Exogenous Disturbances Research Articles

H∞ Filtering of Mean Field Stochastic Differential Systems

This paper addresses the H∞ filtering problem for mean field stochastic differential systems that involve both state-dependent and disturbance-dependent noise. We assume that the state as well as the measurement output is distracted by an uncertain exogenous disturbance. Firstly, a sufficient condition for the stochastic-bounded real lemma is given. Next, H∞ filtering, which is built upon a stochastic-bounded real lemma, is put forward by two linear matrix inequalities. Furthermore, the validation of the theoretical analysis is demonstrated with two examples.

Q‐learning‐based H∞ control for LPV systems

AbstractIn this paper, a model‐free H∞ control method is developed for discrete‐time linear parameter‐varying (LPV) systems by leveraging Q‐learning, which employs the data encompassing system states, control inputs, exogenous disturbance, and time‐varying convex hull rather than the dynamical model known a priori. A policy iteration algorithm presented via linear matrix inequality formed by such collected data is developed with convergence guarantee. Our analysis demonstrates that, in the presence of sufficiently rich disturbances, the attenuation level converges to a lower value than the traditional H∞ control solution derived from an exact LPV model. A numerical example is demonstrated to verify the stabilization, disturbance attenuation, adaptivity, and convergence of the H∞ attenuation level. Moreover, a continuous stirred tank reactor (CSTR) approximated by a discrete‐time LPV system is employed to show the practical potential of the developed model‐free approach.

An Identification-Based Control Method for an Overhead Crane with a New Combined Sensor Placement

This paper is devoted to an automatic control method for an overhead crane under the current parametric uncertainty of the crane, transported cargo, and exogenous disturbances. The control objective is to move the cargo in the horizontal plane to a point ensuring the final delivery of the cargo to the designated place while parrying the angular oscillations of the suspension and reaching given dynamic characteristics. The approach is based on a control scheme with a current parametric identification algorithm, an implicit reference model, and “simplified” adaptability conditions to track cargo movements directly. The control law generates a given trolley speed for the servo drive. The passport data of the crane installation are used to select the control law parameters. Unlike previous publications on the topic, the solution proposed below is simpler, more reliable in terms of operation, and less expensive. This is achieved by placing a combined sensor (an accelerometer with an angular rate sensor (ARS)) on a suspension cable near the crane trolley and applying, first, an algorithmic solution without the preliminary calculation of the ARS drift and, second, a current parametric identification procedure of higher efficiency. Computer simulation results are provided to confirm these advantages of the new solution. A similar example is implemented on an experimental installation.

Asynchronous time dependent switched model predictive control for nonlinear systems considering feasibility constraints

AbstractThis paper presents a model predictive control for nonlinear asynchronous switched systems, aiming to achieve H∞ performance and addressing feasibility issues. The method proposed guarantees the recursive feasibility of each sub‐system after switching moments in the presence of exogenous disturbances and unknown matched and mismatched time intervals due to asynchronous switching. The boundaries of the feasibility region for each sub‐system are determined in order to impose constraints on decision parameters and switching signals. These constraints aim to maximize the mentioned region while ensuring stability. Additionally, by identifying the common region of feasibility among different sub‐systems, conditions are established for initializing the sub‐systems at the switching moments to ensure that the system states remain within this feasibility region even under the worst switching scenario. Therefore, by ensuring the initial feasibility at the switching moments and demonstrating recursive feasibility, the overall feasibility of the developed MPC is guaranteed at all times. The benefits of the proposed approach are thoroughly investigated through the simulation of a chemical system. The results demonstrate the effectiveness of the proposed method.

Disturbance rejection for switched singular systems using state decomposition technique and equivalent-input-disturbance with a dynamic state observer

In this study, an equivalent-input-disturbance (EID) method with a dynamic state observer and a state decomposition technique (SDT) are used to explore the disturbance rejection of a class of linear switched singular systems. The EID approach defines an EID signal, is defined for the control input channel and has the same impact on the system as exogenous disturbances. Additionally, it employs an observer to estimate the EID and achieves good disturbance-rejection performance. However, in the EID method, the coefficient matrix of the observer needs to be consistent with the coefficient matrix of the original system, which limits the application of the method. So, a dynamic state observer is designed to reconstruct the system state and estimate the disturbance in this study. Based on the state feedback control strategy, a disturbance-rejection control law containing disturbance information is designed and a closed-loop control system structure is established. Subsequently, the state equation of the closed-loop system is reorganized and decomposed into an algebraic equation and a differential equation using the SDT. Then, a Lyapunov function with few decision variables is designed to obtain an admissible criterion for the closed-loop system and the controller gains under arbitrary switching signals. Finally, the effectiveness of the presented method is verified via numerical simulations.

Observer-based proportional-retarded controller for payload swing attenuation of 2D-crane systems including load hoisting-lowering

Crane systems are essential systems utilized in industry and for research. Nevertheless, they are always affected by endogenous and exogenous disturbances, which may generate undesirable payload oscillations, compromising people’s security and the system itself. Thus, to deal with these issues and control these mechatronic systems efficiently, this manuscript develops a novel robust observer-based proportional-retarded controller for perturbed two-dimensional cranes, considering variation in the rope length. This novel scheme makes the trolley follow a desired reference signal while reducing the payload variations. The controller structure allows for compensating disturbances, while a new control approach introduces artificial delays that stabilize the closed-loop system and attain the desired control objective. A formal theoretical analysis demonstrates the validity of the new proposal. Then, experimental results show the outstanding performance of the proposed control scheme and its superior performance against other methodologies from the literature.

Data-Driven Dynamic Internal Model Control.

A data-driven dynamic internal model control (D3IMC) scheme is proposed for unknown nonlinear nonaffine systems bypassing modeling steps. Different from the traditional internal model constructed by either a first-principle or an identified model, a dynamic internal model (DIM) is developed in this work using I/O data where a compact form dynamic linearization approach is introduced for addressing the nonlinearity and nonaffine structure. Then, the D3IMC is proposed with both a nominal control algorithm and an uncertainty compensation control algorithm. The former can quickly respond to the feedback errors and the latter can compensate the model-plant mismatch and external disturbances. Meanwhile, the adaptive parameter updating law in the proposed D3IMC method inherits the robustness against uncertainties. A nominal D3IMC is also designed without including the compensator when there is no exogenous disturbance since the adaptive mechanism can handle system uncertainty. Further, the results are extended and a full-form dynamic linearization-based D3IMC is developed to address control of nonlinear systems with more complex dynamics. All the proposed D3IMC methods are data-driven without need of an explicit model, and thus they are significant extensions from the traditional model-based IMC. Simulation study verifies the results.

Observer-Based Asynchronous Boundary Stabilization for Stochastic Markovian Reaction-Diffusion Neural Networks.

This work investigates the observer-based asynchronous boundary stabilization for a kind of stochastic Markovian reaction-diffusion neural networks with exogenous disturbances. Specifically, parameter uncertainties are considered in the drift item. First, a hidden Markov model is introduced that guarantees the observer modes run asynchronously with the system modes. It should be noted that the asynchronous observer constructed in this work only uses the boundary measurement information. Then a nonfragile asynchronous observer-based boundary controller is designed. Taking advantage of inequality techniques and stochastic analysis method, sufficient criterion is provided to satisfy input-to-state exponentially mean-square stability, and the asynchronous boundary observer/controller gains are further derived. As a special case, the synchronous observer-based boundary stabilization is also obtained. Finally, a numerical example is exploited to manifest the validity of the established results.

Disturbance observer-based event-triggered impulsive control for nonlinear systems with unknown external disturbances

Input-to-state practical stability (ISpS) of a kind of nonlinear systems suffering from unknown exogenous disturbances is explored in this article, where a disturbance observer is established to estimate the information of the exogenous disturbances. To achieve ISpS of the system, the impulsive controller as well as state-feedback controller are both considered to regulate the discrete and continuous dynamics of the system, respectively. Especially, a novel disturbance observer-based event-triggered mechanism is devised to decide the release of impulsive control signal. Furthermore, several adequate conditions are given for excluding the occurrence of Zeno phenomenon. To confirm the feasibility of the proposed results, two numerical instances and their corresponding simulation results are presented.

Modeling of servo dynamic stiffness for multiple-periodic repetitive learning control system

Servo dynamic stiffness is a pivotal index in characterizing the rejecting performance for the exogenous periodic disturbances of the repetitive learning control system. In this paper, the mathematical modeling of the servo dynamic stiffness for the well-designed repetitive learning control system with multiple-periodic signals is studied by the frequency analysis method. To analysis the complex form of the servo dynamic stiffness, the magnitudes of the direct (real part) and quadrature (imaginary part) servo dynamic stiffness at harmonics of the disturbance are discussed based on the parameters of the repetitive learning controller. An illustrated example of the two linear servomotors with the mechanical coupling is given in this study. Computer simulation are presented to illustrate the effect of the proposed measurement method of the servo dynamic stiffness for the multiple-periodic repetitive learning control system. The proposed servo dynamic stiffness modeling can be used to accurate design the parameters of the repetitive learning control system, such that the batter control performance of the repetitive learning control system at most of the harmonics of the multi-periodic input signal can be achieved.

A dual scale spatio‐temporal control for complex distributed parameter systems

AbstractIt is very difficult to control the distributed parameter system (DPS) for consistent spatial performance. In this paper, a dual scale spatio‐temporal control is designed for the DPS to achieve a consistent performance across the entire workspace under unknown exogenous disturbances. First, the generalized “spatial observer” should be designed under spectral decomposition/synthesis, to act as the nominal model of the DPS, through which the spatial mismatch between the model and the process could be estimated. Then a distributed disturbance compensator can be constructed to suppress all the undesirable spatial disturbance through the inner loop, and the compensated system will become closer to the nominal model and easier to control. Third, a dual controller will be designed in the outer loop for the final consistent spatial performance. Since the spatial performance is mainly affected by the dominant dynamics on the slow scale, a convex optimization algorithm can be effectively established in terms of nonlinear matrix inequalities for the dual controller. In this way, the nonlinear optimization problem is solved by converting it into the problem of a linear matrix inequalities with constraints. Besides, the spatio‐temporal state variable of the controlled plant is demonstrated to converge in Hilbert space. The feasibility and effectiveness of the proposed control method are verified by temperature control of a catalytic rod, a benchmark in chemical reactors.

Interval Observers for Estimating Unknown Inputs in Discrete Time-Invariant Dynamic Systems

This paper considers discrete time-invariant systems (with constant parameters) described by dynamic models in the presence of exogenous disturbances. For such systems, the problem of estimating unknown inputs using interval observers is studied. The solution is based on a minimal-dimension disturbance-insensitive model of the original system. For this model, an interval observer is designed and then used to estimate the unknown inputs. The theoretical results are illustrated with a practical example.

Adaptive dynamic‐surface repetitive control for uncertain nonlinear systems with mismatched disturbances and input delay

AbstractBased on additive state decomposition technique, this article presents an adaptive dynamic‐surface repetitive control method for a class of uncertain nonlinear systems with mismatched disturbances and input delay. First, the original uncertain nonlinear system is decomposed into a linear time invariant (LTI) primary system responsible for the periodic signal tracing and rejection task, and a nonlinear secondary system with input time delay responsible for the robust stabilization task. A modified repetitive controller with a small correction to the delay constant is then independently designed for the LTI primary system, while an adaptive dynamic surface controller is designed for the nonlinear secondary system. Stability analysis is performed for each subsystem and the design procedure of the whole system is presented in detail. Finally, comparative simulations with other repetitive control and dynamic surface control methods show that the presented method not only relaxes the constraints on the reference inputs and exogenous disturbances, but also ensures that the system has better disturbance rejection and periodic‐signal tracking performance in both transient and steady states. As a result, this method broadens the application of both repetitive control and dynamic surface control.

Leader-following consensus tracking control for fractional-order multi-motor systems via disturbance-observer

Abstract The leader-following consensus tracking control of fractional-order (FO) multi-motor systems (FOMMSs) in the presence of exogenous disturbances is investigated. It is widely recognized that FO models are better than integer-order (IO) ones for representing systems with memory effects. Therefore, studying the consensus tracking control of FOMMSs is essential. In this paper, a consensus tracking protocol is developed using a disturbance-observer and state feedback to deal with unknown exogenous disturbances. The closed-loop system stability is analyzed via Lyapunov and graph theory. Novel sufficient conditions for the stabilization of each motor are derived in the form of linear matrix inequalities. Simulation results illustrate the validity and efficacy of the proposed consensus protocol, namely its strong synchronization ability and robustness.

Effects of adolescent alcohol exposure on oligodendrocyte lineage cells and myelination in mice: Age and subregion differences

Adolescence is an important phase for the structural and functional development of the brain. The immaturity of adolescent brain development is associated with high susceptibility to exogenous disturbances, including alcohol. In this study, the acquisition of conditioned place preference (CPP) in adolescent mice by alcohol (2 g/kg) and the parvalbumin-positive interneurons (PV+ interneurons), oligodendrocyte lineage cells (OPCs), and myelination in the medial prefrontal cortex (mPFC) were assessed. We aim to determine the age- and subregional-specificity of the effects of alcohol. Alcohol (2 g/kg) was injected intraperitoneally on even days, and saline was injected intraperitoneally on odd days. The control group received a continuous intraperitoneal injection with saline. Differences in alcohol-induced CPP acquisition were assessed, followed by immunohistochemical staining. The results showed a pronounced CPP acquisition in 4- and 5-week-old mice. In the mPFC, there were reduced PV+ interneurons and OPCs in 3-week-old mice and reduced oligodendrocyte numbers in 4-week-old mice. The 5-week-old mice showed impaired myelination and a decrease in the number of PV+ interneurons, mature oligodendrocytes, and OPCs in the mPFC. Since the alterations in 5-week-old mice are more pronounced, we further explored the mPFC-associated subregional-specificity. In the alcohol-exposed mice, the oligodendrocyte numbers were decreased in the anterior cingulate cortex (ACC), PV+ interneuron numbers were declined in the prelimbic cortex (PL), and the number of oligodendrocytes, PV+ interneurons, and OPCs was also decreased with impaired myelination in the infralimbic cortex (IL). Our data suggest that adolescent alcohol exposure notably affected the acquisition of CPP, myelin formation, and the counts of PV+ interneurons, mature oligodendrocytes, and OPCs in the mPFC in 5-week-old mice. Also, the IL subregion was the worst-affected subregion of the mPFC in alcohol-exposed 5-week-old mice. It reveals that the effects of alcohol on adolescence and its mPFC myelination show obvious age- and subregional-specificity.

A switching approach to repetitive control for Takagi-Sugeno fuzzy systems

Repetitive control has learning properties and exhibits high accuracy in periodic control but struggles with nonlinearities and disturbances. To address this issue, the study presents a composite method of repetitive control and equivalent input disturbance based on the Takagi-Sugeno fuzzy model. The control structure takes into account both the continuous-discrete two-dimensional characteristics of the repetitive control and the membership function of the fuzzy system. As the first component of the control configuration, a repetitive controller is adopted for the high-precision tracking of periodic references. Then, an equivalent-input-disturbance estimator is used to compensate for exogenous disturbances. The closed-loop system is stabilized using the state feedback and the state observer. To ensure stability, membership function-dependent Lyapunov candidates are used to derive a less conservative stability condition. Consequently, all gains in the controller switch with the derivative sign of the premise variables. Finally, the developed approach is validated through comparisons with typical methods, demonstrating its effectiveness and advantages.

Robust H∞ Static Output Feedback Control for TCP/AQM Routers Based on LMI Optimization

This paper proposes a new static output feedback control method to address the congestion control problem in transmission control protocol networks using active queue management routers. Based on linear matrix inequality optimization, this method determines a static output feedback control law to minimize the norm of the transfer function between the controlled queue length of the buffer and the exogenous disturbance affecting the available link bandwidth. A linear matrix inequality formulation is presented as a sufficient condition to guarantee the closed-loop system’s asymptotic stability while maintaining disturbance rejection within a specified level, regardless of round-trip time delays. The proposed robust static output feedback control eliminates the need to measure or estimate all system states, thus simplifying practical implementation. The effectiveness of the proposed design method is demonstrated by applying it in a practical process, as illustrated through a numerical example.

Regret optimal control for uncertain stochastic systems

We consider control of uncertain linear time-varying stochastic systems from the perspective of regret minimization. Specifically, we focus on the problem of designing a feedback controller that minimizes the loss relative to a clairvoyant optimal policy that has foreknowledge of both the system dynamics and the exogenous disturbances. In this competitive framework, establishing robustness guarantees proves challenging as, differently from the case where the model is known, the clairvoyant optimal policy is not only inapplicable, but also impossible to compute without knowledge of the system parameters. To address this challenge, we embrace a scenario optimization approach, and we propose minimizing regret robustly over a finite set of randomly sampled system parameters. We prove that this policy optimization problem can be solved through semidefinite programming, and that the corresponding solution retains strong probabilistic out-of-sample regret guarantees in face of the uncertain dynamics. Our method naturally extends to include satisfaction of safety constraints with high probability. We validate our theoretical results and showcase the potential of our approach by means of numerical simulations.

Nonfragile Filtering under Bounded Exogenous Disturbances

Nonfragile Filtering under Bounded Exogenous Disturbances

Nonfragile Filtering under Bounded Exogenous Disturbances

Nonfragile Filtering under Bounded Exogenous Disturbances