Distributed Parameter Systems Research Articles

Formula omitted] fuzzy intermittent boundary control for nonlinear parabolic distributed parameter systems

For nonlinear space-varying parabolic distributed parameter systems, this paper introduces an H∞ fuzzy intermittent boundary control, where the output measurements are only available at some specified boundary position (i.e., boundary measurements). Initially, a Takagi–Sugeno fuzzy parabolic partial differential equation is used to precisely describe the nonlinear space-varying parabolic distributed parameter system. Then, under boundary measurements, an H∞ fuzzy intermittent boundary control design based on the Takagi–Sugeno fuzzy parabolic partial differential equation model ensuring the exponential stability with an H∞ performance for closed-loop space-varying distributed parameter system is subsequently obtained via spatial linear matrix inequalities by employing inequality techniques and piecewise switching-time-dependent Lyapunov function. Furthermore, in order to solve the H∞ fuzzy intermittent boundary controller design of nonlinear space-varying parabolic distributed parameter systems under boundary measurements, we express spatial linear matrix inequalities as linear matrix inequalities and further present some linear matrix inequality based fuzzy intermittent boundary control design conditions respecting the property of membership functions. Finally, two simulation examples are offered to demonstrate the effectiveness of the proposed H∞ fuzzy intermittent boundary control method.

Finite-time anti-disturbance control of an information-constrained autonomous helicopter flexible slung-load system with compound disturbance

This study investigates the finite-time anti-disturbance control problem of an autonomous helicopter flexible slung-load system (AHFSLS) by describing it as a distributed parameter system with matched disturbance, mismatched disturbance, and vibration information constraint. Here, initially, a novel compound disturbance observer is proposed to simultaneously compensate for matched and mismatched disturbances. Then, by executing a rigorous Lyapunov stability analysis, with the help of a barrier Lyapunov function, the vibration amplitude converges into a compact set for the AHFSLS. The simulation results demonstrated the efficiency of the developed control strategy in dealing with matched and mismatched disturbances, vibration information constraint, and vibration in the AHFSLS.

A Conceptual model of mixed-integer linear programming water distribution system

Water is a basic part of our daily lives, as such effective water supply is of paramount importance. Thus, as a result of the rise in population size and water shortage there is the need for proper, suitable and optimal utilization of water resources to efficiently be distributed among the populace. The proper allocation and distribution of water in the field of network planning need to be modelled through mathematical parameters for objective of water distribution system. This mathematical approach requires of solving an optimization problem based on multi-objective function subjected to certain constraints of mixed integer linear programming objective function which is proportional to the cost of the water distribution network. This study present a conceptual model of multi-objective optimization proposed for determination of design parameters of water distribution system by considering the significant number of constraints, decision variables, cost and reliability objective functions. The model was proposed to solve the reliability problem of water production and reduce the design and operational costs.

A spatiotemporal fuzzy control approach for complex distributed parameter system with application to thermal processes

Many industrial processes belong to distributed parameter systems (DPSs) with unknown spatiotemporal dynamics and complex boundary conditions. However, attentions to both temporal and spatial dynamics in the control law are less paid in the existing control methods, which often makes them challenging to achieve accurate control. Here, a spatiotemporal fuzzy control approach with consideration of both temporal and spatial dynamics is proposed for unknown and complex DPSs. First, a spatiotemporal fuzzy model is developed to reconstruct dynamics of nonlinear DPS. Since it constructs a two-layer fuzzy rules (i.e., temporal fuzzy rule and spatial fuzzy rule) to consider both the nonlinear dynamics on time and the nonlinear energy transfer on space, it can effectively achieve the model of DPSs. On this basis, a spatiotemporal fuzzy controller is developed according to the developed two-layer fuzzy rules, which means that this derived control law considers both temporal and spatial dynamics. Then, a two-step solution method is designed for the spatiotemporal control law. Stability conditions of the control system are rigorously deduced by transforming the solving process to a series of linear matrix inequalities (LMIs). The stability and effect of the proposed spatiotemporal control strategy are demonstrated by mathematical proof and case studies. Comparison results demonstrate that the proposed method has better control performance (relative errors and mean absolute percentage errors are bounded in 4%).

From Online Systems Modeling to Fault Detection for a Class of Unknown High-Dimensional Distributed Parameter Systems

Fault detection for distributed parameter systems reported so far is model-based in general and the performance heavily relies on the prior known model information. This restricts the usability of these methods in industrial applications. In this paper, we make the first attempt to establish a brand-new framework that contains both on-line systems modeling and fault detection of unknown high-dimensional DPSs. These two parts interact with each other in the sense that the systems modeling error is transformed into the residual signal for fault detection while the on-line modeling switches to off-line mode depending on the fault detection results. The high-dimensional DPSs are first decomposed into spatial features and temporal sequences. Then a receding-horizon scheme is applied for the temporal dynamics learning and the residual signal is converted by the temporal validation error. Experiments on sensor faults diagnosis for the thermal process of a 2-D battery cell are provided for method validation.

Event-Triggered Optimal Control for Temperature Field of Roller Kiln Based on Adaptive Dynamic Programming.

Temperature field control is crucial for the comprehensive performance of Ni-Co-Mn layered cathode material that is the most important part of lithium-ion batteries. Starting from the aspect of a class of distributed parameter systems described by highly dissipative partial differential equations (PDEs), an event-triggered optimal control (ETOC) method based on adaptive dynamic programming (ADP) for the roller kiln temperature field is proposed. First, we formulate the event-triggered control problem of the temperature field under the general framework of PDE systems. Then, an event-triggered condition is designed based on the stability of the closed-loop PDE system, which also guarantees the upper bound of the performance index. Subsequently, ADP technology is adopted to realize the ETOC, where the critic network is employed to approximate the optimal value function. Since the studied system can be regarded as an impulsive dynamic system with flow dynamics and jump dynamics simultaneously, the stability of the impulsive dynamic system combined with the ADP-based closed-loop PDE system is proved. Finally, simulation results on the temperature field verify the effectiveness of the proposed method.

A temporal–spatiotemporal domain transformation-based modeling method for nonlinear distributed parameter systems

Abstract 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.

Robust Event-Triggered Sampled-Data Fuzzy Control with Non-fragile for Nonlinear Delayed Distributed Parameter Systems

Robust Event-Triggered Sampled-Data Fuzzy Control with Non-fragile for Nonlinear Delayed Distributed Parameter Systems

Temperature field prediction of lithium-ion batteries using improved local tangent space alignment

The temperature field prediction of lithium-ion batteries (LIBs) plays a crucial role in the safety of electric vehicles and their lifetime. However, it is essentially a nonlinear distributed parameter system (DPS), and suitable partial differential equations are difficult to obtain. Further, the existing methods are weak in handling nonlinear sparse data. To address this problem, a nonlinear DPS modeling approach based on kernel and weighted local tangent space alignment (KWLTSA) is proposed in this paper. Firstly, the nonlinear dimensionality reduction method of KWLTSA is used to construct basic functions (BFs) by using spatiotemporal data. Secondly, the low-order temporal coefficients are obtained according to the spatial BFs. Subsequently, the coefficients are fed into a backpropagation neural network (BP-NN) with the input signals for training. Finally, the temperature distribution of LIBs is obtained by spatiotemporal reconstruction. Comparative experiments are designed to estimate the model performance using existing evaluation metrics. The root mean square error (RMSE) is 0.1000 and the R-square (R2) is 0.9972 of the temperature prediction by the proposed scheme. The experimental results indicate that the proposed method is more robust than the traditional dimensionality reduction method.

Fuzzy Output Regulation of Nonlinear Time-Delay Distributed Parameter Systems With Quantization and Actuator Failures: Application to Hot Strip Mill Cooling Process

The output regulation of nonlinear distributed parameter systems (DPSs) with time-varying delay is studied in this article. By employing the Takagi–Sugeno (T–S) fuzzy model, the nonlinear time-delay DPSs are described as a fuzzy partial differential equation. To deal with the limited capability of communication channels, the state information and output regulation error are quantized by a kind of dynamic quantizer. The actuator failures which occur frequently in practice are considered in two cases: to be unknown and to follow the Bernoulli stochastic distribution. Then, the boundary-control-based output regulation controllers are designed based on the derived T–S fuzzy model. And fuzzy controller design strategies are proposed to ensure the system state and the output regulation error are finite-time bounded. By constructing appropriate Lyapunov functionals, sufficient conditions for the control gains and the quantizer’s adjusting parameters are provided in forms of linear matrix inequalities. Finally, an application of the output regulation strategies into the cooling process in a hot strip mill is explored. The feasibility and effectiveness of the design strategies are indicated through the simulation results.

Tracking Distributed Parameters System Dynamics with Recursive Dynamic Mode Decomposition with Control

The goal of this work is to introduce a new online data driven modeling solution for tracking the dynamics of systems, the behavior of which is governed by (nonlinear) partial differential equations (PDEs). In order to reach this goal, this paper introduces a recursive algorithm for black box time varying model identification along with an online algorithm for reducing the order of the identified model. The resulting system model is a linear time varying low order state space representation usable, e.g., for controller design or prediction. The model reduction step relies on the recursive determination of the orthonormal basis of a specific data based proper orthogonal decomposition. The system identification procedure is initialized with the dynamic mode decomposition with control and updated recursively via the introduction of a specific recursive least squares algorithm. In both steps, a forgetting factor is used to focus on the most recent variations of the system. As case studies, a linear heat diffusion equation with a time varying diffusion parameter is first considered. The Burgers equation, a nonlinear hyperbolic PDE, is then utilized to assess the introduced methods applicability with nonlinear systems. Identification results based on simulation show the high accuracy of this new approach.

Finite‐time stable of time‐varying delay distributed parameter systems with input saturation via periodically intermittent control

A class of time‐varying delay distributed parameter systems with input saturation is investigated in this paper. The periodic intermittent control method is adopted to make the system stable in finite time, improve the control performance of the system, and save on control cost. A periodic intermittent controller combined saturated input is designed to ensure the stability of the proposed system in finite time. Lyapunov–Krasoviskii stability theory and matrix inequality techniques are used to analyze the finite‐time stability of the system, and sufficient conditions for the system to be stable in finite time are obtained. Finally, the correctness of the theorems is verified by simulation experiments.

Data‐based learning control for optimization of nonlinear systems

Data‐based learning control for optimization of nonlinear systems

Global fuzzy adaptive asymptotic tracking control for unknown semi-linear parabolic distributed parameter systems

This paper is mainly devoted to investigating the globally asymptotic tracking problem of unknown semi-linear parabolic distributed parameter systems (SLPDPSs) with uncertain external disturbance. Firstly, an analysis of the well-posedness of the system solution is given based on the operator semigroup theory. Then, from the Lyapunov direct method, a distributed adaptive fuzzy controller (AFC) is designed so that the unknown SLPDPSs can asymptotically track target systems. More importantly, the globally asymptotic tracking condition can be obtained, which overcomes the semi-global stability results in the existing literatures. Finally, several simulation cases are introduced to verify the availability and practicability of the proposed method.

Deep Extreme Learning Machines Based Two-Phase Spatiotemporal Modeling for Distributed Parameter Systems

Accurate and robust modeling of complex distributed parameter systems (DPSs) is a challenge for three reasons: 1) they have infinite-dimensional characteristics; 2) they are time/space coupled; and 3) there are model uncertainties. In this article, a two-phase spatiotemporal (S/T) modeling framework based on deep extreme learning machine (DELM) is proposed for DPSs. The modeling process consists of two S/T models in two phases: Phase I: a DELM model and Phase II: a Karhunen–Loève (KL) based ELM (KL-ELM) model. In phase I, the DELM model is constructed by combing the multilayer ELM (ML-ELM), ELM, and kernel-based ELM (K-ELM) to approximate the dominant S/T dynamics of DPSs. Since DPSs have an infinite-dimensional characteristic that can hardly be handled directly, ML-ELM is first employed to transform the infinite-dimensional systems into finite-dimensional systems. Then, the ELM model is adopted to further approximate the finite-dimensional systems to ensure the model can predict future dynamic behavior. Finally, the K-ELM is used to reconstruct the infinite-dimensional systems, which can be considered as the inverse process of ML-ELM. Thus, the final DELM model can be used for prediction in both space and time directions. In phase II, a KL-ELM model is constructed to compensate for modeling errors caused by reconstruction error or unknown nonlinear dynamics. By integrating the obtained DELM and KL-ELM models, the proposed two-phase S/T model can be constructed. Experiments on a typical industrial thermal process verified that the proposed method may work better in complex DPSs.

Data-Driven Real-Time Prediction of Pouch Cell Temperature Field Under Minimal Sensing

The monitoring of temperature distribution is crucial for advanced battery thermal management. This study proposes a data-driven temperature field prediction method for the pouch cell thermal process, a typical distributed parameter system (DPS). First, empirical spatial basis functions (SBFs) that represent underlying spatial modes of the thermal system are extracted from data snapshots collected offline. Then, we apply the obtained SBFs to the time/space (T/S) separation framework and perform online nonlinear modeling using the partial-node feedback data. On this basis, a dynamics reconstruction strategy is designed for full-node temperature prediction. Experimental studies indicate that the proposed method owns encouraging accuracy and allows minimal sensing configuration. In addition, the error source of the proposed method is systematically analyzed.

Fuzzy Boundary Control for Nonlinear Delayed DPSs Under Boundary Measurements.

For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.

Latent-Variable-Modeling-Based Fault Diagnosis for Unknown Nonlinear Distributed Parameter Systems with Application to Snap Curing Oven

A novel fault detection method based on time/space separation and latent variable model is proposed for unknown nonlinear distributed parameter systems in sensor-constrained environments. By performing time/space separation, the augmented matrix formed by the spatio-temporal distribution data of the DPSs can be split into a spatial basis function (SBFs) and a time series model, and the dimensionality reduction capability of the SBF is further utilized to obtain a low-order temporal model. Then, the temporal model is further extracted by using a dynamic latent variable modeling method to obtain the dominant time components and establish the corresponding monitoring statistics. Utilizing the appropriate kernel density function, confidence bounds are selected for the monitoring statistics when the system is normal. As a data-based fault diagnosis method, it requires only the past data records of the system and no reliance on complex mathematical models. Two sets of experiments performed on a snap curing oven verified the effectiveness of the proposed method.

Neural network–based active control of a rigid–flexible spacecraft with bounded input

This paper investigates the simultaneous control of a spacecraft with a rigid central hub and two flexible appendages. Taking into account the coupling between the vibration of flexible appendages and the motion of the hub, the rigid–flexible spacecraft subjected to external disturbance is modeled as a hybrid lumped–distributed parameter system. To attenuate the vibrations of the hub and flexible appendages and simultaneously track the given attitude angle, two boundary control laws are developed based on the original dynamic equation, where all system modes are controlled and spillover instability can be avoided. Using the active disturbance rejection control technique, two extended state observers are designed to obtain the estimation of external disturbances, which can be canceled in the negative feedback loop. The radial basis function neural network with adaptive weight law is employed to deal with the impact of input saturation. The well-posedness of the closed-loop system is proved by applying the semigroup theory. Under the rigorous Lyapunov analysis, the proposed control strategy ensures the practical stability of the rigid–flexible spacecraft system. Simulation verifies the performance of the designed control scheme.

Distributed H ∞ Consensus Filtering for Parabolic Distributed Parameter Systems with Multiple Missing Measurements: A Mobile Sensing Approach

This paper investigates the distributed H ∞ consensus filtering issue for a class of distributed parameter systems with bounded disturbance. In a framework of optimizing performance, a new approach to improving filter performance is proposed by employing mobile sensor networks. Moreover, the information missing in mobile sensor networks is modeled as a conditional probability distribution. The aim of the filtering challenge is to construct a distributed consensus filter such that the filtering error system is globally asymptotically stable in the mean square, and what disturbances do to the estimation accuracy is attenuated at the H ∞ consensus performance level. Utilizing the Lyapunov direct approach and the spatial operator technique, several sufficient criteria are given for the proposed filter to satisfy the H ∞ consensus performance constraint. Finally, a numerical simulation is given to demonstrate the effectiveness of the design scheme of the proposed filter.