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This article studies the output feedback finite‐time boundary control for unstable heat systems with the spatially varying coefficient. First, a finite‐time observer with switched gains under a state‐dependent switching law is designed in order to estimate the states of the system in a finite‐time only exerting one displacement boundary measurement. Next, an observer‐based linear finite‐time control is planned. Namely, a linear switched control under a state‐dependent switching law is proposed to vanish every solution of an unstable heat partial differential equation with spatially varying coefficients in a finite time. We also present explicit forms for the proposed observer gains and output feedback finite‐time controller. Finally, some numerical simulations are provided to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

Distributed parameter systems (DPSs) frequently appear in industrial manufacturing processes, with complex characteristics such as time–space coupling, nonlinearity, infinite dimension, uncertainty and so on, which is full of challenges to the modeling of the system. At present, most DPS modeling methods are offline. When the internal parameters or external environment of DPS change, the offline model is incapable of accurately representing the dynamic attributes of the real system. Establishing an online model for DPS that accurately reflects the real-time dynamics of the system is very important. In this paper, the idea of reinforcement learning is creatively integrated into the three-dimensional (3D) fuzzy model and a reinforcement learning-based 3D fuzzy modeling method is proposed. The agent improves the strategy by continuously interacting with the environment, so that the 3D fuzzy model can adaptively establish the online model from scratch. Specifically, this paper combines the deterministic strategy gradient reinforcement learning algorithm based on an actor critic framework with a 3D fuzzy system. The actor function and critic function are represented by two 3D fuzzy systems and the critic function and actor function are updated alternately. The critic function uses a TD (0) target and is updated via the semi-gradient method; the actor function is updated by using the chain derivation rule on the behavior value function and the actor function is the established DPS online model. Since DPS modeling is a continuous problem, this paper proposes a TD (0) target based on average reward, which can effectively realize online modeling. The suggested methodology is implemented on a three-zone rapid thermal chemical vapor deposition reactor system and the simulation results demonstrate the efficacy of the methodology. [ABSTRACT FROM AUTHOR]

Under the action of earthquakes, the large chassis twin towers structure adopting a control scheme of isolated layer and dampers has better control effects. However, the energy flow between substructures under this system has not been thoroughly studied. This paper simplifies the large chassis twin towers passive control system into a distributed parameter system, and utilizes the multi-objective particle swarm optimization (MOPSO) algorithm to obtain the optimal parameters of dampers. Based on this, the variations in power flow variance, power flow direction of each tower, and the variance of random power flow with changes in the frequency and damping ratio of the left tower are explored. The research indicates that the adopted integrated design process can enhance the overall energy dissipation capacity of the large chassis twin towers passive control structure. The isolated layer and dampers make the right tower with a base isolation similar to a large tuned mass damper (TMD) control device. Additionally, the dynamic differences provided by the asymmetric design of the left and right towers further enhance the seismic performance of structure. At this point, the energy of lower floors will flow into the isolation layer, while the energy of higher floors will be absorbed and dissipated by the dampers. The composite passive control scheme can help the structure enter a stable state more quickly. This scheme can also reduce the peak value of variance in random power flow fluctuations significantly. [ABSTRACT FROM AUTHOR]

With the rapid development of unmanned aerial vehicle technology and the continuous growth of requirements demanded in engineering applications, flapping-wing unmanned aerial vehicles are playing an increasingly important role in the national economy and livelihood because of their advantages such as good concealment, rapid maneuverability, high flexibility, and excellent economic performance. However, due to the limitations of the operating environment and their rapid maneuvering, the wings of flapping-wing unmanned aerial vehicles often have continuous high-frequency vibrations. These undesirable vibrations can affect the stability of the system and reduce its service life. In addition, flapping-wing unmanned aerial vehicles adjust their attitude rapidly and accurately during operation to accomplish assigned tasks. Therefore, this study focuses on the issues of vibration suppression and attitude control for flapping-wing unmanned aerial vehicles with rigid–flexible coupling wings. First, considering the impact of external disturbances on a flapping-wing unmanned aerial vehicle, using the Hamiltonian principle, the flapping-wing system comprising the homogeneous rigid link connected with the heterogeneous flexible link is modeled as an infinite dimensional distributed parameter system. The dynamic equations of the flapping-wing unmanned aerial vehicle are expressed as nonhomogeneous partial differential equations coupled with ordinary differential equations. Afterward, based on the original model with infinite-dimensional state space, two boundary control laws are designed to stabilize the system of the flapping-wing unmanned aerial vehicle by applying the back-stepping method. Different from the traditional modal control methods, the proposed control scheme can avoid overflow instability and control all system modals. An auxiliary input signal and disturbance adaptive law are constructed to cancel the impact of external disturbances via the robust control strategy. The developed disturbance rejection technique greatly relaxes the assumptions about external disturbances. By arranging the sensors and actuators at the body of the flapping-wing unmanned aerial vehicle and the connection point of the rigid–flexible coupling wing, the vibrations of the flexible wing are regulated into the vicinity around the original position and the attitude angle positions of the rigid and flexible wings are adjusted to the desired angular positions. It is worth noting that the proposed boundary control scheme exhibits great feasibility, cost-effectiveness, and robustness. Using the Lyapunov stability theory, it is rigorously proven that the closed-loop system is uniformly bounded stable. Finally, numerical simulations are conducted to demonstrate the effectiveness and performance of the designed control scheme.

Many systems in the manufacturing industry have spatial distribution characteristics, which correlate with both time and space. Such systems are known as distributed parameter systems (DPSs). Due to the spatiotemporal coupling characteristics, the modeling of such systems is quite complex. The paper presents a new approach for three-dimensional fuzzy modeling using Simultaneous Perturbation Stochastic Approximation (SPSA) for nonlinear DPSs. The Affinity Propagation clustering approach is utilized to determine the optimal number of fuzzy rules and construct a collection of preceding components for three-dimensional fuzzy models. Fourier space base functions are used in the resulting components of three-dimensional fuzzy models, and their parameters are learned by the SPSA algorithm. The proposed three-dimensional fuzzy modeling technique was utilized on a conventional DPS within the semiconductor manufacturing industry, with the simulation experiments confirming its efficacy. [ABSTRACT FROM AUTHOR]

The problem of controllability for problems of optimal control and optimization of distributed parameter systems governed by partial differential equations is considered. The concept of controllability understood as Tikhonov correctness for solving optimization problems is introduced. A theorem formulating controllability conditions for directly solving optimization problems (direct minimization of the objective functional) is presented. A test example of the numerical solution of the optimization problem for a nonlinear hyperbolic system describing the unsteady flow of water in an open channel is considered. The analysis of controllability is demonstrated that ensures the correctness of the problem solution and high accuracy of optimization of the distributed friction coefficient in the flow equations. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization of Euler-Bernoulli beam systems modeled by a partial differential equation (PDE) with unknown time-varying disturbance. An iterative learning controller is designed using only boundary state feedback to realize the vibration control subject to unknown boundary disturbance. The well-posedness for the closed-loop system is given by the operator semigroup theory. Furthermore, the exponentially stable for the closed-loop system is proved by the Lyapunov method. The comparisons with existing results are made to demonstrate the effectiveness and advantages of the proposed boundary iterative learning control method. [ABSTRACT FROM AUTHOR]

The authors considered the problem of optimal control of loading points and the corresponding reaction functions described by a loaded parabolic equation. They obtained optimality conditions for control actions. The authors used the objective functional gradient formulas contained in these conditions in the algorithm for numerically solving the problem of controlling the movement of loading points and corresponding reaction functions based on first-order optimization methods. The paper provides the results of numerical experiments. [ABSTRACT FROM AUTHOR]

This article develops the fundamentals of the tip position control of flexible single‐link robotic manipulators in the frequency domain without approximating the model. Analytic transfer functions of the hub angle and tip position are derived without any model order reduction. Conditions for the stability of the transfer functions are presented by considering the payload mass change as an uncertain parameter. Using the D‐decomposition method, a simple procedure is introduced to design an output feedback controller which guarantees the stability and a desired tracking performance. The introduced design method leads to less conservatism comparing with design methods established upon model reduction. The controller structure includes two proportional‐derivative and integral loops and needs only two measurements of joint angle and tip position which are easily implementable. A numerical example is provided to demonstrate the merit of the achieved results. [ABSTRACT FROM AUTHOR]

Many systems in the manufacturing industry have spatial distribution characteristics, which correlate with both time and space. Such systems are known as distributed parameter systems (DPSs). Due to the spatiotemporal coupling characteristics, the modeling of such systems is quite complex. The paper presents a new approach for three-dimensional fuzzy modeling using Simultaneous Perturbation Stochastic Approximation (SPSA) for nonlinear DPSs. The Affinity Propagation clustering approach is utilized to determine the optimal number of fuzzy rules and construct a collection of preceding components for three-dimensional fuzzy models. Fourier space base functions are used in the resulting components of three-dimensional fuzzy models, and their parameters are learned by the SPSA algorithm. The proposed three-dimensional fuzzy modeling technique was utilized on a conventional DPS within the semiconductor manufacturing industry, with the simulation experiments confirming its efficacy.

In this paper, the boundary feedback control problem for the Euler–Bernoulli beam with unknown time-varying distributed load and boundary disturbance is investigated. Based on the Lagrangian–Hamiltonian mechanics, the model of the beam is derived as a partial differential equation. To suppress the external disturbance, two disturbance rejection control approaches are adopted in the control design. Firstly, a disturbance observer is designed to estimate the boundary disturbance online. Thus, the effect of the boundary disturbance can be canceled directly in the feedback loop. A time-varying function is applied in the disturbance observer to prevent an excessively large control input. Secondly, a new observer is developed to estimate the upper bound of the disturbance and a sign function is introduced to suppress the influence of the disturbance without demanding the boundedness of the derivative of the boundary disturbance. The well-posedness and the uniform boundedness of the closed-loop system are proved using the operator semigroup theory and the Lyapunov method. Numerical comparisons with existing results are made for demonstrating the advantages of the proposed approaches. [ABSTRACT FROM AUTHOR]

This article addresses the problem for vibration suppression of a multiple-sectioned marine riser system subject to time-varying external disturbances and asymmetric output constraint. Under the assumption that continuity constraint, multiple-sectioned marine riser's dynamics are described by some continuously connected partial differential equations (PDEs) coupled with an ordinary differential equation (ODE). We only employ boundary control mechanism that suppresses system's vibration displacements and compensate the influence of external disturbances. A novel and improved disturbance observer is proposed to estimate unknown boundary disturbance and two different barrier Lyapunov functions are constructed to prevent the time-varying constraint violation. Based on the backstepping technology and Lyapunov-based control, a boundary controller is presented to accomplish the control objectives. Moreover, the uniform boundedness and stability of the closed-loop system are rigorously guaranteed. Finally, simulation results are provided to illustrate the effectiveness of the designed control scheme. [ABSTRACT FROM AUTHOR]

The synthesis problem of control of objects with distributed parameters with feedback is investigated on the example of the process of heating a rod in a furnace. To generate the values of control actions, we propose to use their linear de- pendence on the values of the state at the measurement points, both at the current and previous moments of time. The unknown coefficients involved in this dependence of control on the measured state values are feedback parameters. They are deter- mined by minimizing the objective functional using numerical methods of first-order optimization. Formulas for the gradient of the objective functional with respect to the feedback parameters are obtained. The results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

In actual industrial systems, numerous processes are characterized as distributed parameter systems (DPSs) that exhibit strong nonlinearity, complex boundary conditions, and unknown dynamics. Achieving accurate control of such processes poses a significant challenge. In light of this, a data-driven spatiotemporal least squares support vector machine (LS-SVM) inverse control method has been developed specifically for complex DPSs. First, a spatiotemporal LS-SVM model is proposed to capture the dynamics of DPSs by leveraging available data. Subsequently, by employing Taylor expansion on this spatiotemporal model, a state model is derived to explicitly establish the relationship between the control input and output variables. Building upon this foundation, an explicit control input is obtained through inversion and spatial fuzzy strategy, allowing for effective tracking of spatiotemporal dynamics. This control approach takes into account the influence of each input on all spatial points, thereby ensuring a favorable control effect for DPSs. Theoretical analysis and stability proofs affirm the stability of the proposed control approach for nonlinear DPSs. Furthermore, the efficacy of this controller is demonstrated through two actual experiments. First, the proposed approach exhibits superior control performance, as evidenced by a nearly threefold improvement in tracking accuracy on several sensors compared to the fuzzy controller. Second, the proposed controller maintains a smaller error during the tracking process, with deviations bounded within 1 °C even in the presence of disturbances. [ABSTRACT FROM AUTHOR]

In this paper, a heating process control law with steam supply is designed for a fluid in a heat exchanger. The process is described by a linear hyperbolic equation of the first order with a nonlocal boundary condition with a time-delayed argument. The temperature of the supplied steam is found as a linear dependence on fluid temperature values at measurement points in the heat exchanger. Explicit formulas are obtained for the gradient of the objective functional of the control problem in the space of the feedback coefficients (parameters) of this dependence. A numerical scheme is developed for determining the feedback parameters based on these formulas. Finally, an algorithm is proposed for determining the rational (optimal) number of measurement points. [ABSTRACT FROM AUTHOR]

Complex nonlinear distributed parameter systems (DPSs) exist widely in advanced industrial thermal processes. The modeling of such highly nonlinear systems is a challenge for traditional time/space-separation-based methods since they employ linear methods for the model reduction and spatiotemporal reconstruction, which may lead to an inefficient application of the nonlinear spatial structure features represented by the spatial basis functions. To overcome this problem, a novel spatiotemporal modeling framework composed of nonlinear temporal domain transformation and nonlinear spatiotemporal domain reconstruction is proposed in this paper. Firstly, local nonlinear dimension reduction based on the locally linear embedding technique is utilized to perform nonlinear temporal domain transformation of the spatiotemporal output of nonlinear DPSs. In this step, the original spatiotemporal data can be directly transformed into low-order time coefficients. Then, the extreme learning machine (ELM) method is utilized to establish a temporal model. Finally, through the spatiotemporal domain reconstruction based on the kernel-based ELM method, the prediction of the temporal dynamics obtained from the temporal model can be reconstructed back to the spatiotemporal output. The effectiveness and performance of the proposed method are demonstrated in experiments on the thermal processes of a snap curing oven and a lithium-ion battery. [ABSTRACT FROM AUTHOR]

This paper discusses a nonlinear direct joint control scheme for manipulation of a flexible payload by a single-arm system with disturbances, parametric uncertainty and output constraints. The flexible payload can be considered as an Euler–Bernoulli beam. The equations of the coupled rigid-flexible motion are established on the basis of the ordinary differential equations (ODEs) and partial differential equation (PDE), which can avoid system spillover instability. A novel nonlinear disturbance observer-based control approach is proposed to enhance its disturbance attenuation ability. To handle the system parametric uncertainty, we apply adaptive direct joint control to approximate the unknown parameter, which does not require endpoint boundary control. Then a Barrier Lyapunov Function (BLF) is adopted to eliminate the impact of output restriction. The asymptotic stability of the closed-loop system is rigorously proven by semi-group theory and LaSalle's Invariance Principle extended to an infinite-dimensional system. Finally, the performance of the direct joint control is validated via numerical simulations. [ABSTRACT FROM AUTHOR]

This paper proposes a nonparametric identification method based on Gaussian process regression (GPR) for completely unknown nonlinear distributed parameter systems (DPSs). Inspired by linear parameter-varying (LPV) modelling approach, an interpolated spatio-temporal Volterra model is developed to represent the DPSs in nonparametric form, in which local Volterra models are interpreted as Gaussian processes. According to the empirical Bayesian approach, we design the third-order stable kernel structure used for embedding prior knowledge and derive the estimation of hyperparameters. The hyperparameters included in local weighting functions and kernel functions are determined by the maximum likelihood method. By utilising the nonparametric identification approach to avoid model structure selection, the proposed method can improve identification result for completely unknown distributed parameter systems. Finally, two case studies validate the effectiveness of the proposed identification method. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach for one-dimensional thermoacoustic combustor models. Our new model is a transfer function estimated from the frequency response of the linearised Euler equation to a spatially normalised and temporally impulsive input. The proposed approach can deal with combustors with varying cross-sectional areas under a non-zero mean flow, distributed heating/cooling, and outlet boundary conditions involving entropy waves, overcoming limitations of the popular network model. In addition our new approach can provide a more reliable thermoacoustic model for combustors with entropy-related boundary conditions, remedying the inaccurate entropy model of the network model. Numerical comparisons of our new model with a network model show apparent similarities between the two, validating the new model. It is also observed that, compared to our new model, the network model is more sensitive to mean flow and significantly overestimates the entropy wave effects on combustor acoustics. [ABSTRACT FROM AUTHOR]

The inverse calculation of burden distribution matrix (BDM) is one of the most important challenges in the blast furnace operation in iron-making processes. In general, blast furnace consumes 65% of the total energy for the whole steel-making. Focusing on this practical challenge, this article proposes a new burden distribution spatial model in calculating burden charging process, and develops a B-spline approximation-based probability density function (PDF) control algorithm to assign the expected thickness distribution of burden layer and, thus, develops a new method for the required inverse calculation of BDM. First, a novel method for the thickness distribution of burden layer is given using B-spline model to produce an expected distribution shape subjected to a desired tracking within a specific spatial constraint. Then, according to the coexistence of continuous and bounded discrete variables in BDM, a novel hybrid optimization control method by combining integer programming and PDF tracking is further established for the effective inverse calculation of BDM. Finally, the proposed PDF-based iterative inverse calculation of BDM using B-spline models are tested using various data from industrial examples. The simulation results show that the proposed method is well suited to solve the BDM inverse calculation problem in practice. [ABSTRACT FROM AUTHOR]

In this paper, we propose an adaptive fault‐tolerant boundary vibration control approach for the flexible aerial refueling hose with variable length, variable speed, and multiple actuators. A distributed parameter system (DPS) is utilized to represent the dynamic behavior of the flexible refueling hose more precisely and accurately. Based on the established DPS model, we present a boundary vibration controller to suppress the vibration of the flexible refueling hose. In the controller, fault‐tolerant control with multiple actuators is considered to tackle the failure issues, and both multiplicative and additive failures are discussed in the fault situation. Then, by the Lyapunov direct method, we prove that the stability of the closed‐loop system is guaranteed under the proposed control approach. Numerical examples are presented to support the theoretical derivation. [ABSTRACT FROM AUTHOR]

This paper employs the observer-based output feedback control technique to deal with the problem of spatiotemporally asynchronous sampled-data control for a linear parabolic PDE on a hypercube. By the spatiotemporally asynchronous sampled-data observation outputs, an observer-based output feedback control law is constructed, where the sampling interval in time is bounded. By constructing an appropriate Lyapunov–Krasovskii functional candidate and applying a weighted Poincaré–Wirtinger inequality on a hypercube, it is shown under a sufficient condition presented in terms of standard linear matrix inequalities that the suggested spatiotemporally asynchronous sampled-data control law asymptotically stabilises the PDE in the spatial H 1 (Ω) norm but its convergence speed can be regulated by a known constant. Moreover, both open-loop and closed-loop well-posedness analysis are done within the framework of C 0 semi-group. Finally, numerical simulation results are presented to support the proposed design method. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model of an electric power system which consists of a three-phase power line with distributed parameters and an equivalent, unbalanced RLC load cooperating with the line. The above model was developed on the basis of the modified Hamilton–Ostrogradsky principle, which extends the classical Lagrangian by adding two more components: the energy of dissipative forces in the system and the work of external non-conservative forces. In the developed model, there are four types of energy and four types of linear energy density. On the basis of Hamilton's principle, the extended action functional was formulated and then minimized. As a result, the extremal of the action functional was derived, which can be treated as a solution of the Euler–Lagrange equation for the subsystem with lumped parameters and the Euler–Poisson equation for the subsystem with distributed parameters. The derived system of differential equations describes the entire physical system and consists of ordinary differential equations and partial differential equations. Such a system can be regarded as a full mathematical model of a dynamic object based on interdisciplinary approaches. The partial derivatives in the derived differential state–space equations of the analyzed object are approximated by means of finite differences, and then these equations are integrated in the time coordinate using the Runge–Kutta method of the fourth order. The results of computer simulation of transient processes in the dynamic system are presented as graphs and then discussed. [ABSTRACT FROM AUTHOR]

In actual distributed parameter systems (DPSs), each spatial point has nonlinear energy transfer with its local neighbor points. Also, this energy transfer is affected by the past states. However, these properties are often ignored by most of modeling methods, which causes these methods ineffective in modeling of DPSs. Aiming for this problem, a spatiotemporal kernel-local-embedding (STKLLE) Modeling approach is proposed here to reconstruct the nonlinear spatiotemporal dynamics of DPSs. First, in order to present the complex dynamics on space, a STKLLE strategy is developed to extract space basis functions (SBFs). On the one hand, this STKLLE method represents the energy transfer relation with its neighboring points and maintains this local relation in model. On the other hand, it considers the influence of the adjacent past states to the current state. Then, using T–S fuzzy algorithm, a temporal model is designed to represent the temporal dynamics of DPSs in each sampling period. Integrating these SBFs and the temporal fuzzy model, a spatiotemporal model is constructed to well present and predict the nonlinear spatiotemporal dynamics in DPSs. Through the actual experiment on Lithium-ion batteries and heating oven, the effectiveness of this proposed model is detailly verified, and quantitative comparisons with several data-driven modeling algorithms are further carried out to demonstrate the model efficiency. • A spatiotemporal KLLE method is designed to extract nonlinear relations of the local neighbor points and adjacent states. • A T-S fuzzy temporal model is developed to construct the temporal dynamics of DPSs. • A spatiotemporal model is developed to reconstruct the spatiotemporal dynamics of DPSs. • This proposed method is verified by theoretical analysis and experimental studies. [ABSTRACT FROM AUTHOR]

To predict the process states of nonlinear distributed parameter systems (DPS) using various process variables, a novel multi-source spatiotemporal modeling method is proposed in this paper to improve conventional temporal modeling methods. To tackle the challenge of modeling industrial process data of DPS with multi-source spatiotemporal characteristics, a multi-source spatiotemporal network (MS-STN) model, which is the integration of a long short-term memory (LSTM) network to extract information containing temporal characteristics and a convolutional long short-term memory (ConvLSTM) network to extract information containing spatiotemporal characteristics, is constructed. The comprehensive use of various process information is beneficial to improving the fitting accuracy of the model, and the generalization ability of the model can be enhanced at the same time. To prevent the gradient vanishing or gradient explosion in presenting complex spatiotemporal data due to the increase of network layers, a model structure of the residual network based on ConvLSTM is proposed in performing model training. Finally, the industrial ethylene oxychlorination reaction process is taken as an example. The experimental results of predicting the temperature of the reaction tube well demonstrate the effectiveness of the proposed method. • Temporal models cannot meet requirements of distributed parameter system (DPS). • The multi-source spatiotemporal modeling method enhances state prediction of DPS. • LSTM and ConvLSTM extract temporal and spatiotemporal information, respectively. • ConvLSTM-based residual networks prevent gradient vanishing or gradient explosion. [ABSTRACT FROM AUTHOR]

In this paper, we treat the problem of constructing secure communication systems using chaotic synchronization of distributed parameter systems. In particular, we concentrate on the chaotic vibration of a wave equation with a van der Pol boundary condition. In general, a secure communication system consists of three components, a synchronization system, and modulation and demodulation components. In the present work, a wave equation generating non-isotropic spatiotemporal chaotic vibration is used. The non-isotropic characteristic makes it harder for the mechanism behind the synchronization system to be detected. To simulate the chaotic vibration accurately, a numerical algorithm is also developed. Finally, through security analysis by numerical simulations, it is shown that the introduction of non-isotropy makes one of the system parameters more sensitive. [ABSTRACT FROM AUTHOR]

This article discusses cooperative control of a mobile dual flexible manipulator system with asymmetric time-varying output constraints and actuator failures. The shift function and a barrier Lyapunov function (BLF) are used to guarantee output constraints when the initial states of the system violate the prescribed constraints. Moreover, an adaptive fault-tolerant control scheme is developed to deal with actuator failures, while suppressing system’s vibration and achieving cooperative operation. Finally, theoretic analysis proves the uniform bounded stability of the system and numerical simulation verifies the effectiveness of the proposed control method. Note to Practitioners—The purpose of this article is to develop a cooperative dual flexible manipulator system with performance limitations and actuator failures. The system can realize the task of stably grasping and moving a rigid object. The existing research on the grasping task of flexible manipulators only focuses on coordinated operation, which limits the application of the dual flexible manipulator system in practical engineering. To further study the problem, this article considers the output constraints and actuator failures of the dual flexible manipulator system in the actual process and proposes a cooperative fault-tolerant control framework. The control framework uses shift function and BLF to deal with output constraints and adopts adaptive technology to deal with actuator failures. In addition, the cooperative operation task of grasping object with dual flexible manipulators is realized. Simulation shows that this control strategy is feasible. [ABSTRACT FROM AUTHOR]

This paper addresses the stabilization problem of an Euler–Bernoulli beam system subject to an unknown time-varying distributed load and boundary disturbance. Based on Lagrangian–Hamiltonian mechanics, the model of the beam system is derived as a partial differential equation. Based on Lyapunov functions, a sliding surface is designed, on which the system exhibits exponential bounded stability and robustness against the external disturbances. A sliding mode controller which only uses boundary information is further proposed to drive the system to reach the sliding surface in finite time. Numerical simulations are shown to illustrate the validity of the proposed boundary control. [ABSTRACT FROM AUTHOR]

This brief mainly considers trajectory tracking and vibration suppression for a 3-D flexible wing. The dynamical model of the flexible wing is regarded as a distributed parameter system, which is described by partial differential equations and ordinary differential equations. A control strategy regulates the flexible wing to track the desired trajectory by controlling two angles. Meanwhile, two active boundary controllers are proposed to restrain the vibrations both in bending and twisting. By using Lyapunov’s direct method, the stability of the flexible wing system can be ensured. Numerical simulations based on the finite-difference method demonstrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

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Within the scope of the presented work, a mathematical model of a prototype of a complex motion transmission on a ship was developed. The abovementioned motion transmission includes long elastic elements with distributed mechanical parameters. The system, containing the motion transmission under consideration, is driven by an engine via epicyclic gearing. The torque is transmitted via a long drive shaft to a propeller working with a variable blade geometry. The rotor of a synchronous generator is mounted on the ship's long drive shaft. This shaft generator produces electricity that is fed to the ship's electrical network. With the use of the developed mathematical model, electromechanical transients occurring during the transmission of mechanical power are analyzed. This paper analyzes the motion transmission with the use of computer simulation and presents the results of research. [ABSTRACT FROM AUTHOR]

The vibration control problem was investigated in this study in the presence of unknown loss of actuator effectiveness fault and loss of sensor effectiveness fault in a flexible aircraft wing system. A series of partial differential equations was used as the mathematical model of the wing with unknown boundary disturbances. An adaptive fault-tolerant boundary controller was designed accordingly. All signals of the closed-loop control system are globally uniformly bounded and the controlled state asymptotically converges. Numerical simulations were conducted to validate the proposed control scheme. [ABSTRACT FROM AUTHOR]

Many distributed parameter systems (DPSs) have strongly nonlinear spatiotemporal dynamics, unknown parameters and complex boundary conditions, which make it difficult to obtain accurate prediction and control in actual practice. In this paper, a data-driven spatiotemporal model predictive control (MPC) strategy is proposed for nonlinear DPSs. It first develops a low-order nonlinear spatiotemporal model by using kernel principal component analysis to reconstruct the nonlinear spatial dynamics, so that the spatial nonlinearity is better reserved in contrast with the traditional data-driven DPS modeling methods. On this basis, a spatiotemporal MPC is proposed for nonlinear DPSs. In this control strategy, a new objective function is constructed with consideration of errors on not only time but also space, which overcomes the shortcoming of the traditional MPC due to the ignorance of nonlinear spatial dynamics. The stability and effectiveness of the proposed spatiotemporal control strategy are demonstrated by mathematical stability and comparative case studies. [ABSTRACT FROM AUTHOR]

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link's transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link's transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to prevent the amount of boundary deflection from violating the constraints and avoiding any simplifications, in the presence of external boundary disturbance, proper control feedbacks and boundary disturbance observer are adopted in order to reach control objectives and to compensate external boundary disturbance effects simultaneously. By choosing proper boundary feedback, system states are proven to be uniform ultimate bounded and converge exponentially toward a small neighbourhood of zero. In order to illustrate the performance of the proposed control approach, numerical simulation results are provided. [ABSTRACT FROM AUTHOR]

As a kind of large flexible structure, high-rise buildings need to consider wind-resistant and anti-seismic problems for the safety of occupants and properties, especially in coastal areas. This article proposes an infinite dimensional model and an adaptive boundary control law for an active mass damper (AMD) on this question. The dynamic model of the high-rise building is a combination of some storeys which have flexible walls and rigid floors under a series of physical conditions. Then the adaptive boundary controller is acted on an AMD which is equipped on the top floor, in order to suppress the vibration of every floor and guarantee the comfort of residents. Moreover, simulations and experiments are carried out on a two-floor flexible building to illustrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper considers the consensus control problem of multi‐agent systems (MAS) with distributed parameter models. Based on the framework of network topologies, a second‐order PI‐type iterative learning control (ILC) protocol with initial state learning is proposed by using the nearest neighbor knowledge. A discrete system for proposed ILC is established, and the consensus control problem is then converted to a stability problem for such a discrete system. Furthermore, by using generalized Gronwall inequality, a sufficient condition for the convergence of the consensus errors between any two agents is obtained. Finally, the validity of the proposed method is verified by two numerical examples. [ABSTRACT FROM AUTHOR]

Using the process of heating a rod in a furnace as an example, we study the feedback control synthesis problem for plants with distributed parameters. To form the control values, it is proposed to use their linear dependence on the state values at the points of measurement, both at the current and at the preceding moments of time. The unknown coefficients involved in this dependence of the control on the measured state values are the feedback parameters. They are determined by minimizing the objective functional using first-order numerical optimization methods. To this end, formulas for the gradient of the objective functional with respect to the feedback parameters are obtained. The results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

Flexible inverted pendulum is distributed parameter SIMO system which is developed from cart and pole, a popular robot with all solid links. A structure of PID controller for this model is suggested. Approximated dynamic equations of this model is used to obtain the PID controller by genetic algorithm through simulation. After survey in simulation, a hardware platform is presented and tested. In experiment, PID is proven to work well and suit most theoretical points.

Two approximate representations are proposed for distributed parameter systems described by two linear hyperbolic PDEs with two time- and space-dependent state variables and two collocated boundary inputs. Using the method of lines with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of a finite number of dynamical subsystems (sections). Each section of the approximation model is described by state-space equations with matrix-valued state, input and output operators, or, equivalently, by a rational transfer function matrix. The cascade interconnection of a number of sections results in the overall approximation model expressed in finite-dimensional state-space or rational transfer function domains, respectively. The discussion is illustrated with a practical example of a parallel-flow double-pipe heat exchanger. Its steady-state, frequency and impulse responses obtained from the original infinite-dimensional representation are compared with those resulting from its approximate models of different orders. The results show better approximation quality for the “crossover” input–output channels where the in-domain effects prevail as compared with the “straightforward” channels, where the time-delay phenomena are dominating.

This paper presents a new tracking controller for a crowd dynamics system. The crowd dynamics are described by a continuum model in the macro-scale. An appropriate control variable is chosen to solve the problem of the multi-directionality of crowd movement. In order to stabilize the state density of the disturbed crowd dynamics system at a given reference density, a unit sliding mode controller based on the integral barrier Lyapunov function is designed, and the reaching law approach is used to avoid chattering. By ensuring the boundedness of the integral barrier Lyapunov function in the closed-loop, the global constraints of the system state variables are obtained. The design of the controller and the stability analysis of the closed-loop system are all done in the distributed parameter system. A numerical example illustrates the utility of the proposed controller.

This paper investigates vibration suppression of uncertain hose and drogue systems in the presence of actuator nonlinearities. Firstly, a previously presented model of the hose and drogue systems is extended to describe how the hose and drogue systems restrain the vibration, while the accompanying unknown aerodynamic coefficients are estimated by invoking the parameter projection method. Subsequently, for the actuator nonlinearities of dead-zone and saturation, a smooth dead-zone approximate function is constructed to design the dead-zone compensation method, based upon which the proposed control scheme can handle actuator dead-zone and saturation simultaneously while improving the output efficiency of the actuator. Next, for the actuator nonlinearities of backlash and saturation, a smooth backlash inverse is constructed based upon which the presented control scheme can cope with the both actuator nonlinearities simultaneously. Finally, by utilizing backstepping method and hyperbolic tangent function, the proposed control schemes can also achieve the control objectives of vibration suppression and external disturbance attenuation. Simulation examples are included to demonstrate the validity of the proposed control schemes.

Based on Timoshenko beam theory and considering the layer bending deformation and shear deformation of the structure, a semi analytical solution method (SAM) is proposed for the interlayer isolation structure system. The equivalent mechanical model of cantilever beam is established by using the distributed parameter system, on which the dynamic partial differential equation is derived; the boundary condition and continuity condition are used to solve the equation to obtain the natural vibration characteristics; the orthogonal conditions are deduced by Betti's law and the seismic response of the structure can be solved by the mode superposition method. A 10 story isolated structure is designed as well as analysed by the semi analytical method (SAM) and the ETABS finite element simulation (FESE) separately. The results show that: the existence of the isolation layer may reduce the response of the superstructure and amplify the response of the substructure, and the amplification can be solved by increasing the mass, bending stiffness of the superstructure and shear stiffness of the isolation layer. In regular interlayer isolation structure, the optimal frequency ratio of the superstructure and substructure increases with the rising of isolation layer position. The results also prove the correctness and accuracy of the SAM, which enriches the analysis theory of interlayer isolation structure and provides reference for the accurate analysis of structural response in engineering. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel framework on the state estimation for a class of positive real infinite-dimensional systems, which suffer from unknown actuator and sensor faults and uncertain exogenous disturbance. Four cases of fault occurrence are taken into account: single multiplicative actuator fault, single multiplicative sensor fault, simultaneous actuator and sensor faults, and single actuator fault with a dead-zone nonlinearity. We develop new adaptive laws for the estimation of fault parameters and embed the proposed laws into the infinite dimensional state observer design. Moreover, by considering the actuator fault with a dead-zone nonlinearity, an infinite dimensional observer associated with coupled parameter update laws is developed to help to complete the fault accommodation. This is achieved by reconfiguring the actuator input based on the estimated information of parameters in the actuator fault map with a dead-zone nonlinearity. [ABSTRACT FROM AUTHOR]

This article deals with the problem of observer‐based feedback compensator design for a linear reaction–advection–diffusion equation subject to a time‐varying diffusion coefficient, a time‐varying advection coefficient, and a space‐time‐varying reaction coefficient. To solve such a problem, these coefficients are written in parametric forms under their boundedness assumptions. By considering these parametric forms of the coefficients and the distribution functions for control actuation and non‐collocated measurement, a parameter‐dependent observer‐based feedback compensator is constructed such that the resulting closed‐loop coupled equation exponentially converges to a bounded set of the equilibrium profile in the spatial L2 norm. With the aid of the Lyapunov technique and variants of Poincaré–Wirtinger's inequality, a sufficient condition for the existence of such feedback compensator is presented in the form of convex constraints. Finally, extensive simulation results for a numerical example and a class of steelmaking processes are presented to support the proposed design method. For the collocated measurement case, both theoretical and simulation results show that the proposed observer‐based feedback compensator can provide a better control performance than the static feedback compensator in the presence of measurement disturbances. [ABSTRACT FROM AUTHOR]

In this article, we investigate the stabilization control problem of a flexible marine riser system with a failed and bounded control action and time‐varying boundary constraints. The considered system is modeled as a distributed parameter system dominated by a partial differential equation. The involved problems are extended to some more general conditions. The saturation and failures of the actuator make the input and output of the actuator a nonlinear relationship, which leads to the normally designed control input invalid. By applying the Nussbaum gain technique, we report a synthetical control method to tackle the input nonlinearity. A piecewise barrier Lyapunov function (BLF) is introduced to reduce the boundary displacement in an asymmetric open set. Compared with the traditional BLFs, the initial boundary displacement is not forced to retain within the given region by integrating a shifting function into the BLF design. In addition, the adaptive method is combined with the hyperbolic tangent function to provide a smooth control solution to the unknown parameters from nonlinear input and external perturbation. Relying on a Lyapunov‐based analysis and a numerical simulation, it is proven that the actuated riser system is uniformly bounded and the boundary displacement always keeps in the limited set even subject to actuator failures and limitations. [ABSTRACT FROM AUTHOR]

Most distributed parameter systems (DPSs) are unknown, including unknown parameter, boundary and even structure, and have a strongly nonlinear spatiotemporal nature. In order to achieve desirable modeling accuracy, the models from the commonly used DPS modeling methods often have a high order, which makes them difficultly used for prediction and control. Here, a novel low-order spatiotemporal least squares support vector machine (LS-SVM) method is proposed for modeling unknown and nonlinear DPSs. Generally, the information of a certain sensor may be represented by information of its neighboring sensors due to the spatial correlation between them. Making use of this feature, a kernel-space based spatial correlation analysis method is developed for deleting redundant spatial kernel functions, from which a low-order model can be achieved and it is without loss of any spatial information. On this basis, a LS-SVM model is constructed to represent the nonlinear temporal dynamics. Integration of the without-redundant spatial kernel functions and the LS-SVM temporal model, a low-order spatiotemporal model is created to reconstruct the spatiotemporal dynamics of the nonlinear DPSs. Additional analysis and proof show that: (1) the proposed method has the same modeling performance with the without-order-reduction spatiotemporal modeling method; and (2) it has better modeling performance than the model with the same order achieved by the without-order-reduction one. Using case studies, the effectiveness of the proposed method and its superior modeling ability compared to several common methods are demonstrated. • A low-order spatiotemporal modeling method is proposed for nonlinear DPS. • A correlation analysis method is developed for deleting redundant spatial kernel functions. • A LS-SVM model is constructed to represent the nonlinear temporal dynamics. • A low-order spatiotemporal model is created to describe nonlinear DPS. • Analyses and experiments demonstrate the effectiveness of proposed method. [ABSTRACT FROM AUTHOR]

The present paper is concerned with stability and L 2 gain analysis of switched distributed parameter system (SDPS) with time delay. First, exponential stability is discussed, and the state decay estimate of the system is explicitly given by using linear matrix inequalities (LMIs) incorporating with the average dwell time (ADT) method. Second, L 2 gain analysis is also studied. At last, illustrative examples are given to show the effectiveness of the proposed method. The main contribution of the paper is: some criteria of exponential stability and L 2 gain for multiple-input multiple-output (MIMO) switched PDE are developed in the form of LMIs and ADT signal for the first time. The advantage of the work is we generalize the application range of the related research. The proposed method is expected to provide an effective tool for stability and H ∞ control analysis of SDPS. [ABSTRACT FROM AUTHOR]