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.

Impact of correlated private signals on continuous-time insider trading

A model of continuous-time insider trading in which a risk-neutral in-sider possesses two imperfect correlated signals of a risky asset is studied.By conditional expectation theory and filtering theory,we first establish three lemmas:normal corre-lation,equivalent pricing and equivalent profit,which can guarantee to turn our model into a model with insider knowing full information.Then we investigate the impact of the two correlated signals on the market equilibrium consisting of optimal insider trading strategy and semi-strong pricing rule.It shows that in the equilibrium,(1)the market depth is constant over time;(2)if the two noisy signals are not linerly correlated,then all private information of the insider is incorporated into prices in the end while the whole information on the asset value can not incorporated into prices in the end;(3)if the two noisy signals are linear correlated such that the insider can infer the whole information of the asset value,then our model turns into a model with insider knowing full information;(4)if the two noisy signals are the same then the total ex ant profit of the insider is increasing with the noise decreasing,while down to O as the noise going up to infinity;(5)if the two noisy signals are not linear correlated then with one noisy signal fixed,the total ex ante profit of the insider is single-peaked with a unique minimum with respect to the other noisy signal value,and furthermore as the noisy value going to O it gets its maximum,the profit in the case that the real value is observed.

Perturbation Analysis of Continuous-Time Linear Time-Invariant Systems

In this paper, we consider the perturbation analysis of linear time-invariant systems, which arise from the linear optimal control in continuous-time. We provide a method to compute condition numbers of continuous-time linear time-invariant systems. It solves the perturbed linear time-invariant systems via Riccati differential equations and continuous-time algebraic Riccati equations in finite and infinite time horizons. We derive the explicit expressions of measuring the perturbation bounds of condition numbers with respect to the solution of the linear time-invariant systems. Furthermore, condition numbers and their upper bounds of Riccati differential equations and continuous-time algebraic Riccati equations are also discussed. Numerical simulations show the sharpness of the perturbation bounds computed via the proposed methods.

Chaos Synchronization of Nonlinear Bloch Equations Based on Input-to-State Stable Control

In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.

Robust Linear Regression Models:Use of a Stable Distribution for the Response Data

In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.

Estimating distribution of water uptake with depth of winter wheat by hydrogen and oxygen stable isotopes under different irrigation depths

Crop root system plays an important role in the water cycle of the soil-plant-atmosphere continuum. In this study, com- bined isotope techniques, root length density and root cell activity analysis were used to investigate the root water uptake mechanisms of winter wheat （Triticum aesfivum L.） under different irrigation depths in the North China Plain. Both direct inference approach and multisource linear mixing model were applied to estimate the distribution of water uptake with depth in six growing stages. Results showed that winter wheat under land surface irrigation treatment （Ts） mainly absorbed water from 10-20 cm soil layers in the wintering and green stages （66.9 and 72.0%, respectively）; 0-20 cm （57.0%） in the jointing stage; 0-40 （15.3%） and 80-180 cm （58.1%） in the heading stage; 60-80 （13.2%） and 180-220 cm （35.5%） in the filling stage; and 0-40 （46.8%） and 80-100 cm （31.0%） in the ripening stage. Winter wheat under whole soil layers irrigation treatment （Tw） absorbed more water from deep soil layer than Ts in heading, filling and ripening stages. Moreover, root cell activity and root length density of winter wheat under TW were significantly greater than that of Ts in the three stages. We concluded that distribution of water uptake with depth was affected by the availability of water sources, the root length density and root cell activity. Implementation of the whole soil layers irrigation method can affect root system distribution and thereby increase water use from deeper soil and enhance water use efficiency.

On the Stable Method Computing Values of Unbounded Operators

Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.

On use of the alpha stable self-similar stochastic process to model aggregated VBR video traffic

The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated VBR video traffic is made. Different methods to estimate stability parameter a and self-similar parameter H are compared. Processes to generate the linear fractional stable noise （LFSN） and the alpha stable random variables are provided. Model construction and the quantitative comparisons with fractional Brown motion （FBM） and real traffic are also examined. Open problems and future directions are also given with thoughtful discussions.

Hybrid Continuous-Time MILP Model for Crude Oil Scheduling under the Influence of High Tides

Vessels,especially very large or ultra large crude carriers(VLCCs or ULCCs),often can only dock and leave the berth during high tide periods to prevent being stranded.Unfortunately,the current crude scheduling models do not take into account tidal conditions,which will seriously affect the feasibility of crude schedule.So we first focus on the docking and leaving operations under the tidal actions,and establish a new hybrid continuous-time mixed integer linear programming(MILP)model which incorporates global event based formulation and unit-specific event based formulation.Upon considering that the multiple blending of crude oil can easily cause the production fluctuating,there are some reasonable assumptions that storage tanks can only store pure crude,and charging tanks just can be refilled after being emptied,which helps us obtain a simple MILP model without composition discrepancy caused by crude blending.Two cases are used to demonstrate the efficacy of proposed scheduling model.The results show that the optimization schedule can minimize the demurrage of the vessels and the number of feeding changeovers of crude oil distillation units(CDUs).

Comparison of isotope-based linear and Bayesian mixing models in determining moisture recycling ratio

Stable water isotopes are natural tracers quantifying the contribution of moisture recycling to local precipitation,i.e.,the moisture recycling ratio,but various isotope-based models usually lead to different results,which affects the accuracy of local moisture recycling.In this study,a total of 18 stations from four typical areas in China were selected to compare the performance of isotope-based linear and Bayesian mixing models and to determine local moisture recycling ratio.Among the three vapor sources including advection,transpiration,and surface evaporation,the advection vapor usually played a dominant role,and the contribution of surface evaporation was less than that of transpiration.When the abnormal values were ignored,the arithmetic averages of differences between isotope-based linear and the Bayesian mixing models were 0.9%for transpiration,0.2%for surface evaporation,and–1.1%for advection,respectively,and the medians were 0.5%,0.2%,and–0.8%,respectively.The importance of transpiration was slightly less for most cases when the Bayesian mixing model was applied,and the contribution of advection was relatively larger.The Bayesian mixing model was found to perform better in determining an efficient solution since linear model sometimes resulted in negative contribution ratios.Sensitivity test with two isotope scenarios indicated that the Bayesian model had a relatively low sensitivity to the changes in isotope input,and it was important to accurately estimate the isotopes in precipitation vapor.Generally,the Bayesian mixing model should be recommended instead of a linear model.The findings are useful for understanding the performance of isotope-based linear and Bayesian mixing models under various climate backgrounds.

Quantization and Stable Attractors in a DissipativeOrbital Motion

We present a method for determining the motion of an electron in a hydrogen atom, which starts from a field Lagrangean foundation for non-conservative systems that can exhibit chaotic behavior. As a consequence, the problem of the formation of the atom becomes the problem of finding the possible stable orbital attractors and the associated transition paths through which the electron mechanical energy varies continuously until a stable energy state is reached.

SOLVERS FOR SYSTEMS OF LARGE SPARSE LINEAR AND NONLINEAR EQUATIONS BASED ON MULTI-GPUS

Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications.So,practical solvers for systems of linear and nonlinear equations based on multi graphic process units（GPUs）are proposed in order to accelerate the solving process.In the linear and nonlinear solvers,the preconditioned bi-conjugate gradient stable（PBi-CGstab）method and the Inexact Newton method are used to achieve the fast and stable convergence behavior.Multi-GPUs are utilized to obtain more data storage that large size problems need.

Compressed Least Squares Algorithm of Continuous-Time Linear Stochastic Regression Model Using Sampling Data

In this paper,the authors consider a sparse parameter estimation problem in continuoustime linear stochastic regression models using sampling data.Based on the compressed sensing(CS)method,the authors propose a compressed least squares(LS) algorithm to deal with the challenges of parameter sparsity.At each sampling time instant,the proposed compressed LS algorithm first compresses the original high-dimensional regressor using a sensing matrix and obtains a low-dimensional LS estimate for the compressed unknown parameter.Then,the original high-dimensional sparse unknown parameter is recovered by a reconstruction method.By introducing a compressed excitation assumption and employing stochastic Lyapunov function and martingale estimate methods,the authors establish the performance analysis of the compressed LS algorithm under the condition on the sampling time interval without using independence or stationarity conditions on the system signals.At last,a simulation example is provided to verify the theoretical results by comparing the standard and the compressed LS algorithms for estimating a high-dimensional sparse unknown parameter.

Exponential passive filtering for a class of nonlinear jump systems

The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.

Alternating segment explicit-implicit scheme for nonlinear third-order KdV equation

A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.

Global Optimization of Nonlinear Blend-Scheduling Problems

The scheduling of gasoline-blending operations is an important problem in the oil refining industry. Thisproblem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but alsonon-convex nonlinear behavior, due to the blending of various materials with different quality properties.In this work, a global optimization algorithm is proposed to solve a previously published continuous-timemixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimi-zation, the distribution problem, and several important operational features and constraints. The algorithmemploys piecewise McCormick relaxation （PMCR） and normalized multiparametric disaggregation tech-nique （NMDT） to compute estimates of the global optimum. These techniques partition the domain of oneof the variables in a bilinear term and generate convex relaxations for each partition. By increasing the num-ber of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates ofthe global solution. The algorithm is compared to two commercial global solvers and two heuristic methodsby solving four examples from the literature. Results show that the proposed global optimization algorithmperforms on par with commercial solvers but is not as fast as heuristic approaches.

Observer design for matrix second-order linear systems: a parametric approach

The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.

Robust Stabilization for Uncertain Linear Delay Markow Jump System

Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem of jump linear delay system with umcerratnty was studied. By using of linear matrix inequalities, the existence conditions of robust stabilizing and the state feedback controller designing methods are also presented and proved. Finally, an illustrated example shows the effectiveness of this approach.

Geometric representation for numerical stability region of linear multistep methods

Studies the numerical stability region of linear multistep(LM) methods applied to linear test equation of the form y′(t)=ay(t)+by(t-1), t>0, y(t)=g(t)-1≤t≤0, a,b∈R, proves through delay dependent stability analysis that the intersection of stability regions of the equation and the method is not empty, in addition to approaches to the boundary of the delay differential equation(DDEs) in the limiting case of step size boundary of the stability region of linear multistep methods.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.