Parallel Control for Optimal Tracking via Adaptive Dynamic Programming

This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems.Unlike existing optimal state feedback control,the control input of the optimal parallel control is introduced into the feedback system.However,due to the introduction of control input into the feedback system,the optimal state feedback control methods can not be applied directly.To address this problem,an augmented system and an augmented performance index function are proposed firstly.Thus,the general nonlinear system is transformed into an affine nonlinear system.The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically.It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function.Moreover,an adaptive dynamic programming(ADP)technique is utilized to implement the optimal parallel tracking control using a critic neural network(NN)to approximate the value function online.The stability analysis of the closed-loop system is performed using the Lyapunov theory,and the tracking error and NN weights errors are uniformly ultimately bounded(UUB).Also,the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals.Finally,the effectiveness of the developed optimal parallel control method is verified in two cases.

The DAO to MetaControl for MetaSystems in Metaverses:The System of Parallel Control Systems for Knowledge Automation and Control Intelligence in CPSS

An investigation and outline of MetaControl and DeControl in Metaverses for control intelligence and knowledge automation are presented.Prescriptive control with prescriptive knowledge and parallel philosophy is proposed as the starting point for the new control philosophy and technology,especially for computational control of metasystems in cyberphysical-social systems.We argue that circular causality,the generalized feedback mechanism for complex and purposive systems,should be adapted as the fundamental principle for control and management of metasystems with metacomplexity in metaverses.Particularly,an interdisciplinary approach is suggested for MetaControl and DeControl as a new form of intelligent control based on five control metaverses:MetaVerses,MultiVerses,InterVerses,TransVerse,and DeepVerses.

Parallel Control for Continuous-Time Linear Systems:A Case Study

In this paper,a new parallel controller is developed for continuous-time linear systems.The main contribution of the method is to establish a new parallel control law,where both state and control are considered as the input.The structure of the parallel control is provided,and the relationship between the parallel control and traditional feedback controls is presented.Considering the situations that the systems are controllable and incompletely controllable,the properties of the parallel control law are analyzed.The parallel controller design algorithms are given under the conditions that the systems are controllable and incompletely controllable.Finally,numerical simulations are carried out to demonstrate the effectiveness and applicability of the present method.Index Terms-Continuous-time linear systems,digital twin,parallel controller,parallel intelligence,parallel systems.

Research Progress of Parallel Control and Management

Based on ACP(artificial systems,computational experiments,and parallel execution)methodology,parallel control and management has become a popularly systematic and complete solution for the control and management of complex systems.This paper focuses on summarizing comprehensive review of the research literature of parallel control and management achieved in the recent years including the theoretical framework,core technologies,and the application demonstration.The future research,application directions,and suggestions are also discussed.

Parallel Neural Network-Based Motion Controller for Autonomous Underwater Vehicles

A parallel neural network-based controller （PNNC） is presented for the motion control of underwater vehicles in this paper. It consists of a real-time part, a self-learning part and a desired-state programmer, and it is different from normal adaptive neural network controller in structure. Owing to the introduction of the self-learning part, on-line learning can be performed without sample data in several sample periods, resulting in high learning speed of the controller and good control performance. The desired-state programmer is utilized to obtain better learning samples of the neural network to keep the stability of the controller. The developed controller is applied to the 4-degree of freedom control of the AUV “IUV- IV” and is successful on the simulation platform. The control performance is also compared with that of neural network controller with different structures such as normal adaptive neural network and different learning methods. Current effects and surge velocity control are also included to demonstrate the controller＇ s performance. It is shown that the PNNC has a great possibility to solve the problems in the control system design of underwater vehicles.

MODELING AND CONTROLLING OF PARALLEL MANIPULATOR JOINT DRIVEN BY PNEUMATIC MUSCLES

A parallel manipulator joint driven by three pneumatic muscles and its posture control strategy are presented. Based on geometric constraints and dynamics, a system model is developed through which some influences on dynamic response and open-loop gain are analyzed including the supply pressure, the initial pressure and the volume of pneumatic muscle. A sliding-mode controller with a nonlinear switching function is applied to control posture, which adopts the combination of a main method that separates control of each muscle and an auxiliary method that postures error evaluation of multiple muscles, especially adopting the segmented and intelligent adjustments of sliding-mode parameters to fit different expected postures and initial states. Experimental results show that this control strategy not only amounts to the steady-state error of 0. 1° without overshoot, but also achieves good trajectory tracking.

Adaptive control of parallel manipulators via fuzzy-neural network algorithm

This paper considers adaptive control of parallel manipulators combined with fuzzy-neural network algorithms （FNNA）. With this algorithm, the robustness is guaranteed by the adaptive control law and the parametric uncertainties are eliminated. FNNA is used to handle model uncertainties and external disturbances. In the proposed control scheme, we consider modifying the weight of fuzzy rules and present these rules to a MIMO system of parallel manipulators with more than three degrees-of-freedom （DoF）. The algorithm has the advantage of not requiring the inverse of the Jacobian matrix especially for the low DoF parallel manipulators. The validity of the control scheme is shown through numerical simulations of a 6-RPS parallel manipulator with three DoF.

Dynamic Feedforward Control of a Novel 3-PSP 3-DOF Parallel Manipulator

Parallel manipulators with less than six degrees of freedom （DOF） have been increasingly used in high-speed hybrid machine tools. The structural features of parallel manipulators are dynamic, a characteristic that is particularly significant when these manipulators are used in high-speed machine tools. However, normal kinematic control method cannot satisfy the requirements of the control system. Many researchers use model-based dynamic control methods, such as the dynamic feedforward control method. However, these methods are rarely used in hybrid machine tools because of the complex dynamic model of the parallel manipulator. In order to study the dynamic control method of parallel manipulators, the dynamic feedforward control method is used in the dynamic control system of a 3-PSP （prismatic-spherical-prismatic） 3-DOF spatial parallel manipulator used as a spindle head in a high-speed hybrid machine tool. Using kinematic analysis as basis and the Newton-Euler method, we derive the dynamic model of the parallel manipulator. Furthermore, a model-based dynamic feedforward control system consisting of both kinematic control and dynamic control subsystems is established. The dynamic control subsystem consists of two modules. One is used to eliminate the influence of the dynamic characteristics of high-speed movement, and the other is used to eliminate the dynamic disturbances in the milling process. Finally, the simulation model of the dynamic feedforward control system of the 3-PSP parallel manipulator is constructed in Matlab/Simulink. The simulations of the control system eliminating the influence of the dynamic characteristics and dynamic disturbances are conducted. A comparative study between the simulations and the normal kinematic control method is also presented.The simulations prove that the dynamic feedforward control method effectively eliminates the influence of the dynamic disturbances and dynamic characteristics of the parallel manipulator on high-speed machine tools, and significantly improves the trajectory accuracy. This is the first attempt to introduce the dynamic feedfordward control method into the 3-PSP spatial parallel manipulator whose dynamic model is complex and provides a study basis for the real-time dynamic control of the high-speed hybrid machine tools.

Series-parallel Hybrid Vehicle Control Strategy Design and Optimization Using Real-valued Genetic Algorithm

Despite the series-parallel hybrid electric vehicle inherits the performance advantages from both series and parallel hybrid electric vehicle, few researches about the series-parallel hybrid electric vehicle have been revealed because of its complex co nstruction and control strategy. In this paper, a series-parallel hybrid electric bus as well as its control strategy is revealed, and a control parameter optimization approach using the real-valued genetic algorithm is proposed. The optimization objective is to minimize the fuel consumption while sustain the battery state of charge, a tangent penalty function of state of charge（SOC） is embodied in the objective function to recast this multi-objective nonlinear optimization problem as a single linear optimization problem. For this strategy, the vehicle operating mode is switched based on the vehicle speed, and an ＂optimal line＂ typed strategy is designed for the parallel control. The optimization parameters include the speed threshold for mode switching, the highest state of charge allowed, the lowest state of charge allowed and the scale factor of the engine optimal torque to the engine maximum torque at a rotational speed. They are optimized through numerical experiments based on real-value genes, arithmetic crossover and mutation operators. The hybrid bus has been evaluated at the Chinese Transit Bus City Driving Cycle via road test, in which a control area network-based monitor system was used to trace the driving schedule. The test result shows that this approach is feasible for the control parameter optimization. This approach can be applied to not only the novel construction presented in this paper, but also other types of hybrid electric vehicles.

Synchronous tracking control of 6-DOF hydraulic parallel manipulator using cascade control method

The synchronous tracking control problem of a hydraulic parallel manipulator with six degrees of freedom (DOF) is complicated since the inclusion of hydraulic elements increases the order of the system.To solve this problem,cascade control method with an inner/outer-loop control structure is used,which masks the hydraulic dynamics with the inner-loop so that the designed controller takes into account of both the mechanical dynamics and the hydraulic dynamics of the manipulator.Furthermore,a cross-coupling control approach is introduced to the synchronous tracking control of the manipulator.The position synchronization error is developed by considering motion synchronization between each actuator joint and its adjacent ones based on the synchronous goal.Then,with the feedback of both position error and synchronization error,the tracking is proven to guarantee that both the position errors and synchronization errors asymptotically converge to zero.Moreover,the effectiveness of the proposed approach is verified by the experimental results performed with a 6-DOF hydraulic parallel manipulator.

Optimal Design and Force Control of a Nine-Cable-Driven Parallel Mechanism for Lunar Takeoff Simulation

Traditional simulation methods are unable to meet the requirements of lunar takeo simulations, such as high force output precision, low cost, and repeated use. Considering that cable-driven parallel mechanisms have the advantages of high payload to weight ratio, potentially large workspace, and high-speed motion, these mechanisms have the potential to be used for lunar takeo simulations. Thus, this paper presents a parallel mechanism driven by nine cables. The purpose of this study is to optimize the dimensions of the cable-driven parallel mechanism to meet dynamic workspace requirements under cable tension constraints. The dynamic workspace requirements are derived from the kinematical function requests of the lunar takeo simulation equipment. Experimental design and response surface methods are adopted for building the surrogate mathematical model linking the optimal variables and the optimization indices. A set of dimensional parameters are determined by analyzing the surrogate mathematical model. The volume of the dynamic workspace increased by 46% after optimization. Besides, a force control method is proposed for calculating output vector and sinusoidal forces. A force control loop is introduced into the traditional position control loop to adjust the cable force precisely, while controlling the cable length. The e ectiveness of the proposed control method is verified through experiments. A 5% vector output accuracy and 12 Hz undulation force output can be realized. This paper proposes a cable-driven parallel mechanism which can be used for lunar takeo simulation.

Robustly stable model predictive control based on parallel support vector machines with linear kernel

Robustly stable multi-step-ahead model predictive control (MPC) based on parallel support vector machines (SVMs) with linear kernel was proposed. First, an analytical solution of optimal control laws of parallel SVMs based MPC was derived, and then the necessary and sufficient stability condition for MPC closed loop was given according to SVM model, and finally a method of judging the discrepancy between SVM model and the actual plant was presented, and consequently the constraint sets, which can guarantee that the stability condition is still robust for model/plant mismatch within some given bounds, were obtained by applying small-gain theorem. Simulation experiments show the proposed stability condition and robust constraint sets can provide a convenient way of adjusting controller parameters to ensure a closed-loop with larger stable margin.

The Paralleling of High Power High Frequency Amplifier Based on Synchronous and Asynchronous Control

The vertical position of plasma in the HT-7U Tokamak is inherently unstable. In order to realize active stabilization, the response rate of the high-power high-frequency amplifier feeding the active control coils must be fast enough. This paper analyzes the paralleling scheme of the power amplifier through two kinds of control mode. One is the synchronous control; the other is the asynchronous control. Via the comparison of the two kinds of control mode, both of their characteristics are given in the text. At last, the analyzed result is verified by a small power experiment.

Distributed Control of Multiple-Bus Microgrid With Paralleled Distributed Generators

A microgrid is hard to control due to its reduced inertia and increased uncertainties. To overcome the challenges of microgrid control, advanced controllers need to be developed.In this paper, a distributed, two-level, communication-economic control scheme is presented for multiple-bus microgrids with each bus having multiple distributed generators(DGs) connected in parallel. The control objective of the upper level is to calculate the voltage references for one-bus subsystems. The objectives of the lower control level are to make the subsystems' bus voltages track the voltage references and to enhance load current sharing accuracy among the local DGs. Firstly, a distributed consensusbased power sharing algorithm is introduced to determine the power generations of the subsystems. Secondly, a discrete-time droop equation is used to adjust subsystem frequencies for voltage reference calculations. Finally, a Lyapunov-based decentralized control algorithm is designed for bus voltage regulation and proportional load current sharing. Extensive simulation studies with microgrid models of different levels of detail are performed to demonstrate the merits of the proposed control scheme.

Nested Transaction Concurrency Control in Parallel Real-Time Dat-abases

An integrated method for concurrency control in parallel real-time databases has been proposed in this paper. The nested transaction model has been investigated to offer more atomic execution units and finer grained control within in a transaction. Based on the classical nested locking protocol and the speculative concurrency control approach, a two-shadow adaptive concurrency control protocol, which combines the Sacrifice based Optimistic Concurrency Control (OPT-Sacrifice) and High Priority two-phase locking (HP2PL) algorithms together to support both optimistic and pessimistic shadow of each sub-transaction, has been proposed to increase the likelihood of successful timely commitment and to avoid unnecessary replication overload.

Pressure observer based adaptive robust trajectory tracking control of a parallel manipulator driven by pneumatic muscles

This paper presents a pressure observer based adaptive robust controller (POARC) for posture trajectory tracking of a parallel manipulator driven by three pneumatic muscles without pressure sensors. Due to model errors of the static forces and friction forces of pneumatic muscles, simplified average flow rate characteristics of valves, unknown disturbances of entire system, and unmeasured pressures, there exist rather severe parametric uncertainties, nonlinear uncertainties and dynamic uncertainties in modeling of the parallel manipulator. A nonlinear pressure observer is constructed to estimate unknown pressures on the basis of a single-input-single-output (SISO) decoupling model that is simplified from the actual multiple-input-multiple-output (MIMO) coupling model of the parallel manipulator. Then, an adaptive robust controller integrated with the pressure observer is developed to accomplish high precision posture trajectory tracking of the parallel manipulator. The experimental results indicate that the system with the proposed POARC not only achieves good control accuracy and smooth movement but also maintains robustness to disturbances.

Cross-coupling integral adaptive robust posture control of a pneumatic parallel platform

A pneumatic parallel platform driven by an air cylinder and three circumambient pneumatic muscles was considered. Firstly, a mathematical model of the pneumatic servo system was developed for the MIMO nonlinear model-based controller designed. The pneumatic muscles were controlled by three proportional position valves, and the air cylinder was controlled by a proportional pressure valve. As the forward kinematics of this structure had no analytical solution, the control strategy should be designed in joint space. A cross-coupling integral adaptive robust controller(CCIARC) which combined cross-coupling control strategy and traditional adaptive robust control(ARC) theory was developed by back-stepping method to accomplish trajectory tracking control of the parallel platform. The cross-coupling part of the controller stabilized the length error in joint space as well as the synchronization error, and the adaptive robust control part attenuated the adverse effects of modelling error and disturbance. The force character of the pneumatic muscles was difficult to model precisely, so the on-line recursive least square estimation(RLSE) method was employed to modify the model compensation. The projector mapping method was used to condition the RLSE algorithm to bound the parameters estimated. An integral feedback part was added to the traditional robust function to reduce the negative influence of the slow time-varying characteristic of pneumatic muscles and enhance the ability of trajectory tracking. The stability of the controller designed was proved through Laypunov's theory. Various contrast controllers were designed to testify the newly designed components of the CCIARC. Extensive experiments were conducted to illustrate the performance of the controller.

Validation concurrency control protocol in parallel real-time database systems

In parallel real-time database systems, concurrency control protocols must satisfy time constraints as well as the integrity constraints. The authors present a validation concurrency control(VCC) protocol, which can enhance the performance of real-time concurrency control mechanism by reducing the number of transactions that might miss their deadlines, and compare the performance of validation concurrency control protocol with that of HP2PL(High priority two phase locking) protocol and OCC-TI-WAIT-50(Optimistic concurrency control-time interval-wait-50) protocol under shared-disk architecture by simulation. The simulation results reveal that the protocol the author presented can effectively reduce the number of transactions restarting which might miss their deadlines and performs better than HP2PL and OCC-TI-WAIT-50. It works well when arrival rate of transaction is lesser than threshold. However, due to resource contention the percentage of missing deadline increases sharply when arrival rate is greater than the threshold.

The nonlinear control of simulator of hexapod parallel mechanism

In order to enhance the innervation fidelity of simulators,a nonlinear controller is developed,which guarantees parallel mechanisms closed loop system global asymptotical stability and the convergence of posture tracking error in Cartesian space. The problems of rapid tracking under the condition of the wide range,nonlinear and variable load are solved. After the nonlinear controller is actually applied to the hexapod parallel mechanisms of simulator,the dynamic-static capabilities of motion system are tested by amplitude-frequency response and posture precision. The experimental results show that the static precision improves ten times and system output amplitude increases and the phase lag reduces with respect to the same input signal in Cartesian space in comparison with the traditional proportional and derivative (i.e. PD) controlling method in joint space. Therefore the nonlinear controller can effectively improve the dynamic-static response performance of the hexapod parallel mechanisms of simulators in Cartesian space.