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Physics-informed machine learning (PIML) has proven to be a valuable approach for overcoming data scarcity challenges by incorporating physical models into machine learning methods. However, PIML faces limitations in handling complex spatial relationships, as its process information is obtained from disordered collocation points. Fuzzy systems, based on expert knowledge, can provide an interpretable way for tackling strong process nonlinearities. This article proposes a brand-new physics-informed spatial fuzzy system framework (PiFuz) to capture the essential system information of complex distributed parameter systems. PiFuz utilizes spatial membership functions to transform collocation points into a 3-D fuzzy input. This input is processed by the inference mechanism, leveraging its 3-D nature to produce fuzzy outputs with distinctive spatial characteristics. A feature fusion module is utilized to integrate these characteristics and generate the distributed system state. Utilizing the known physical knowledge base, the proposed framework undergoes automatic tuning while preserving process interpretability, resulting in an optimal model that aligns with the actual physical process. A reliable prediction of strong spatial nonlinear behaviors is achieved without the dependency of process data. For modeling higher dimensional spatiotemporal problems, the extension, a multikernel PiFuz framework (MKPiFuz), is further developed to improve the representation of heterogeneous time-varying nonlinear behaviors. By incorporating spatial and wavelet kernels, MKPiFuz extracts underlying features from spatial and temporal dimensions, respectively. Experimental investigations on thermal process of the battery module demonstrate the good accuracy in modeling complex spatiotemporal systems.

Fault detection for distributed parameter systems (DPSs) generally requires the complete model information to be known so far. However, for numerous industrial applications, it is common that accurate first-principles physical models are extremely difficult to obtain. Hence, the applicability of traditional model-based methods is being restricted. To pave the way, an adaptive neural network (AdNN) is constructed to simultaneously estimate the state variable and the unknown nonlinearity for a class of partially known nonlinear DPSs. Moreover, considering that full-state measurement is unrealistic in applications, the proposed adaptive neural observer is based on a reduced-order model, which also increases the computation efficiency. Then, the residual generation and evaluation are conducted using the output estimation error of the proposed adaptive neural observer. Bearing the effects of the neglected fast dynamics in mind, a data-driven threshold generation scheme is proposed. Extensive experimental results are presented and analyzed to validate the effectiveness of the proposed method.

The charging process design is crucial for optimizing the performance of lithium-ion batteries by identifying protocols that meet diverse demands. The main challenges include: 1) the high costs of battery experiments; 2) the multiple user preferences associated with the demands; and 3) the intricate high-dimensional search space of charging protocols. In light of this, this article presents a Gaussian process-accelerated multiobjective evolutionary design method for effective charging process design. To resolve the first concern, an electrochemical-thermal-aging model is constructed to evaluate charging protocols precisely, substituting the need for expensive battery experiments. Besides, the Gaussian process is applied to accelerate the evaluation process further. Regarding the second issue, a Gaussian process-accelerated two-archive evolutionary algorithm (GPA-TAEA) is developed to efficiently search for a set of optimal charging protocols that satisfy multiple user preferences. To address the third challenge, differential evaluation—an evolutionary algorithm proven effective for large-scale optimization—is employed to enhance the search process. The simulation results demonstrate that: 1) the proposed method effectively reduces the time required for charging process design, yielding a collection of optimal charging protocols that includes 530 solutions within 1000 simulations; 2) compared with five other multiobjective optimization algorithms, GPA-TAEA exhibits superior convergence and diversity; and 3) compared with fixed preference-based methods, GPA-TAEA demonstrates greater efficiency, saving 54% in simulation evaluations and 70% in time when considering seven user preferences.

Distributed parameter systems (DPSs) are commonly used to characterize various industrial processes, but the coupling of spatiotemporal data and time-delay effects poses challenges for their fault detection. This article proposes a fault detection method for a class of nonlinear parabolic DPSs with limited sensors. A time/space separation method is first applied to decouple the spatiotemporal data to obtain time coefficients that are available for data-driven modeling. Then, the obtained dominant time coefficients are modeled by a dynamic partial least-squares (D-PLSs) method. Finally, the residual space is utilized to establish two monitoring statistics and a reference boundary is established with the aid of the mirrored data kernel density estimation (KDE). This method exploits the separable characteristics of parabolic DPSs and is a data-driven method that is independent of an explicit mathematical model of the system processes. The proposed method is validated on a curing oven experimental platform, and comparative results with other methods show that it achieves satisfactory performance in fault detection accuracy and first-time detection timeliness.

Surface defect detection is very important for the printed circuit board (PCB) to ensure their quality requirements. This article proposes a reliable and lightweight adaptive convolution (LAC) network for PCB surface defect detection. First, an automated optical inspection (AOI) for collecting PCB defects is introduced, and the formation mechanism of PCB defects is systematically analyzed. After that, LAC strategically aggregates multiple convolution kernels and simplifies model complexity through tensor decomposition. Furthermore, the confidence gate learning (CGL) strategy aims to cope with dataset noise by combining collaborative learning (CL) and confidence evaluation. Complexity and convergence analyses support the theoretical basis of the method. Finally, three industrial defect datasets are used to evaluate the effectiveness. The results show that the methodology has powerful feature representation, visual interpretability, and detection robustness.

Modeling the temperature distribution of a battery is critical to its safe operation. Data-based modeling methods are computationally efficient, but require a large number of sensors, whereas physics-based modeling methods have better generalization, but the unknown dynamics of the actual scene are ignored. A physics-dominated neural network is presented to integrate electric–thermal mechanism of the battery and data information through a weight adaptive function. The electric–thermal coupling equation of the battery under complex conditions is taken as the prior knowledge to update parameters of the network, whereas the characteristic data obtained by the unique sensor are used to compensate the unknown disturbance in the actual scene. A well-trained model can predict the temperature distribution of the battery over entire space with a single sensor, and can also provide reasonable predictions for longer periods of time under extreme conditions. Experiments show that the proposed method outperforms traditional methods that rely only on pure data or pure physics.

This study focuses on the novel reinforcement learning control strategy of a nonlinear two-degrees-of-freedom (2-DOF) helicopter system for tracking the desired trajectory while minimizing the tracking error. First, gradient descent algorithm is incorporated in the context of the reinforcement learning control scheme to obtain the adaptive laws. Subsequently, considering the uncertainties in the nonlinear system, radial basis function (RBF) neural networks (NNs) are exploited to approximate the unknown internal dynamics. In contrast to the previous studies, aiming at accelerating the convergence in reinforcement learning control, a barrier Lyapunov function is constructed to constrain the states to ensure that the tracking error rapidly converges to a neighborhood of zero. Under the proposed control strategy, the states of the closed-loop system are proven to be semi-globally uniformly ultimately bounded through rigorous Lyapunov analyses, and the state constraints are satisfied. Furthermore, the simulations and experiments conducted on a Quanser laboratory platform reveal that the proposed control functions are suitable and effective. Note to Practitioners—This paper is motivated by designing a reinforcement learning control strategy to enhance online learning capability and control performance of the controller for a nonlinear 2-DOF helicopter system. The control framework is divided into the design of the critic and actor NNs, responsible primarily for evaluating the control performance and approximating uncertainties in the system separately. Unlike the adaptive NN control, the actor NN weights are updated by combining information of states and inputs from the critic NN. In addition, aiming at accelerating the convergence, a barrier Lyapunov function is constructed to constrain the states to ensure that the tracking error rapidly converges to a neighborhood of zero. Finally, the proposed control strategy is validated in simulation and experiment on the Quanser laboratory platform.

Temperature is a key factor affecting the safety of the Lithium-ion (Li-ion) battery. Therefore, real-time thermal fault diagnosis is becoming more and more prominent, as battery faults can lead to local overheating and thermal runaway in severe cases. This article proposes a Chebyshev–Galerkin-based thermal fault detection and localization framework for the pouch-type Li-ion battery under limited sensing. First, the Chebyshev function is used to construct the spatial basis functions with global and orthonormal properties. Under the time–space (T-S) separation framework, the time coefficients can be derived through the Galerkin method using six sensors. Then, by decomposing the time coefficients using the independent component analysis, the temporal and spatial reference statistics can be formed for real-time fault detection. Finally, considering the detected fault snapshots, the thermal fault location can be identified by finding the maximum contributed position through T-S synthesis. Simulations and experiments demonstrate the effectiveness of the proposed method.

Li-ion battery (LIB) packs have been widely used in the vehicle industry. The abnormality detection and localization of battery systems are receiving more and more attention. In this article, the spatiotemporal entropy is proposed to detect and locate thermal abnormalities of LIB packs. Based on the Karhunen–Loève (KL) decomposition, the spatial entropy and temporal entropy can be constructed from different scales, and then appropriately integrated into the comprehensive spatiotemporal entropy. The kernel density estimation is employed to derive the detection threshold of the spatiotemporal entropy, based on which the abnormality detection can be achieved. The entropy contribution function is designed for abnormality localization based on the spatial basis function (SBF) variations in different modes. The physical meaning of the spatiotemporal entropy is explained from the perspective of the system disorder degree, energy concentration, and information theory. Experiments on the LIB pack under different fault conditions demonstrate that the proposed method can timely detect and precisely locate the abnormal cells at the early stage.

Ultrahigh-frequency radio frequency identification (UHF RFID) with a transducer-integrated antenna offers a cost-effective sensing solution for industrial applications. However, the analog backscattered signal contains the coupling effects between the antenna’s nearby environment and the unknown measurement setup, such as mutual distance and orientation between the read/write device (RWD) and sensor tags, and line-of-sight obstruction, which affects measurement accuracy. This article proposes an optimal power-oriented setup-independent technique that utilizes commercially self-tuning RFID tags to extract the environment in the vicinity of the antenna, independent of the measurement setup. The concept is based on an observation that the level of the radiated power of the RWD and the received power of the self-tuning RFID IC are linearly regressed. The condition of the environment is identified by the self-tuned value from the RFID chip under an optimal chip impedance. In the offline state, the optimal received power level is determined to maximize the pairwise Euclidean distance of the tuned values of the environment state near the tag. The radiated power level of the RWD is adjusted linearly to implement the sensing at the optimal power level. A water-filling sensor tag operated with polyvinyl chloride (PVC) pipes is demonstrated. Experiments show that the proposed system provides accurate sensing information under different measurement setups. The RFID tags can also be used in installations with heterogeneous environments. The proposed technique has been experimentally validated by applying it to two sizes of PVC pipes, confirming the sensing accuracy and adaptability.

In this article, we propose a new adaptive fuzzy fault-tolerant control (FTC) for a three-dimensional riser-vessel system with unknown backlash nonlinearity. A model for the smooth inverse dynamics of the backlash is introduced; then, the control input is divided into an expected input and a compensation error. Considering the imprecision of system modeling and unknown external disturbances, we employ a fuzzy adaptive technology to achieve compensation. By incorporating the actuator fault term and backlash error, the adaptive FTC is developed to resolve loss faults in the actuator and compensate for the unknown backlash to some extent. The direct Lyapunov method is used to demonstrate the system’s bounded stability. Finally, simulation results demonstrate the effectiveness of the derived scheme.

This article proposes an adaptive control for a flexible manipulator (FM) under the influence of distributed disturbances, unknown dead zones, and input quantization. First, the hybrid effect of the unknown dead zone and input quantization is formulated and represented based on some essential transformations. Then, an adaptive robust quantized control with online updating laws is developed to address the uncertainty of the dead zone, ensure robustness and angle position, and dampen the vibration in the FM system. Subsequently, the Lyapunov theoretical analysis is employed to ensure the bounded stability of the system. Finally, numerical simulations and experiments with a Quanser platform are given to further verify the feasibility and superiority of the designed scheme.

In industrial applications, the modeling of distributed parameter systems (DPSs) is of significance for process control and monitoring. Due to infinite dimension, spatiotemporal coupled dynamics, nonlinearity, and model uncertainties, however, modeling and online applications of DPSs are very difficult. To address these issues, an online spatiotemporal modeling method is proposed based on confidence-aware multiscale learning. From the spacial-scale perspective, an evolutionary learning-based spatial basis function is designed by learning from two dimensionality reduction methods, including Karhunen–Lo$\grave{e}$ ve and diffusion maps. From the temporal-scale perspective, an efficient broad learning system is developed as reduced-order model to online address temporal dynamics of DPSs. As for the spatiotemporal-scale learning, Gaussian process regression is proposed as confidence-aware estimator to compensate for model generalization errors caused by spatiotemporal coupled dynamics. Through integration with the three-scale learning, the proposed method enables online confidence-aware prediction for DPSs. Experiments based on the curing process in snap curing oven demonstrate the effectiveness of proposed method.

This article investigates robust non-fragile event-triggered sampled-data fuzzy (ETSDF) control for uncertain nonlinear delayed distributed parameter systems. Initially, a T-S fuzzy delayed partial differential equation model is presented to exactly describe the uncertain nonlinear delayed distributed parameter systems (DPS). secondly, a robust non-fragile ETSDF control strategy is proposed to reduce the unnecessary SD and cope with the uncertainties in controller and system. Then, based on an appropriate Lyapunov functional, the exponential stability conditions of closed-loop nonlinear delayed DPS via linear matrix inequalities are presented. Lastly, one example is presented to illustrate the design method.

For nonlinear delayed parabolic partial differential equation (PDE) systems, this article addresses fault-tolerant stochastic sampled-data (SD) fuzzy control under spatially point measurements (SPMs). Initially, a T–S fuzzy PDE model is given to accurately describe the nonlinear delayed parabolic PDE system. Second, in consideration of possible actuator failure, a fault-tolerant SD fuzzy controller with stochastic sampling under SPMs is designed for nonlinear delayed parabolic PDE system, where two sampling periods are considered whose occurrence probabilities are given constants and satisfy the Bernoulli distribution. Then, by constructing a novel time-dependent Lyapunov functional, sufficient conditions that guarantee the mean square exponential stability of closed-loop delayed PDE system are obtained based on linear matrix inequalities. Last, three examples are given to illustrate the designed approach.

In this paper, we consider the robust non-fragile H∞fuzzy control for uncertain nonlinear delayed hyperbolic partial differential equation (PDE) systems, which can represent the dynamics of most industrial processes, such as plug-flow reactors, fixed-bed reactors, tubular heat exchangers, traffic flows, and wave equations. Initially, a Takagi–Sugeno (T–S) fuzzy-delayed hyperbolic PDE model is presented to describe the uncertain nonlinear delayed hyperbolic PDE system. Subsequently, based on the T–S fuzzy delayed hyperbolic PDE model, spatial linear matrix inequality (SLMI) based sufficient conditions to ensure exponential stability with an H∞performance are obtained via utilizing the Lyapunov direct method. Then, to solve the SLMIs, the robust non-fragile H∞fuzzy control problem for uncertain nonlinear delayed hyperbolic PDE systems is formulated as an LMI feasibility problem. Finally, two examples on a Lotka–Volterra PDE system and a non-isothermal plug-flow reactor (PFR) are presented to illustrate the effectiveness of the presented control method.

Due to its spatiotemporal property and time-varying complexity, it is difficult to obtain the accurate model of the actual distributed parameter system (DPS), posing a significant obstacle to control. In this article, a spatial model predictive control (MPC) is proposed for the nonlinear DPS. A data-driven modeling method is first constructed for the performance prediction using the input–output data measured by sensors. In order to capture the most recent dynamics, a dual adaptation approach is devised. This includes updates to the spatial basis functions (SBFs) utilizing recursive techniques, as well as temporal updates employing sliding windows to enable online model updates. Based on the spatiotemporal model, a spatial MPC methodology with a novel objective function is designed for global space tracking. Theoretical analysis demonstrates that the stability of the proposed controller is guaranteed. The simulations and experiments conducted demonstrate that the proposed method satisfactorily achieves global tracking of targets and maintains robustness against time-varying input disturbances.

Defect detection is an essential part of quality management for bare printed circuit board (PCB) production. Existing vision-based methods are not effective in detecting PCB defects when uncertainty exists. This article proposes a multiscale convolution-based detection methodology to classify bare PCB defects under uncertainty. First, a novel window-based loss function is designed to tackle the inter-class imbalance and uncertainty. Then, a multiscale convolution network is constructed to process the defects with intra-class variance, and large scale extraction features are fused on the small scale to guide the extraction process. After that, the classification probability is extracted and assembled into a multiscale probability matrix, on which entropy-based probabilistic decisions are integrated for the final decision. Finally, experimental studies indicate that the proposed methodology can achieve satisfactory detection performance and demonstrate visual interpretability compared to baseline methods.

Recently, with the development of the marine economy, marine risers have garnered increasing attention as they present facile and reliable methods for oil and gas transportation. However, these risers are susceptible to vibrations, which can lead to system performance degradation and fatigue damage. Therefore, effective vibration control strategies are required to address this issue. In this study, a novel adaptive fault-tolerant control (FTC) strategy is adopted to suppress the vibrations of a 3-D riser-vessel system against the effects of actuator failures, backlash-like hysteresis, and external disturbances. A barrier-based Lyapunov function is merged to eliminate the time-varying output constraints of the system. Adaptive FTC laws with projection mapping operators are designed to compensate for parameter uncertainties and consider input nonlinearities to improve system robustness. Finally, a rigorous Lyapunov analysis and numerical simulations are performed to verify the validity of the proposed controller and guarantee uniformly bounded stability of the system.

This paper addresses mixed H2/H∞fault-tolerant sampled-data (SD) fuzzy control for nonlinear space-varying parabolic partial differential equation (PDE) system under deception attacks. Firstly, a T–S fuzzy PDE model is given to exactly describe the nonlinear space-varying parabolic PDE system. Secondly, a fault-tolerant SD fuzzy controller via the spatial linear matrix inequalities (SLMIs) is developed based on a Lyapunov functional which is continuous at sampling times but not necessary to be positive definite in sampling intervals such that the closed-loop PDE system is exponentially stable with a mixed H2/H∞performance. Then, to solve the SLMIs, the fault-tolerant SD fuzzy control problem for space-varying parabolic PDE system is formulated as linear matrix inequality feasibility problem. Furthermore, the design condition of the suboptimal mixed H2/H∞fault-tolerant SD controller subject to deception attacks can be derived by considering the property of membership functions. Lastly, two examples are given to illustrate the design method.

Modeling of the parabolic distributed parameter system (DPS) with the Karhunen-Loéve (KL) method under sparse sensing will become very difficult because the information from the measurements is incomplete. A novel information completion and learning strategy is proposed for spatiotemporal modeling under sparse sensing. During the offline initialization phase, the initial full spatial basis functions (SBFs) are constructed first in the full sensing environment under the framework of time-space separation. Subsequently, during the normal operation phase of fewer sensors, the sparse SBFs are obtained and further used to complete the lost spatial information with the help of the initial full SBFs, which are then recursively calibrated by the incremental KL. By iteratively repeating these two steps, the sparse spatiotemporal output can be completed in a streaming data environment. Finally, the proper spatiotemporal model can be constructed through time-space synthesis. The experimental results of a nonlinear transport-reaction process on a catalytic rod demonstrate the effectiveness of the proposed method.

•Spatial multivariable SVR based 3-D fuzzy modeling methodology is proposed for distributed parameter systems.•Multivariable SVR with spatial kernel functions is proposed to cope with a set of spatiotemporal data.•Spatial multivariable SVR builds up a complete 3-D fuzzy rule-base.•3-D fuzzy model is constructed in the form of data-driven design.

In this paper, a systematic incremental learning method is presented for reinforcement learning in continuous spaces where the learning environment is dynamic. The goal is to adjust the previously learned policy in the original environment to a new one incrementally whenever the environment changes. To improve the adaptability to the ever-changing environment, we propose a two-step solution incorporated with the incremental learning procedure: policy relaxation and importance weighting. First, the behavior policy is relaxed to a random one in the initial learning episodes to encourage a proper exploration in the new environment. It alleviates the conflict between the new information and the existing knowledge for a better adaptation in the long term. Second, it is observed that episodes receiving higher returns are more in line with the new environment, and hence contain more new information. During parameter updating, we assign higher importance weights to the learning episodes that contain more new information, thus encouraging the previous optimal policy to be faster adapted to a new one that fits in the new environment. Empirical studies on continuous controlling tasks with varying configurations verify that the proposed method achieves a significantly faster adaptation to various dynamic environments than the baselines.

The battery thermal process, as a typical distributed parameter system (DPS), is critical to battery management. In practice, the process information is often partially known. Data-driven spatiotemporal modeling is always used to approximate the battery thermal process. However, purely data-driven spatiotemporal modeling methods suffer from expensive costs for data acquirement, unsatisfactory accuracies for long-term prediction, and poor generalization performance. These inherent shortcomings significantly limit the applications of this kind of method in DPS modeling. To address these issues, we propose a novel physics-reserved spatiotemporal modeling method that embeds the partially known physics into deep learning architecture. Specifically, the proposed method constructs a composite network with the battery current and terminal voltage as extra control inputs to model the battery thermal process. By fully using the information conveyed by the partially known physics and the observed temperature data, it can predict the battery temperature accurately. Meanwhile, it can identify the unknown parameters and estimate the heat generation rate of the battery thermal process, which has not yet been achieved by data-driven spatiotemporal modeling methods. This paper makes an attempt to bridge the gap between physics and observed data for spatiotemporal modeling. The effectiveness of the proposed method has been demonstrated by extensive experiments.

A reinforcement learning-based bat algorithm is proposed for solving structural design problems. By incorporating reinforcement learning, the algorithm's performance feedback is formulated to adaptively select between algorithm's different operators. To improve the solution diversity, a new metric of individual difference is designed. The individual difference-based strategies are proposed to adaptively tune the algorithm's parameters. The variations of the pulse rates and loudness are newly designed to formulate their effects on the local search and foraging efficiency. Simulations and comparisons based on ten structural design problems with continuous/discrete variables demonstrate the superiority of the proposed algorithm.

Differential evolution (DE) is a kind of evolutionary algorithms, which is suitable for solving complex optimization problems. Mutation is a crucial step in DE that generates new solutions from old ones. It was argued and has been commonly adopted in DE that the solutions selected for mutation should have mutually different indices. This restrained condition, however, has not been verified either theoretically or empirically yet. In this paper, we empirically investigate the selection of solutions for mutation in DE. From the observation of the extensive experiments, we suggest that the restrained condition could be relaxed for some classical DE versions as well as some advanced DE variants. Moreover, relaxing the restrained condition may also be useful in designing better future DE algorithms.

Uncertain data clustering has been recognized as an essential task in the research of data mining. Many centralized clustering algorithms are extended by defining new distance or similarity measurements to tackle this issue. With the fast development of network applications, these centralized methods show their limitations in conducting data clustering in a large dynamic distributed peer-to-peer network due to the privacy and security concerns or the technical constraints brought by distributive environments. In this paper, we propose a novel distributed uncertain data clustering algorithm, in which the centralized global clustering solution is approximated by performing distributed clustering. To shorten the execution time, the reduction technique is then applied to transform the proposed method into its deterministic form by replacing each uncertain data object with its expected centroid. Finally, the attribute-weight-entropy regularization technique enhances the proposed distributed clustering method to achieve better results in data clustering and extract the essential features for cluster identification. The experiments on both synthetic and real-world data have shown the efficiency and superiority of the presented algorithm.

The Made in China 2025 initiative will require full automation in all sectors, from customers to production. This will result in great challenges to manufacturing systems in all sectors. In the future of manufacturing, all devices and systems should have sensing and basic intelligence capabilities for control and adaptation. In this study, after discussing multiscale dynamics of the modern manufacturing system, a five-layer functional structure is proposed for uncertainties processing. Multiscale dynamics include: multi-time scale, space-time scale, and multi-level dynamics. Control action will differ at different scales, with more design being required at both fast and slow time scales. More quantitative action is required in low-level operations, while more qualitative action is needed regarding high-level supervision. Intelligent manufacturing systems should have the capabilities of flexibility, adaptability, and intelligence. These capabilities will require the control action to be distributed and integrated with different approaches, including smart sensing, optimal design, and intelligent learning. Finally, a typical jet dispensing system is taken as a real-world example for multiscale modeling and control.

The microcantilever used in micro–nanomanipulator is a spatially distributed and flexible mechanical system. An accurate model of the microcantilever is essential for the accurate tip positioning and force sensing. Traditional lumped parameter model will lose the spatial dynamics. Though the nominal Euler–Bernoulli model is a distributed parameter model, in practice there are still some unknown nonlinear dynamics. In this study, a neural network-based distributed parameter model identification approach is proposed for modelling the microcantilever. First, a nominal Euler–Bernoulli beam model is derived. To compensate unknown nonlinear dynamics, a nonlinear term that needs to be estimated is added in the nominal model. For finite-dimensional implementation, the infinite-dimensional partial differential equation model is reduced into a finite-dimensional ordinary differential equation model using the Galerkin method. Next, a neural network-based intelligent learning approach is developed to learn the unknown nonlinearities from the input–output data. A radial basis function recurrent neural network observer is designed to estimate the finite-dimensional states from a few sensors of measurements. After that, a general regression neural network model is identified to establish the nonlinear spatiotemporal dynamic model between the inputs and outputs. The effectiveness of the proposed neural network-based distributed parameter modelling approach is verified by the simulations on a typical microcantilever.

The balance between exploration and exploitation is a key problem for reinforcement learning methods, especially for Q-learning. In this paper, a fidelity-based probabilistic Q-learning (FPQL) approach is presented to naturally solve this problem and applied for learning control of quantum systems. In this approach, fidelity is adopted to help direct the learning process and the probability of each action to be selected at a certain state is updated iteratively along with the learning process, which leads to a natural exploration strategy instead of a pointed one with configured parameters. A probabilistic Q-learning (PQL) algorithm is first presented to demonstrate the basic idea of probabilistic action selection. Then the FPQL algorithm is presented for learning control of quantum systems. Two examples (a spin-1/2 system and a Λ-type atomic system) are demonstrated to test the performance of the FPQL algorithm. The results show that FPQL algorithms attain a better balance between exploration and exploitation, and can also avoid local optimal policies and accelerate the learning process.

A data-driven 3-D fuzzy-logic controller (3-D FLC) design methodology based on support vector regression (SVR) learning is developed for nonlinear spatially distributed dynamic systems. Initially, the spatial information expression and processing as well as the fuzzy linguistic expression and rule inference of a 3-D FLC are integrated into spatial fuzzy basis functions (SFBFs), and then the 3-D FLC can be depicted by a three-layer network structure. By relating SFBFs of the 3-D FLC directly to spatial kernel functions of an SVR, an equivalence relationship of the 3-D FLC and the SVR is established, which means that the 3-D FLC can be designed with the help of the SVR learning. Subsequently, for an easy implementation, a systematic SVR learning-based 3-D FLC design scheme is formulated. In addition, the universal approximation capability of the proposed 3-D FLC is presented. Finally, the control of a nonlinear catalytic packed-bed reactor is considered as an application to demonstrate the effectiveness of the proposed 3-D FLC.

This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

Abstract: As a widely used reinforcement learning method, Q-learning is bedeviled by the curse of dimensionality: The computational complexity grows dramatically with the size of state-action space. To combat this difficulty, an integrated hierarchical Q-learning framework is proposed based on the hybrid Markov decision process (MDP) using temporal abstraction instead of the simple MDP. The learning process is naturally organized into multiple levels of learning, e.g., quantitative (lower) level and qualitative (upper) level, which are modeled as MDP and semi-MDP (SMDP), respectively. This hierarchical control architecture constitutes a hybrid MDP as the model of hierarchical Q-learning, which bridges the two levels of learning. The proposed hierarchical Q-learning can scale up very well and speed up learning with the upper level learning process. Hence this approach is an effective integral learning and control scheme for complex problems. Several experiments are carried out using a puzzle problem in a gridworld environment and a navigation control problem for a mobile robot. The experimental results demonstrate the effectiveness and efficiency of the proposed approach.

Understanding the relationship between genotype and phenotype is a challenge in systems biology. An interesting yet related issue is why a particular circuit topology is present in a cell when the same function can supposedly be obtained from an alternative architecture. Here we analyzed two topologically equivalent genetic circuits of coupled positive and negative feedback loops, named NAT and ALT circuits, respectively. The computational search for the oscillation volume of the entire biologically reasonable parameter region through large-scale random samplings shows that the NAT circuit exhibits a distinctly larger fraction of the oscillatory region than the ALT circuit. Such a global robustness difference between two circuits is supplemented by analyzing local robustness, including robustness to parameter perturbations and to molecular noise. In addition, detailed dynamical analysis shows that the molecular noise of both circuits can induce transient switching of the different mechanism between a stable steady state and a stable limit cycle. Our investigation on robustness and dynamics through examples provides insights into the relationship between network architecture and its function.

Distributed parameter systems (DPS) are a class of infinite dimensional systems. However implemental control design requires low-order models. This work will focus on developing a low-order model for a class of quasi-linear parabolic distributed parameter system with unknown linear spatial operator, unknown linear boundary condition as well as unknown non-linearity. The Karhunen-Loeve (KL) Empirical Eigenfunctions (EEFs) are used as basis functions in Galerkin's method to reduce the Partial Differential Equation (PDE) system to a nonlinear low-order Ordinary Differential Equation (ODE) system. Since the states of the system are not measurable, a recurrent Radial Basis Function (RBF) Neural Network (NN) observer is designed to estimate the states and approximate unknown dynamics simultaneously. Using the estimated states, a hybrid General Regression Neural Network (GRNN) is trained to be a nonlinear offline model, which is suitable for traditional control techniques. The simulations demonstrate the effectiveness of this modeling method.

In this paper, a straightforward approach is presented to design functional observers for linear systems with unknown inputs. Necessary and sufficient conditions are provided for the existence of the observers. Some illustrated examples are included.

Many industrial processes are distributed parameter systems that require complete spatial information for decisions and control. For modeling unknown distributed parameter systems (DPSs), a spatial construction method is proposed to preserve the spatial information between sensing locations. With the help of the spatial construction method, continuous spatial basis functions (SBFs) can be constructed to capture the spatial information lost in the time-space separation. The corresponding temporal dynamics can be identified using the generalized radial basis function network with the orthogonal least-squares (OLS) algorithm. After the time-space synthesis, the constructed spatiotemporal model can provide continuous modeling in the spatial domain with satisfactory performance. Convergence analysis proves that the proposed method can guarantee bounded errors. Finally, the experiments on a linear thermal process and a nonlinear catalytic process validate the effectiveness of the proposed method under limited sensors and its robustness when one of the sensors fails.