THE STATE SPACE RECONSTRUCTION TECHNOLOGY OF DIFFERENT KINDS OF CHAOTIC DATA OBTAINED FROM DYNAMICAL SYSTEM

Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.

MLP training in a self-organizing state space model using unscented Kalman particle filter

Many Bayesian learning approaches to the multi-layer perceptron （MLP） parameter optimization have been proposed such as the extended Kalman filter （EKF）. This paper uses the unscented Kalman particle filter （UPF） to train the MLP in a self- organizing state space （SOSS） model. This involves forming augmented state vectors consisting of all parameters （the weights of the MLP） and outputs. The UPF is used to sequentially update the true system states and high dimensional parameters that are inherent to the SOSS moder for the MLP simultaneously. Simulation results show that the new method performs better than traditional optimization methods.

Configuration Selection for Reconfigurable Manufacturing Systems by Means of Characteristic State Space

The configuration selection for reconfigurable manufacturing systems（RMS） have been tackled in a number of studies by using analytical or simulation models. The simulation models are usually based on fewer assumptions than the analytical models and therefore are more wildly used in modeling complex RMS. But in the absence of an efficient gradient analysis method of the objective function, it is time-consuming in solving large-scale problems by using a simulation model coupled with a meta-heuristics algorithm. In this paper, a new approach by means of characteristic state space is presented to improve the efficiency of the configuration selection for an RMS. First, a characteristic state equation is set up to represent the input and the output resources of each basic activity in an RMS. A production process model in terms of matrix equations is established by iterating the equations of basic activities according to the resource flows. This model introduces the production process into a characteristic state space for further analysis. Second, the properties of the characteristic state space are presented. On the basis of these properties, the configuration selection in an RMS is considered as a path-planning problem, and the gradient of the objective function is computed. Modified simulated annealing（SA） is also presented, in which neighborhood generation is guided by the gradient to accelerate convergence and reduce the run time of the optimization procedure. Finally, several case studies on the configuration selection for some actual reconfigurable assembly job-shops are presented and compared to the classical SA. The comparison shows relatively positive results. This study provides a more efficient configuration selection approach by using the gradient of the objective function and presents the relevant theories on which it is based.

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.

Application of the state space model to the system of wave energy conversion Analytical method for wave forces on singleoscillating rectangular buoy

A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves.In the method a new analytical expression for the diffraction velocity potential is obtained first by use of theeigenfunction expansion method and then the wave excitation force is calculated by use of the known incident wavepotential and the diffraction potential. Compared with the classical analytical method, it can be seen that the presentmethod is simpler for a two-dimensional problem due to the comparable effort needed for the computation ofdiffraction potential and for that of radiated potential. To verify the correctness of the method, a classical example inthe reference is recomputed and the obtained results are in good accordance with those by use of other methods,which shows that the present method is correct.

Design Criterion for Fixture Layout Based on the State Space Model in M ultistation Assembly Processes

The fixture layout is crucial to assure the product quality in a multistation assembly process （MAP）. A well-designed fixture layout will make the final product＇s variability be insensitive to the fixture variation inputs. As the basis of the fixture layout design, the design criterion plays an important role in the effectiveness of a solution and the optimization efficiency. In this paper, an effective and efficient design criterion is proposed for the fixture layout with a fixed reference point （FRP） in an MAP. First of all, a state space model for the individual port＇s variation propagation and accumulation is developed, which is the mathematical foundation of the proposed criterion. Then, based on this model, a novel design criterion used to evaluate the performance of the fixture layout is proposed for the fixture layout with an FRP. Finally, a method extracted from the proposed design criterion is developed for quick fixture layout design. A four-station assembly process is used to validate the effectiveness and efficiency of the proposed models and methods.

STATIONARY DISTRIBUTIONS OF INFINITE PARTICLE SYSTEMS WITH NONCOMPACT STATE SPACE.

This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4.

State Space Approach to Mass Exchange Network Synthesis

State space approach is an effective method to mass-exchange network (MEN) synthesis. By decomposing the network into two interactive parts, a distribution network and a process operator, the synthesis problem can be formulated into a mixed integer nonlinear programming (MINLP) model. In this article, a generalized state space model based on typical MEN is established and verified in two cases. A new asymmetrical operator and cost index are also adopted to speed up the solution process. The results demonstrate the efficiency of the proposed approach.

Quantum-dot Semiconductor Optical Amplifiers in State Space Model

A state space model(SSM) is derived for quantum-dot semiconductor optical amplifiers(QD-SOAs).Rate equations of QD-SOA are formulated in the form of state update equations,where average occupation probabilities along QD-SOA cavity are considered as state variables of the system.Simulations show that SSM calculates QD-SOA′s static and dynamic characteristics with high accuracy.

A Generalized State Space Average Model for Parallel DC-to-DC Converters

The high potentiality of integrating renewable energies,such as photovoltaic,into a modern electrical microgrid system,using DC-to-DC converters,raises some issues associated with controller loop design and system stability.The generalized state space average model(GSSAM)concept was consequently introduced to design a DC-to-DC converter controller in order to evaluate DC-to-DC converter performance and to conduct stability studies.This paper presents a GSSAM for parallel DC-to-DC converters,namely:buck,boost,and buck-boost converters.The rationale of this study is that modern electrical systems,such as DC networks,hybrid microgrids,and electric ships,are formed by parallel DC-to-DC converters with separate DC input sources.Therefore,this paper proposes a GSSAM for any number of parallel DC-to-DC converters.The proposed GSSAM is validated and investigated in a time-domain simulation environment,namely a MATLAB/SIMULINK.The study compares the steady-state,transient,and oscillatory performance of the state-space average model with a fully detailed switching model.

Variable dimensional state space based global path planning for mobile robot

A variable dimensional state space（VDSS） has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid state space.In VDSS,the lattice state space is only used to construct search space in the local area which is a small circle area near the robot,and grid state space elsewhere.We have tested VDSS with up to 80 indoor and outdoor maps in simulation and on segbot robot platform.Through the simulation and segbot robot experiments,it shows that exploring on VDSS is significantly faster than exploring on lattice state space by Anytime Dynamic A＊（AD＊） planner and VDSS is feasible to be used on robotic systems.

New coordination scheme for multi-robot systems based on state space models

A new coordination scheme for multi-robot systems is proposed. A state space model of the multi- robot system is defined and constructed in which the system＇s initial and goal states are included along with the task definition and the system＇s internal and external constraints. Task accomplishment is considered a transition of the system state in its state space （SS） under the system＇s constraints. Therefore, if there exists a connectable path within reachable area of the SS from the initial state to the goal state, the task is realizable. The optimal strategy for the task realization under constraints is investigated and reached by searching for the optimal state transition trajectory of the robot system in the SS. Moreover, if there is no connectable path, which means the task cannot be performed Successfully, the task could be transformed to be realizable by making the initial state and the goal state connectable and finding a path connecting them in the system＇s SS. This might be done via adjusting the system＇s configuration and/or task constraints. Experiments of multi-robot formation control with obstacles in the environment are conducted and simulation results show the validity of the proposed method.

Discrete state space method and modal extension method based impact sound synthesis model

The efficient and accurate synthesis of physical parameter-controllable impact sounds is essential for sound source identification. In this study, an impact sound synthesis model of a cylinder is proposed based on discrete state space（DSS） method and modal extension method（MEM）. This model is comprised of the whole three processes of the physical interaction, i.e., the Hertz contact process, the transient structural response process, and the sound radiation process. Firstly,the modal expanded DSS equations of the contact system are constructed and the transient structural response of the cylinder is obtained. Then the impact sound of the cylinder is acquired using improved discrete Raleigh integral. Finally, the proposed model is verified by comparing with existing models. The results show that the proposed impact sound synthesis model is more accurate and efficient than the existing methods and easy to be extended to the impact sound synthesis of other structures.

Probe of topological invariants using quantum walks of a trapped ion in coherent state space

We present a protocol to realize topological discrete-time quantum walks,which comprise a sequence of spindependent flipping displacement operations and quantum coin tossing operations,with a single trapped ion.It is demonstrated that the information of bulk topological invariants can be extracted by measuring the average projective phonon number when the walk takes place in coherent state space.Interestingly,the specific chiral symmetry owned by our discrete-time quantum walks simplifies the measuring process.Furthermore,we prove the robustness of such bulk topological invariants by introducing dynamical disorder and decoherence.Our work provides a simple method to measure bulk topological features in discrete-time quantum walks,which can be experimentally realized in the system of single trapped ions.

State space solution to 3D multilayered elastic soils based on order reduction method

Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.

AN ANALYTIC AND APPLICATION TO STATE SPACE RECONSTRUCTION ABOUT CHAOTIC TIME SERIES

The state space, reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: AT. H. Packard, F. Takens, M. Casdagli, J. F. Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time tau were identified. The influence for state space reconstruction of lag time tau was discussed. The result tells us that is a good practical method for state space reconstruction.

Deviation Diagnosis and Analysis of Hull Flat Block Assembly Based on a State Space Model

Dimensional control is one of the most important challenges in the shipbuilding industry. In order to predict assembly dimensional variation in hull flat block construction, a variation stream model based on state space was presented in this paper which can be further applied to accuracy control in shipbuilding. Part accumulative error, locating error, and welding deformation were taken into consideration in this model, and variation propagation mechanisms and the accumulative rule in the assembly process were analyzed. Then, a model was developed to describe the variation propagation throughout the assembly process. Finally, an example of fiat block construction from an actual shipyard was given. The result shows that this method is effective and useful.

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.

State Space Modeling and Implementation of a New Transformer Based Multilevel Inverter Topology with Reduced Switch Count

This paper presents a new transformer based multilevel inverter, with a novel pulse width modulation scheme to achieve seven-level inverter output voltage. The proposed inverter switching pattern consists of three fundamental frequency sinusoidal reference signals with an offset value, and one high frequency triangular carrier signal. This switching scheme has been implemented using an 8-bit Xilinx SPARTAN-3E field programmable gate array based controller. In addition, the state space model of the proposed inverter is developed. The significant features of the proposed topology are: reduction of the power switch count and the gate drive power supply unit, the provision of a galvanic isolation between load and sources by a centre tap transformer. An exhaustive comparison has been made of the existing multilevel inverter topologies and the proposed topology. The performances of the proposed topology with resistive, resistive-inductive loads are simulated in a MATLAB environment and validated experimentally on a laboratory prototype.

Remaining Useful Life Model and Assessment of Mechanical Products: A Brief Review and a Note on the State Space Model Method

The remaining useful life(RUL) prediction of mechanical products has been widely studied for online system performance reliability, device remanufacturing, and product safety(safety awareness and safety improvement). These studies incorporated many di erent models, algorithms, and techniques for modeling and assessment. In this paper, methods of RUL assessment are summarized and expounded upon using two major methods: physics model based and data driven based methods. The advantages and disadvantages of each of these methods are deliberated and compared as well. Due to the intricacy of failure mechanism in system, and di culty in physics degradation observation, RUL assessment based on observations of performance variables turns into a science in evaluating the degradation. A modeling method from control systems, the state space model(SSM), as a first order hidden Markov, is presented. In the context of non-linear and non-Gaussian systems, the SSM methodology is capable of performing remaining life assessment by using Bayesian estimation(sequential Monte Carlo). Being e ective for non-linear and non-Gaussian dynamics, the methodology can perform the assessment recursively online for applications in CBM(condition based maintenance), PHM(prognostics and health management), remanufacturing, and system performance reliability. Finally, the discussion raises concerns regarding online sensing data for SSM modeling and assessment of RUL.