Quasi Controlled K-Metric Spaces over C^(*)-Algebras with an Application to Stochastic Integral Equations

Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.

Research on the principle of space high-precision temperature control system of liquid crystals based Stokes polarimeter

The magnetic field is one of the most important parameters in solar physics,and a polarimeter is the key device to measure the solar magnetic field.Liquid crystals based Stokes polarimeter is a novel technology,and will be applied for magnetic field measurement in the first space-based solar observatory satellite developed by China,Advanced Space-based Solar Observatory.However,the liquid crystals based Stokes polarimeter in space is not a mature technology.Therefore,it is of great scientific significance to study the control method and characteristics of the device.The retardation produced by a liquid crystal variable retarder is sensitive to the temperature,and the retardation changes 0.09°per 0.10℃.The error in polarization measurement caused by this change is 0.016,which affects the accuracy of magnetic field measurement.In order to ensure the stability of its performance,this paper proposes a high-precision temperature control system for liquid crystals based Stokes polarimeter in space.In order to optimize the structure design and temperature control system,the temperature field of liquid crystals based Stokes polarimeter is analyzed by the finite element method,and the influence of light on the temperature field of the liquid crystal variable retarder is analyzed theoretically.By analyzing the principle of highprecision temperature measurement in space,a high-precision temperature measurement circuit based on integrated operational amplifier,programmable amplifier and 12 bit A/D is designed,and a high-precision space temperature control system is developed by applying the integral separation PI temperature control algorithm and PWM driving heating films.The experimental results show that the effect of temperature control is accurate and stable,whenever the liquid crystals based Stokes polarimeter is either in the air or vacuum.The temperature stability is within±0.0150℃,which demonstrates greatly improved stability for the liquid crystals based Stokes polarimeter.

Establishing formal state space models via quantization forquantum control systems

Formal state space models of quantum control systems are deduced and a scheme to establish formal state space models via quantization could been obtained for quantum control systems is proposed. State evolution of quantum control systems must accord with Schrdinger equations, so it is foremost to obtain Hamiltonian operators of systems. There are corresponding relations between operators of quantum systems and corresponding physical quantities of classical systems, such as momentum, energy and Hamiltonian, so Schrdinger equation models of corresponding quantum control systems via quantization could been obtained from classical control systems, and then establish formal state space models through the suitable transformation from Schrdinger equations for these quantum control systems. This method provides a new kind of path for modeling in quantum control.

STUDY ON DYNAMICS, STABILITY AND CONTROL OF MULTI-BODY FLEXIBLE STRUCTURE SYSTEM IN FUNCTIONAL SPACE

The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern Mathematics. First, the dynamical control model of the distributed parameter system with multi-body flexible and multi-topological structure was established which has damping, gyroscopic parts and constrained damping. Secondly, the necessary and sufficient condition of controllability and observability, the stability theory and asymptotic property of the system were obtained. These results expand the theory of the field about the dynamics and control of the system with multi-body flexible structure, and have important engineering significance.

Research on Fault-Tolerant Control System for Space Modular Manipulator System

This paper studies a fault-tolerant control system for a space modular manipulator system mounted on space station or other spacecrafts such as satellites, located in low earth orbit. Design technologies for traditional industrial manipulator systems cannot be directly used to the space ones due to the special space environment and compactness. Considering the extremely tight constraints on mass, power consumption, volume, cost and ＂design-to-orbit＂ schedules, the fault-tolerant control system is developed mainly based on commercial-off-the-shaft components. The features of the hardware and software of the fault-tolerant control system are presented. The performance specifications are also discussed. Because many space proven design technologies and experiences are adopted, the fault-tolerant control system is characterized by high reliability and practicability.

Perturbation and robust controllability of singular distributed parameter control systems in Hilbert space

Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained, in which the controllability for singular distributed parameter control system is not destroyed, if we perturb the equation by small bounded linear operator.

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper,we study the Noether-form invariance of nonholonomic mechanical controllable systems inphase space.Equations of motion of the controllable mechanical systems in phase space are presented.The definitionand the criterion for this system are presented.A new conserved quantity and the Noether conserved quantity deducedfrom the Noether-form invariance are obtained.An example is given to illustrate the application of the results.

Solution Domain Boundary Analysis Method and Its Application in Parameter Spaces of Nonlinear Gear System

Mastering the influence laws of parameters on the solution structure of nonlinear systems is the basis of carrying out vibration isolation and control.Many researches on solution structure and bifurcation phenomenon in parameter spaces are carried out broadly in many fields,and the research on nonlinear gear systems has attracted the attention of many scholars.But there is little study on the solution domain boundary of nonlinear gear systems.For a periodic non-autonomous nonlinear dynamic system with several control parameters,a solution domain boundary analysis method of nonlinear systems in parameter spaces is proposed,which combines the cell mapping method based on Poincaré point mapping in phase spaces with the domain decomposition technique of parameter spaces.The cell mapping is known as a global analysis method to analyze the global behavior of a nonlinear dynamic system with finite dimensions,and the basic idea of domain decomposition techniques is to divide and rule.The method is applied to analyze the solution domain boundaries in parameter spaces of a nonlinear gear system.The distribution of different period domains,chaos domain and the domain boundaries between different period domains and chaotic domain are obtained in control parameter spaces constituted by meshing damping ratio with excitation frequency,fluctuation coefficient of meshing stiffness and average exciting force respectively by calculation.The calculation results show that as the meshing damping increases,the responses of the system change towards a single motion,while the variations of the excitation frequency,meshing stiffness and exciting force make the solution domain presenting diversity.The proposed research contribution provides evidence for vibration control and parameter design of the gear system,and confirms the validity of the solution domain boundary analysis method.

Advances in dynamics and control of tethered satellite systems

The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. Over the past decades, this exciting topic has attracted significant attention from many researchers and gained a vast number of analytical, numerical and experimental achievements with a focus on the two essential aspects of both dynamics and control. This review article presents the historic background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements.

Inverse Optimal Control of Evolution Systems and Its Application to Extensible and Shearable Slender Beams

An optimal(practical) stabilization problem is formulated in an inverse approach and solved for nonlinear evolution systems in Hilbert spaces. The optimal control design ensures global well-posedness and global practical K∞-exponential stability of the closed-loop system, minimizes a cost functional,which appropriately penalizes both state and control in the sense that it is positive definite(and radially unbounded) in the state and control, without having to solve a Hamilton-Jacobi-Belman equation(HJBE). The Lyapunov functional used in the control design explicitly solves a family of HJBEs. The results are applied to design inverse optimal boundary stabilization control laws for extensible and shearable slender beams governed by fully nonlinear partial differential equations.

Joint space compliance control for a hydraulic quadruped robot based on force feedback

In the realm of quadruped robot locomotion,compliance control is imperative to handle impacts when negotiating unstructured terrains.At the same time,kinematic tracking accuracy should be guaranteed during locomotion.To meet both demands,ajoint space compliance controller is designed,so that compliance can be achieved in stance phase while position tracking performance can be guaranteed in swing phase.Unlike operational space compliance control,the joint space compliance control method is easy to implement and does not depend on robot dynamics.As for each joint actuator,high performance force control is of great importance for compliance design.Therefore,a nonlinear PI controller based on feedback linearization is proposed for the hydraulic actuator force control.Besides,an outer position loop（compliance loop）is closed for each joint.Experiments are carried out to verify the force controller and compliance of the hydraulic actuator.The robot leg compliance is assessed by a virtual prototyping simulation.

The Formation Control of Multi-agent Systems on a Circle

This paper investigates the formation control of a class of multi-agent systems moving on a circle, whose topology is a cyclic graph, and presents several new results for the following two cases: Case I, the agents with single-integrator kinematics,and Case II, the agents with double-integrator kinematics. Firstly,for Case I, two control protocols are proposed under which the multiagent systems keep a uniformly-spaced formation. Secondly,we study Case II, and a control protocol is designed for this case, then the stability of the formation is proved. Finally, three simulations are studied by using our presented results. The study of illustrative examples with simulations shows that our results as well as designed control protocols work very well in studying the formation control of this class of multi-agent systems.

Scaling the Microphysics Equations and Analyzing the Variability of Hydrometeor Production Rates in a Controlled Parameter Space

A set of microphysics equations is scaled based on the convective length and velocity scales. Comparisons are made among the dynamical transport and various microphysical processes. From the scaling analysis, it becomes apparent which parameterized microphysical processes present off-scaled influences in the integration of the set of microphysics equations. The variabilities of the parameterized microphysical processes are also studied using the approach of a controlled parameter space. Given macroscopic dynamic and thermodynamic conditions in different regions of convective storms, it is possible to analyze and compare vertical profiles of these processes. Bulk diabatic heating profiles for a cumulus convective updraft and downdraft are also derived from this analysis. From the two different angles, the scale analysis and the controlled-parameter space approach can both provide an insight into and an understanding of microphysics parameterizations.

Power Control Based on State Space Strategies for Grid⁃Oriented Inverters with LCL Filters

Through a third⁃order mathematical model of grid⁃oriented LCL⁃type converters,this paper analyzes the complicated dynamic characteristics and resonance problems which may influence the system stability.To realize active damping for LCL filters and improve dynamic performance of current regulators,a state space current PI controller is proposed whose parameters can be tuned based on the polynomial equations approach.An extended state observer is integrated with the regulation scheme,where additional sensors are not necessary in contrast with conventional active damping strategies.Synchronous reference frame PLL(SRF⁃PLL)equipped with filter technology is proposed for grid voltage disturbance suppression.This method is then applied to establish a double⁃closed⁃loop power regulator that demonstrates improved performance compared with other controllers.The simulation results are displayed to illustrate the efficiency of the regulation methods.

Control Planning Strategy of Urban Ecological Space Under the Background of Stock Renewal:A Case Study of Beautiful Landscape Planning of Yongchuan District,Chongqing

Under the traditional mode of"incremental"development,urban development has bred urban problems such as lack of land resources,unbalanced distribution of public space,over development of land use,etc.The concept of"stock renewal"is that the construction and development of a city changes from"extensive"construction to"refined"urban construction and management mode.Taking Yongchuan District’s regulatory detailed planning as an example,based on the concept of stock renewal as the guiding ideology of urban control planning,this study made corresponding strategies for the control planning of Yongchuan District’s mountain,water system,green space system,etc.On the basis of the problems of mountain encroachment,water bank erosion,lack of green space and safeguard mechanism,the protection and utilization planning of mountain,water and green were put forward,and safeguard mechanism in the process of planning and implementation was established,so as to provide specific guidance for the construction of Yongchuan central urban area,with a view to providing reference for the preparation and implementation of relevant regulatory detailed planning.

DECENTRALIZED ROBUST CONTROL FOR UNCERTAIN FLEXIBLE SPACE STATION

A decentralized variable-structure robust control technique for uncertain large-scale systems is proposed and using the proposed technique. a decentralized robust control system for uncertain flexible space station is designed. The designed robust control system can guarantee the stability and safe operation of space station in a wide range of system parameters variations and highly intensive external disturbances. In addition. because decentralized adaptation laws for the upper bounds of system uncertainties are introduced, the control technique is particularly applicable to the uncertain flexible space station with complex structure whose bounds of system uncertainties can not be determined or vary with time.

Design of Mechanical Smoke Exhaust System in Large Space of Convention Center

The volumetric flow rate of smoke generated from the fire in large space often reaches to hundreds of thousands CMH because of extended floor height and as it’s more difficult to isolate the smoke to the limited area, comparing to normal-scale building, design and operation of effective smoke control system for large space is more than important. In this study, with the analysis model for such a large space as exhibition hall or conference room in conventional center, design of mechanical smoke exhaust system was conducted based on currently-available design standard which was then followed by numerical analysis of the design using 3D numerical analysis method. For conference room at 2.0 MW heat release rate, 99,173 CMH flow rate is required, if smoke layer is maintained at 60% of the floor height and for exhibition hall at 8.8 MW with 80% of floor height, flow rate required is 219,802 CMH, which are incorporated into the design. In view of 3D numerical analysis, accuracy of the design according to algebraic expression is sufficient.

Experimental Study on Indoor Thermal Stratification in Large Space by under Floor Air Distribution System (UFAD) in Summer

A ventilation method of down-supply up-return has grown popular in large space in recent years for comfort ventilation with low thermal load, especially in China, including gymnasium, factory space, and exhibition hall, etc. The undisturbed flow pattern in the space gives a gradient in temperature, and the vertical thermal stratification appears markedly in large space. The object for this paper is to understand the behaviour of an under floor air distribution system in a ventilated space. The thermal stratification characteristics in a real UFAD experimental space were measured. The effects of different supply conditions on the thermal stratification characteristics are investigated based on the experimental results. The relations between space air stratification and the control parameter is predicted. It can be indicated that there are 4 zones composing the vertical thermal stratification. And different zone has different control parameter.

Design of Wiener-Hopf optimal controller and its application in terrain following system

state space algorithms are proposed for the three degree of freedom (3DOF) optimal Wiener Hopf controller for a class of systems with time delay feedback sensors and employed in the design of a terrain following control system, with the influence caused by the delay of baric altimeter successfully eliminated.

Angular Position Controller and Its Design Model Verification for the Electro-Hydraulic Servo Control System

The angular position controller is system （EHSAS） to control the output of the rotary applied to electro-hydraulic servo actuator actuator. It works as a compensator based on the frequency response of the EHSAS. Its design model is verified on the state-space model of EHSAS by using simulation program SIMULINK. Real data used to test the system. Simulation results give a good agreement for the controller and also for the state-space model.