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This work focuses on developing a forecasting model for the nonlinear system with herding. Firstly, for clear presentation of the mechanism of herding behavior, a concept called intermittent positive feedback is defined. The mathematical expression of intermittent positive feedback is formulated in terms of dead-zone functions with the beginning and ending thresholds in the positive and negative directions. Then a dynamic surrogate based on the intermittent positive feedback multi-dimensional Taylor network is established, and a method for identifying its parameters is proposed. Multi-dimensional Taylor network module simulates the long-term trends of time series. Subsequently, an optimization model based on the alternating iteration of the parameters is developed to enhance the forecast accuracy of the intermittent positive feedback part. Simulation results demonstrate that the forecasting effect of the proposed modeling method is superior to that of conventional non-mechanism data-based surrogates for herding behavior. [ABSTRACT FROM AUTHOR]

In this paper, a recursive d -step-ahead predictive control scheme based on multi-dimensional Taylor network (MTN) is proposed for the real-time tracking control of multiple-input multiple-output (MIMO) nonlinear systems with input time-delay. The MTN predictive model is designed using a recursive approach to compensate the influence of time-delay, and an extended Kalman filter (EKF) is applied as its learning algorithm. An MTN controller is developed based on a proportional–integral–derivative (PID) controller where the closed-loop errors between the reference input and the system output are set as the MTN controller's inputs. Then, a back propagation (BP) algorithm, designed to update its weights according to errors caused by system uncertainty, is used as a learning algorithm for the MTN controller. Meanwhile, the convergence of the MTN predictive model and the stability of the closed-loop system are evaluated. Two numerical examples and a practical example – continuous stirred tank reactor (CSTR) process are presented to verify the superiority of the proposed scheme. The experimental results and the computational complexity analysis show that the proposed scheme is effective, promising its desirable robustness, anti-disturbance, tracking and real-time performance. [ABSTRACT FROM AUTHOR]

Control of stochastic nonlinear systems turns out to be notoriously difficult when stochastic uncertainties and time‐varying delays occur simultaneously. This article presents a tractable adaptive control scheme for the stochastic nonlinear system with time‐varying delays. To mitigate the effects of stochastic uncertainties, an adaptive embedded cubature Kalman filter is developed to realize the robust estimation of the state. Unlike the conventional cubature Kalman filter with fixed construction, a semi‐definite programming is designed to adjust the weights of cubature points dynamically. Such programming guarantees the positive definiteness of the error covariance matrix, which enhances the reliability of the filtering procedure. Based on more accurate state estimations, the multidimensional Taylor network (MTN) is utilized to evaluate the dynamic performance under time‐varying delays and approximate the optimal policy in the deterministic policy gradient framework. Adaptive tracking control with high computational efficiency is achieved due to the concise topological structure of MTN. The exponential convergence of the state estimation error and the semi‐globally uniform ultimate boundness of the tracking error are verified theoretically. The effectiveness of the proposed method is confirmed by a numerical simulation based on a practical electric industrial system. [ABSTRACT FROM AUTHOR]

An aero-engine has to be assembled twice or more to satisfy stringent technical standards. Substandard engines are required to re-enter for additional reassembly, which may trigger rework disruption. Work groups with flexible skills are responsible for the operations and can be reassigned when rescheduling triggers. An integrated problem of rescheduling of engines and reconfiguration of work groups with rework disruption is formulated here. A heuristic is proposed to solve the problem. In self-reconfiguration optimization, work groups are reassigned in accordance with the workload balance criterion without violating the assembly skills constraints. In rescheduling optimization, locally optimal sequencing propositions of operations are derived and applied to generate a feasible schedule. Three neighborhood structures are defined, and a variable neighborhood search is implemented to optimize the assignment and the schedule of operations on parallel work groups. The effectiveness of the proposed algorithm is tested by several numerical experiments. The results show that the proposed algorithm promises apparently lower total cost and more desirable assignment of work groups by scheduling. [ABSTRACT FROM AUTHOR]

In view of the difficulty of modelling time-varying nonlinear systems, a multidimensional Taylor network (MTN) model based on dynamic characteristic clustering is proposed to establish an online time series forecasting model. The construction method of a MTN, the definitions of the dynamic characteristics, and their similarity criteria are discussed. Specific steps of the MTN online model, based on dynamic clustering, are given. A practical example is presented to demonstrate how the proposed method works in a real application, and its effectiveness is verified. [ABSTRACT FROM AUTHOR]

Control input acting on the system in the form of nonlinear implicit tends to exert great impacts on the dynamic behavior of the multiple-input–multiple-output (MIMO) nonaffine nonlinear system with actuator saturation, posing a great challenge to its tracking control and dynamic regulation. Performance optimization and design simplicity are hardly taken simultaneously into account by existing controllers. For this sake, the multidimensional Taylor network (MTN) controller, which involves both transient improvement and design simplicity, is proposed here. The MTN controller, as a novel one with a fixed structure, is capable of making the proposed system asymptotically track the reference with no need of system information except for the control direction. A performance index related to the transient improvement by dynamic regulation is established. Parameters of the MTN controller are adapted for the optimization problem in line with this performance index of the arbitrary approximation by the polynomial function. The existence and the realizability of the solution to the optimization problem are demonstrated. Specific steps of the controller design are given. The effectiveness of the proposed controller is confirmed by its theoretical analysis as well as its application to a two-link manipulator system. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to provide a precise tracking control scheme for multi-input multi-output "MIMO" nonlinear systems with unknown input time-delay in industrial process. Design/methodology/approach: The predictive control scheme based on multi-dimensional Taylor network (MTN) model is proposed. First, for the unknown input time-delay, the cross-correlation function is used to identify the input time-delay through just the input and output data. And then, the scheme of predictive control is designed based on the MTN model. It goes as follows: a recursive d-step-ahead MTN predictive model is developed to compensate the influence of time-delay, and the extended Kalman filter (EKF) algorithm is applied for its learning; the multistep predictive objective function is designed, and the optimal controlled output is determined by iterative refinement; and the convergence of MTN predictive model and the stability of closed-loop system are proved. Findings: Simulation results show that the proposed scheme is of desirable generality and capable of performing the tracking control for MIMO nonlinear systems with unknown input time-delay in industrial process effectively, such as the continuous stirred tank reactor (CSTR) process, which provides a considerably improved performance and effectiveness. The proposed scheme promises strong robustness, low complexity and easy implementation. Research limitations/implications: For the limitations of proposed scheme, the time-invariant time-delay is only considered in time-delay identification and control schemes. And the CSTR process is only introduced to prove that the proposed scheme can adapt to practical industrial scenario. Originality/value: The originality of the paper is that the proposed MTN control scheme has good tracking performance, which solves the influence of time-delay, coupling and nonlinearity and the real-time performance for MIMO nonlinear systems with unknown input time-delay. [ABSTRACT FROM AUTHOR]

This paper focuses on simultaneous optimisation of production planning and scheduling problem over a time period for synchronous assembly lines. Differing from traditional top-down approaches, a mixed integer programming model which jointly considers production planning and detailed scheduling constraints is formulated, and a Lagrangian relaxation method is developed for the proposed model, whereby the integrated problem is decomposed into planning, batch sequencing, tardiness and earliness sub-problems. The scheduling sub-problem is modelled as a time-dependent travelling salesman problem, which is solved using a dynasearch algorithm. A proposition of Lagrangian multipliers is established to accelerate the convergence speed of the proposed algorithm. The average direction strategy is employed to solve the Lagrangian dual problem. Test results demonstrate that the proposed model and algorithm are effective and efficient. [ABSTRACT FROM PUBLISHER]

For the fixed-position assembly workshop, the integrated optimization problem of production planning and scheduling in the uncertain re-entrance environment is studied. Based on the situation of aircraft assembly workshops, the characteristics of fixed-position assembly workshop with uncertain re-entrance are abstracted. As the re-entrance repetition obeys some type of probability distribution, the expected value is used to describe the repetition, and a bi-level stochastic expected value programming model of integrated production planning and scheduling is constructed. Recursive expressions for start time and completion time of assembly classes and teams are confirmed. And the relation between the decision variable in the lower-level model of scheduling and the overtime and earliness of assembly classes and teams in the upper-level model of production planning is identified. Addressing the characteristics of bi-level programming model, an alternate iteration method based on Improved Genetic Algorithm (AI-IGA) is proposed to solve the models. Elite Genetic Algorithm (EGA) is introduced for the upper-level model of production planning, and Genetic Simulated Annealing Algorithm based on Stochastic Simulation Technique (SS-GSAA) is developed for the lower-level model of scheduling. Results from our experiments demonstrate that the proposed method is feasible for production planning and optimization of the fixed-position assembly workshop with uncertain re-entrance. And algorithm comparison verifies the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this study, an adaptive predictive control approach based on the multi-dimensional Taylor network (MTN) is proposed for the real-time tracking control of single-input single-output nonlinear systems with input time-delay. Two MTNs are used to implement the accurate tracking control. First, to compensate for the influence of time-delay, MTN is taken as a predictor and the damped recursive least squares algorithm is used as its online learning algorithm. Second, a feed-forward MTN controller is developed on the basis of the proportional–integral–derivative controller, and the closed-loop errors between the reference input and the system output are directly chosen to be the MTN controller's inputs. The back propagation algorithm is introduced for its learning which can update its weights online at stable learning rate by the errors caused by the system's uncertain factors. Convergence and stability analysis are given to guarantee the performance of our proposed approach. Finally, two examples are given to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Knowledgeable manufacturing system (KMS) transforms all types of advanced manufacturing modes into corresponding knowledge meshes (KMs) and selects the best combination of KMs to satisfy enterprise requirements. Efficiently retrieving and reconfiguring KMs can reduce the complexity of new KMs gained by self-reconfiguration operations and enhance its practicability. This paper presents the method for measuring the KM complexity based on entropy and that for fuzzily classifying and retrieving for KMs based on granularity. Utilising the intrinsic information of KM, knowledge capacity function based on entropy is introduced to measure the KM complexity, and proved to be a monotone function of the number, measure, coefficient and weight of elements in KM. Properties of the KM operations are kept. Taking quality, quantity and complexity into account, the similarity function is defined. As revealed by our analysis, this function is of similarity both in the sense of matching, and in the mode of gaining KM. Then, the KMs in the KM base are fuzzily clustered. The number of classes is not fixed in advance, but can be dynamically adjusted. Each clustering centre is the best state corresponding to certain demands and has the minimum complexity degree. KM features are quantised in importance using the weight vectors. The search space is determined by centring at the clustering, which converts the problem from fine-grained space to coarse-grained space. Our tests and software package developed have proved the method to be quite effective. [ABSTRACT FROM PUBLISHER]

The problems of integrated assembly job shop (AJS) scheduling and self-reconfiguration in knowledgeable manufacturing are studied with the objective of minimising the weighted sum of completion cost of products, the earliness penalty of operations and the training cost of workers. In AJS, each workstation consists of a certain number of teams of workers. A product is assumed to have a tree structure consisting of components and subassemblies. The assembly of components, subassemblies and final products are optimised with the capacity of workstations simultaneously. A heuristic algorithm is developed to solve the problem. Dominance relations of operations are derived and applied in the development of the heuristic. A backward insertion search strategy is designed to locally optimise the operation sequence. Once the optimal schedule is acquired, the teams are reconfigured by transferring them from workstations of lower utilisation to those of higher utilisation. Effectiveness of the proposed algorithm is tested by a number of numerical experiments. The results show that the proposed algorithm promises lower total cost and desirable simultaneous self-reconfiguration in accordance with scheduling. [ABSTRACT FROM PUBLISHER]

During the 8th century, ancient China began to use a steelyard clepsydra to control the waterwheel, giving it a time-keeping function for use in hydromechanical astronomical clocks. In the Tang Dynasty, the monk I-Hsing (683–723 CE) and Liang Lingzan jointly built a water-powered celestial globe (shuiyun huntian), which, according to historical records, was China's first hydromechanical astronomical clock with a waterwheel steelyard clepsydra. However, the original device has since been lost. The objective of this study is to use the design methodology for the reconstruction of lost ancient machinery to systematically reconstruct this lost clock. The methodology included the study of ancient literature to formulate reconstruction design specifications. Through the process of generalization and specialization, the target device was analyzed to determine its function, and different mechanical configurations that achieved the same function were developed. Thereafter, an atlas of possible mechanical sketches that were consistent with the technological level of ancient times was built. A computer 3D reconstruction of the waterwheel steelyard clepsydra, time-reporting device, and astronomical device was carried out, and 50 possible configurations were developed. One was selected to build a physical model. [ABSTRACT FROM AUTHOR]

This paper presents a study on the two-stage assembly flow shop scheduling problem for minimising the weighed sum of maximum makespan, earliness and lateness. There are m machines at the first stage, each of which produces a component of a job. A single machine at the second stage assembles the m components together to complete the job. A novel model for solving the scheduling problem is built to optimise the maximum makespan, earliness and lateness simultaneously. Two optimal operation sequences of jobs are determined and verified. As the problem is known to be NP-hard, a hybrid variable neighbourhood search – electromagnetism-like mechanism (VNS-EM) algorithm is proposed for its handling. To search beyond local optima for a global one, VNS algorithm is embedded in each iteration of EM, whereby the fine neighbourhood search of optimum individuals can be realised and the solution is thus optimised. Simulation results show that the proposed hybrid VNS-EM algorithm outperforms the EM and VNS algorithms in both average value and standard deviation. [ABSTRACT FROM AUTHOR]

This article examines the historical development of ancient water-powered mechanical clocks. The study begins with a comprehensive analysis and comparison of the different types of ancient clepsydra, their use and development and the development of their feedback systems, power systems, and time-reporting systems. Before becoming mechanized, water clocks (clepsydra) were mainly used for astronomical timekeeping, during religious sacrifices, for military affairs, court litigation timekeeping, and the time allocation of water rights. The invention of the feedback system in the 3rd century before common era (BCE) opened the door to the mechanization of water clocks. The float is the earliest power-driven element. In the 8th century, the emergence of waterwheels with timing functions in water-powered mechanical clocks prompted ancient China to develop water-powered mechanical clocks with waterwheel steelyard clepsydra devices, time-reporting devices, astronomical demonstration devices, and multiple time-reporting wooden pavilions. After the 13th century, mechanical clocks started to integrate elements from Chinese and Western cultures. In addition to the development of new styles of water-powered mechanical clocks in ancient China, the Western mercury wheels with timing functions evolved into compartmented cylindrical mercury clocks. [ABSTRACT FROM AUTHOR]

In this paper, an inverse control scheme based on the novel dynamic network (multi-dimensional Taylor network (MTN)) is proposed for the real-time tracking control of nonlinear time-varying systems with noise disturbances. Utilized in this scheme are the three MTNs: the adaptive model identifier for system modeling, the adaptive inverse controller for inverse modeling, and the adaptive nonlinear filter for eliminating the noise disturbances, whose weights are modified by the variable forgetting factor recursive least squares (VFF-RLS), back propagation through model (BPTM), normalized least mean square (NLMS) algorithms, respectively. To avoid "compromise", this scheme is designed into a structure wherein controlling the object dynamic response and eliminating the noise disturbances are implemented in two relatively independent processes. Furthermore, the weight-elimination algorithm is introduced for choice of effective regression items to avoid the dimension explosion, thus overcoming the shortcoming that the number of middle nodes needs to be determined before using the traditional neural network. After a certain number of training, the more streamlined MTNs are observed to contribute to satisfying the real-time requirements of software implementation and engineering application. To ensure that MTN inverse control is strict in theory, the general conditions for the existence of single-input/single-output (SISO) nonlinear inverse systems are identified. Simulation of the MTN inverse control is conducted to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This study is concerned with the robust model predictive control (MPC) based on recurrent multi‐dimensional Taylor network (RMTN) for the discrete‐time non‐linear time‐delay systems. Regarding the MPC algorithm for the discrete‐time time‐delay systems, the existing literature only considers the linear case. In this study, by designing the suitable terminal cost and terminal region, the MPC scheme is firstly investigated for the non‐linear case. Meanwhile, to reduce the computational burden of MPC using the existing model types (e.g. recurrent neural network) as the identified model, an RMTN possessing the concise structure and high computational efficiency is constructed to approximate the state‐space model of the system. After trained by the backpropagation through time algorithm, the RMTN obtaining the high accuracy of prediction over a long‐range horizon is capable of serving as the prediction model in the MPC scheme. Furthermore, aiming at alleviating the adverse effect of the inevitable identification error, the tube‐based MPC is proposed via leveraging dual‐mode MPC to guarantee that actual trajectory is contained within a robust tube. The stability of the considered system is proved theoretically, and numerical simulation is employed to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of multi-dimensional Taylor network (MTN) decentralised adaptive output-feedback tracking control is investigated for large-scale stochastic nonlinear systems. MTNs are used to approximate the unknown nonlinear functions, and a MTN state observer is designed for estimating the unmeasured states. Based on the designed MTN state observer, and by combining the backstepping technique with dynamic surface control (DSC), an adaptive MTN decentralised output-feedback tracking control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability, and the tracking errors converge to an arbitrarily small neighbourhood around the origin in the sense of mean quartic value. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and the simulation results demonstrate that the proposed method promises desirable real-time performance and tracking control. [ABSTRACT FROM AUTHOR]

Summary: In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results. [ABSTRACT FROM AUTHOR]

This work presents the modeling and computer simulation of a novel hybrid transmission with a mechanical reverse driving mode, including an engine, a motor, a simple planetary gear train, and a Ravigneaux planetary gear train. Based on the given teeth number, the reduction ratios of all the clutching condition are acquired. The feasibilities of mode shifts among the clutching conditions are analyzed. Then, a modified rule-based control strategy is introduced. Subject to the vehicle condition, speed command, and predicted equivalent fuel consumptions, the most fuel economy clutching condition is selected by the control strategy. And, a computer model is developed using SIMULINK. Two popular driving cycles are applied to the simulation model, and the simulation results of the novel hybrid transmission are competitive with the existing hybrid electric vehicle models. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive control approach based on the multi‐dimensional Taylor network (MTN) is proposed to control the non‐linear uncertain time‐varying systems with noise disturbances. MTNs are introduced to formulate adaptive filtering, non‐linear identification and optimal control. First, an MTN filter is developed to eliminate the control interference and measurement noise, so that the model output without stochastic disturbance can be obtained. Then, an MTN identifier (MTNI) is so designed as to be capable of dynamic mapping and require fewer weights than traditional neural networks. On the basis of the above, the MTN controller (MTNC) is developed to realise the precise tracking control of the system. The non‐linear uncertain time‐varying system is identified by MTNI, which then provides sensitivity information of the plant to MTNC to make it adaptive. Furthermore, the skeletonisation algorithm is adopted to remove redundant inputs and redundant regression items from MTNI and MTNC for concise MTNs. Successful convergence and faster learning are guaranteed using the Lyapunov theorem, and the optimal learning rates are identified. Simulation results demonstrate that the proposed approach features its accurate identification, excellent tracking and better anti‐interference capability for the adaptive real‐time control of uncertain, stochastic and time‐varying non‐linear systems. [ABSTRACT FROM AUTHOR]

Summary This paper investigates the problem of adaptive multi‐dimensional Taylor network (MTN) decentralized tracking control for large‐scale stochastic nonlinear systems. Minimizing the influence of randomness and complex nonlinearity, which increases computational complexity, and improving the controller's real‐time performance for the stochastic nonlinear system are of great significance. With combining adaptive backstepping with dynamic surface control, a decentralized adaptive MTN tracking control approach is developed. In the controller design, MTNs are used to approximate nonlinearities, the backstepping technique is employed to construct the decentralized adaptive MTN controller, and the dynamic surface control technique is adopted to avoid the "explosion of computational complexity" in the backstepping design. It is proven that all the signals in the closed‐loop system remain bounded in probability, and the tracking errors converge to a small residual set around the origin in the sense of a mean quartic value. As the MTN contains only addition and multiplication, the proposed control method is more simplified and of good real‐time performance, compared with the existing control methods for large‐scale stochastic nonlinear systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this paper has good real‐time performance and control quality, and the dynamic performance of the closed‐loop system is satisfactory. [ABSTRACT FROM AUTHOR]

To secure the quick response of knowledgeable manufacturing system (KMS) to the dynamic production environment and its desirable adaptability and competitiveness, we propose a matching decision method that is based on the improved support vector machine (ISVM for short), and the production environment. Taking into account the uncertainty and fuzziness of the production environment, the triangular fuzzy numbers are introduced to represent the uncertain input factors. Independent penalty coefficients are employed for different categories to address the problem of unbalanced samples. To meet the requirement for classifying small, uncertain input, and unbalanced samples, an improved SVM model based on triangular fuzzy theory is put forward. Considering the mutagenic factor and dynamic weight, we improve the particle swarm algorithm to optimize the model parameters. The matching categories of KMS and dynamic production environment are defined, and the corresponding matching decision method based on ISVM model is built. Case study shows that the proposed ISVM matching decision method is feasible and effective. [ABSTRACT FROM AUTHOR]

A decade ago, electric vehicles (EV) made a boom in the automobile market, as they started to become a growing market section in the transportation space. The reasons behind the boom were to decrease environmental pollution by reducing the use of fossil fuels, lowering transportation operating costs, and increased general consumer interest in the new technology. This work generates a streamlined process for the design and simulation of motor transmissions with eight-link mechanisms. This procedure presents a wide range of motor transmissions such as 34 new clutchless systems and 34 new clutched systems. Two novel feasible motor transmissions of the design process are taken as a sample to dissect the working principle conjoined both power flow paths and operation modes. In addition, these designs are conducted for modeling and computer simulation procedures that obtain the results of the energy management strategy and operation mode variation. [ABSTRACT FROM AUTHOR]

Nonlinear time-varying systems without mechanism models are common in application. They cannot be controlled directly by the traditional control methods based on precise mathematical models. Intelligent control is unsuitable for real-time control due to its computation complexity. For that sake, a multidimensional Taylor network (MTN) based output tracking control scheme, which consists of two MTNs, one as an identifier and the other as a controller, is proposed for SISO nonlinear time-varying discrete-time systems with no mechanism models. A MTN identifier is constructed to build the offline model of the system, and a set of initial parameters for online learning of the identifier is obtained. Then, an ideal output signal is selected relative to the given reference signal. Based on the system identification model, Pontryagin minimum principle is introduced to obtain the numerical solution of the optimal control law for the system relative to the given ideal output signal, with the corresponding optimal output taken as the desired output signal. A MTN controller is generated automatically to fit the numerical solution of the optimal control law using the conjugate gradient (CG) method, and a set of initial parameters for online learning of the controller is obtained. An adaptive back propagation (BP) algorithm is developed to adjust the parameters of the identifier and controller in real time, and the convergence for the proposed learning algorithm is verified. Simulation results show that the proposed scheme is valid. [ABSTRACT FROM AUTHOR]

In this study, the problem of adaptive multi‐dimensional Taylor network (MTN) control for single‐input single‐output (SISO) uncertain stochastic non‐linear systems is investigated. How to minimise the influence of randomness and uncertain non‐linearity for less complex computation, and how to improve the real‐time performance of the controller are of great significance. To this end, a control approach based on MTN is proposed for tracking control of stochastic non‐linear systems. MTNs are used to approximate the non‐linearities, and the backstepping technique is employed to construct the MTN controller (MTNC). MTNC involves only addition and multiplication, featuring desirable simplicity and real‐time performance. Stability of the system is guaranteed via Lyapunov approach, and it is proved that the proposed controller can guarantee that all signals of the closed‐loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighbourhood around the origin. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this study has good real‐time performance and control quality. [ABSTRACT FROM AUTHOR]

Summary: It is difficult or even impossible for the existing nonlinear system control methods to realize the real‐time tracking control of nonlinear systems in the presence of modeling errors by output feedback. For that sake, multidimensional Taylor network (MTN) optimal control method is proposed for the real‐time optimal tracking control of the SISO nonlinear constant system with modeling errors as such. On the basis of the original MTN, the control input item is added to the nonlinear dynamic model, which is then termed as the MTN optimal controller (MTNOC). Its initial parameters are trained by the conjugate gradient method and the minimum principle, according to the calculated optimal input and output of the controlled object in open‐loop status. The propagation learning algorithm is adopted to improve the MTN product term weights and eliminate the modeling errors during the real system adjustment process. Simulation results show that the MTNOC promises a high response rate. Despite the errors in the modeling process, MTNOC manages to stabilize the system for tracking the desired output. The experiment of overlaying an additional signal on the input signal proves MTNOC to be of excellent tracking characteristics, capable of inhibiting the disturbance signal to some extent. In short, by realizing the optimal closed‐loop tracking control of the SISO nonlinear constant system by output feedback, MTNOC guarantees its real‐time control accuracy, dynamic performance, robustness, and anti‐disturbance capability. [ABSTRACT FROM AUTHOR]

The actual controlled objects are generally multi-input and multioutput (MIMO) nonlinear systems with imprecise models or even without models, so it is one of the hot topics in the control theory. Due to the complex internal structure, the general control methods without models tend to be based on neural networks. However, the neuron of neural networks includes the exponential function, which contributes to the complexity of calculation, making the neural network control unable to meet the real-time requirements. The newly developed multidimensional Taylor network (MTN) requires only addition and multiplication, so it is easy to realize real-time control. In the present study, the MTN approach is extended to MIMO nonlinear systems without models to realize adaptive output feedback control. The MTN controller is proposed to guarantee the stability of the closed-loop system. Our experimental results show that the output signals of the system are bounded and the tracking error goes nearly to zero. The MTN optimal controller is proven to promise far better real-time dynamic performance and robustness than the BP neural network self-adaption reconstitution controller. [ABSTRACT FROM AUTHOR]

For non‐linear control, it is important to secure a generally structured controller that promises wide application and desirable performance. This study deals with the problem of asymptotic tracking and dynamic regulation of single‐input single output (SISO) non‐linear systems via output feedbacks by the discrete multi‐dimensional Taylor network (MTN) controller, a novel controller with fixed structure and sampled‐data control mechanism. For verification of its validity, differential geometry and polynomial approximation are adopted. Using the emulation technique and regional pole assignment, the asymptotic tracking and dynamic regulation without online optimisation of the system by discrete MTN controller is tested. With the dynamic change of error signals, the dynamic regulation by given index is realised. As a convex optimisation problem, the controller parameters can be acquired by parametric learning. Based on the delta operator model, the procedure of the controller design is given in detail. Simulation results confirm the feasibility and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The production control of failure-prone manufacturing systems is notoriously difficult because such systems are uncertain and non-linear. Since the introduction of hedging-point policies, many researches have been done in this field. However, there are few literatures that consider the production control problem of tree-structured manufacturing systems. In this article, a hedging-point production control policy is proposed for a multi-machine, tree-structured failure-prone manufacturing system. To obtain the optimal hedging points, an iterative learning algorithm is developed by considering the system’s characteristics. A simulation method is embedded in the iterative learning algorithm to calculate the system cost. To estimate the performance of the proposed algorithm, comparisons are made between our algorithm, genetic algorithm and particle swarm optimization algorithm. The experimental results show that our algorithm works better than others in reducing the computation time and minimizing the production cost. [ABSTRACT FROM AUTHOR]

The Blossoming Flower Clock is an ingenious timepiece made in the 18th century and now preserved in Beijing Palace Museum, China. It generally cannot be disassembled and examined due to its historical value, and hence the inner mechanisms of the clock are unknown. This study provides a systematic design approach for reconstructing the five automata in the clock, namely time keeping, music playing, ducks swimming, flowers blossoming, and figures posturing. For the first two automata, practicable mechanical structures are inferred based on a classification and analysis of known technological customs and practice at the time. A total of seven feasible mechanisms are proposed for the time-keeping automaton, while three possible mechanisms are presented for the music-playing automaton. For the remaining automata, the structural characteristics and design constraints of the associated mechanisms are derived by means of a systematic motion analysis. By applying the concepts of generalization and specialization, a total of seven feasible mechanisms are synthesized for the ducks-swimming automaton, while six mechanisms are presented for the flowers-blossoming automaton and figures-posturing automaton. The proposed methodology is formalized in the form of a flow chart. Overall, the present results suggest that the proposed method provides a useful approach for reconstructing the unknown internal workings of mechanical devices. [ABSTRACT FROM AUTHOR]

A multi-objective scheduling algorithm with self-evolutionary feature for job-shop-like knowledgeable manufacturing cell (JSKMC) is proposed in this paper, targeting such scheduling issues as make-span, mean complete time of tasks, total tardiness of tasks, number of tardy tasks and the maximum tardiness. Four matrixes are designed to represent the scheduling model of JSKMC. Properties of the key arcs of tasks are discussed and it is found helpless to seek a better solution by reversing the direction of the middle key arcs of tasks. A simplified neighborhood is then established whereby the number of feasible solutions to be searched for is greatly reduced. Based on the above a multi-objective scheduling algorithm with self-evolutionary feature for JSKMC is proposed. Adaptive heuristic critic method is adopted in the algorithm, whose associate search element (ASE) module is designed to select the appropriate action for acquisition of a better solution in the next step by using the knowledge obtained from learning; such an ability of this module can be improved progressively with the increasing training. A scheduling algorithm based on ASE is developed, in which a Pareto archive is embedded to obtain the Pareto optimal solutions. Numerical simulation results confirm the strong ability of the proposed algorithm to home in on the optimal solution by self-evolution via learning. [ABSTRACT FROM AUTHOR]