved by using the Riccati differential equation and the principle of average dwell time (ADT). The minimum allowable inter-event interval is obtained by limiting the increment of the Lyapunov function within the transmission interval. Both the static event triggering and no transmission delay are included in the designed dynamic event triggering mechanism as special cases. A numerical example is given to verify the correctness and validity of the proposed method.     

Optimal control for linear systems with time delay in control input

This paper presents the optimal regulator for a linear system with time delay in control input and a quadratic cost function. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with time delay in observations, and then proved using the maximum principle. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included.     

Analysis and robust control of system with uncertainty and disturbance using equivalent-input-disturbance approach

This paper addresses the control problem of an uncertain system suffering from an exogenous disturbance. A new degree of control freedom is developed to handle the problem based on the equivalent-input-disturbance (EID) approach. The effect of the disturbance and uncertainties is equivalent to that of a fictitious disturbance on the control input channel, which is called an EID. A state observer and an improved EID (IEID) estimator are devised to produce an estimate that is used to compensate for the disturbance and uncertainties in a control law. A second-order low-pass filter is employed in the estimator to provide a way to solve a tradeoff between disturbance rejection and noise suppression. The slope of the Bode magnitude curve at high frequencies is two times larger for the IEID estimator than for a conventional one. This makes the IEID estimator less sensitive to measurement noise and more practical. Sufficient analyses reveal the mechanism of disturbance rejection, uncertainty attenuation, and noise suppression of an IEID-based control system. A theorem is derived to guarantee system stability and a procedure is presented for system design. Simulations and experiments of the position control of a magnetic levitation system are carried out to show the validity of the presented method.     

Robust exponential stability of uncertain impulsive delay difference equations with continuous time

In this paper, the robust exponential stability of uncertain impulsive delay difference equations is investigated. First, some robust exponential stability criteria for uncertain impulsive delay difference equations with continuous time in which the state variables on the impulses may relate to the time-varying delays are provided. Then a robust exponential stability result for uncertain linear impulsive delay difference equations with discrete time is given. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results.     

Robust adaptive multistage anti-windup dynamic surface control for dynamic positioning ships with mismatched disturbance

In this paper, a novel robust adaptive multistage anti-windup control strategy is developed for dynamic positioning ships in presence of input constraint, mismatched disturbance and external disturbance. Based on dynamic surface control technique, a composite control law, where both mismatched and matched disturbances are compensated, is established to stabilize the system without the requirement of solving any partial differential equations. In particularly, the mismatched disturbance caused by the model transformation is analyzed firstly and the better steady performance is achieved. In addition, a novel multistage anti-windup control based on anticipatory activation compensation is constructed to handle the input constraint while the transient performance is improved significantly. Moreover, the stability of the closed-loop system is proven via Lyapunov technique rigorously, and the tracking error can be forced into an arbitrarily small neighborhood around zero. Finally, simulations with comparisons demonstrate the effectiveness of the proposed method.     

Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations

The problem of finite-time stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature.     

Robust multivariable predictive control for laser-aided powder deposition processes

This paper presents a robust multivariable predictive control for laser-aided powder deposition (LAPD) processes in additive manufacturing. First, a novel control-oriented MIMO process model is derived. Then, the objective of achieving desired geometrical and thermal properties is formulated as one of generating and tracking nominal reference profiles of layer height and melting pool temperature. This is accomplished via a nonlinear model predictive control with guaranteed nominal stability. Furthermore, a local ancillary feedback law is derived to provide robustness to bounded uncertainties. The paper verifies the effectiveness of the proposed control via a case study on a laser cladding process.     

Offset-free trajectory tracking control for hypersonic vehicle under external disturbance and parametric uncertainty

A novel offset-free trajectory tracking control strategy is proposed for a hypersonic vehicle under external disturbances and parameter uncertainties. In order to realize the real-time control for the hypersonic vehicle, the predictive control law is divided into the on-line design and off-line design. Unlike general nonlinear disturbance observer-based control which involves designing the disturbance compensation strategy, the influences of the disturbances on the velocity and altitude are attenuated by the direct feedback compensation (DFC). Particularly, the offset-free tracking feature is proved for the output reference signal. Simulations show that the real-time control can be realized for the hypersonic vehicle, the controls and angle of attack are all in their given constraint scopes, and the velocity and altitude can track the given references accurately even under mismatched disturbances.     

Robust exponential stability for uncertain time-varying delay systems with delay dependence

This paper investigates the exponential stability problem for uncertain time-varying delay systems. Based on the Lyapunov-Krasovskii functional method, delay-dependent stability criteria have been derived in terms of a matrix inequality (LMI) which can be easily solved using efficient convex optimization algorithms. These results are shown to be less conservative than those reported in the literature. Four numerical examples are proposed to illustrate the effectiveness of our results.     

State bounding for nonlinear time-varying systems with delay and disturbance

This paper deals with the problem of state bounding for a class of nonlinear time-varying systems with delay and bounded disturbance. By using a model transformation and an approach developed in positive systems, new delay-dependent explicit conditions have been established to guarantee all the state trajectories of the system converge exponentially within a ball. Two illustrative examples are given to show that the obtained results can be applied to some cases not covered by preceding results.     

Robust state-feedback control design for active suspension system with time-varying input delay and wheelbase preview information

This paper develops a robust state-feedback controller for active suspension system with time-varying input delay and wheelbase preview information in the presence of the parameter uncertainties. By employing system augmentation technique, a multi-objective control optimization model is first established and then this controller design is converted to a static full-state feedback controller design with robust H_∞ and generalized H₂ performance, wherein the model-dependent control gain is evaluated by transforming the related nonlinear matrix inequalities into their corresponding linear matrix inequality forms based on Lyapunov theory, and then LMI (Linear-Matrix-Inequality) technique is applied to solve and obtain the desired controller. A numerical simulation case is finally provided to reveal the effectiveness and advantages of the proposed controller.     

Adaptive sliding mode trajectory tracking control of robotic airships with parametric uncertainty and wind disturbance

An adaptive sliding mode trajectory tracking controller is developed for fully-actuated robotic airships with parametric uncertainties and unknown wind disturbances. Based on the trajectory tracking model of robotic airships, an adaptive sliding mode control strategy is proposed to ensure the asymptotic convergence of trajectory tracking errors and adaptive estimations. The crucial thinking involves an adaptive scheme for the controller gains to avoid the off-line tuning. Specially, the uncertain physical parameters and unknown wind disturbances are rejected by variable structure control, and boundary layer technique is employed to avoid the undesired control chattering phenomenon. Computer experiments are performed to demonstrate the performance and advantage of the proposed control method.