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...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.展开更多
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-tim...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.展开更多
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 ...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).展开更多
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 establ...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.展开更多
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 ...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.展开更多
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 compre...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.展开更多
Recently a novel algebraic method was proposed for linear continuous-time model identification,which has attracted extensive attention in the literature.This work reveals its connection to classic identification metho...Recently a novel algebraic method was proposed for linear continuous-time model identification,which has attracted extensive attention in the literature.This work reveals its connection to classic identification methods,discusses a limitation and presents a useful modification of the method.The discussions are supported by analysis and numerical experiments.展开更多
A partial eigenstructure assignment method that keeps the open-loop stable eigenvalues and the corresponding eigenspace unchanged is presented. This method generalizes a large class of systems previous methods and can...A partial eigenstructure assignment method that keeps the open-loop stable eigenvalues and the corresponding eigenspace unchanged is presented. This method generalizes a large class of systems previous methods and can be applied to solve the constrained control problem for linear invariant continuous-time systems. Besides, it can be also applied to make a total eigenstructure assignment. Indeed, the problem of finding a stabilizing regulator matrix gain taking into account the asymmetrical control constraints is transformed to a Sylvester equation resolution. Examples are given to illustrate the obtained results.展开更多
A quasi-Newton method (QNM) for solving an unconstrained optimization problem in infinite dimensional spaces is presented in this paper. We apply the QNM algorithm to an identification problem for a nonlinear system o...A quasi-Newton method (QNM) for solving an unconstrained optimization problem in infinite dimensional spaces is presented in this paper. We apply the QNM algorithm to an identification problem for a nonlinear system of differential equations, that is, to identify the parameter vector q = q(t) appearing in the following system of differential equations, based on the measurement of the state , where is a measurement operator. We give two examples to show the algorithm.展开更多
This work presents a PAM4 receiver analog frontend(AFE)operating up to 64 Gb/s.The electronic integrated circuit(EIC)is fabricated in 40-nm CMOS technology.This AFE is composed of a single-stage Continuous-Time Linear...This work presents a PAM4 receiver analog frontend(AFE)operating up to 64 Gb/s.The electronic integrated circuit(EIC)is fabricated in 40-nm CMOS technology.This AFE is composed of a single-stage Continuous-Time Linear Equalizer(CTLE),a Variable Gain Amplifier(VGA),an input impedance matching network,a buffer stage,and an output buffer.The single-stage triple-peaking CTLE proposed employs current reuse technique and a multi-feedback structure,enabling the adjustment of peaking in the low,mid,and high-frequency bands.Thus,only one-stage CTLE is sufficient to achieve an over-20-dB boost at Nyquist frequency to save power.The VGA adopts an enhanced structure based on the Gilbert cell,where the gain is manipulated by controlling the gate voltage of MOS transistors.The CTLE undergoes variations in its DC gain during the adjustment process to equalize channel losses.The role of the VGA is to stable the DC gain changes induced by the adjustment of the CTLE.The output buffer adopts two stages,aiming to ensure that the gain does not attenuate excessively while maintaining output impedance matching.The AFE consumes 21.1 mW with a supply voltage of 1.5/1 V.It can provide a maximum boost of 22.5 dB,and the data rate reaches up to 64 Gb/s.Additionally,it features peaking adjustment capabilities in the low,mid,and high-frequency bands.Finally,the measurement demonstrates its ability to effectively equalize a channel with a 12-dB loss at the Nyquist frequency of 16 GHz.展开更多
基金supported in part by the National Key Research and Development Program of China(2018AAA0101502,2018YFB1702300)the National Natural Science Foundation of China(61722312,61533019,U1811463,61533017)。
文摘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.
文摘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.
文摘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).
文摘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.
基金Support by Ontario Research FoundationMc Master Advanced Control ConsortiumFundacao para a Ciência e Tecnologia(Investigador FCT 2013 program and project UID/MAT/04561/2013)
文摘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.
基金supported by the Major Key Project of Peng Cheng Laboratory under Grant No.PCL2023AS1-2Project funded by China Postdoctoral Science Foundation under Grant Nos.2022M722926 and2023T160605。
文摘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.
基金This work was supported in part by NTU[startup grant number M4080181.050]MOE AcRF[Tier 1 grant number RG 33/10 M4010492.050].
文摘Recently a novel algebraic method was proposed for linear continuous-time model identification,which has attracted extensive attention in the literature.This work reveals its connection to classic identification methods,discusses a limitation and presents a useful modification of the method.The discussions are supported by analysis and numerical experiments.
文摘A partial eigenstructure assignment method that keeps the open-loop stable eigenvalues and the corresponding eigenspace unchanged is presented. This method generalizes a large class of systems previous methods and can be applied to solve the constrained control problem for linear invariant continuous-time systems. Besides, it can be also applied to make a total eigenstructure assignment. Indeed, the problem of finding a stabilizing regulator matrix gain taking into account the asymmetrical control constraints is transformed to a Sylvester equation resolution. Examples are given to illustrate the obtained results.
基金This research is partially supported by the National Natural Science Foundation of China(No. 69774012).
文摘A quasi-Newton method (QNM) for solving an unconstrained optimization problem in infinite dimensional spaces is presented in this paper. We apply the QNM algorithm to an identification problem for a nonlinear system of differential equations, that is, to identify the parameter vector q = q(t) appearing in the following system of differential equations, based on the measurement of the state , where is a measurement operator. We give two examples to show the algorithm.
基金supported by the National Natural Science Foundation of China under Grant 62222409 and Grant 62174153.
文摘This work presents a PAM4 receiver analog frontend(AFE)operating up to 64 Gb/s.The electronic integrated circuit(EIC)is fabricated in 40-nm CMOS technology.This AFE is composed of a single-stage Continuous-Time Linear Equalizer(CTLE),a Variable Gain Amplifier(VGA),an input impedance matching network,a buffer stage,and an output buffer.The single-stage triple-peaking CTLE proposed employs current reuse technique and a multi-feedback structure,enabling the adjustment of peaking in the low,mid,and high-frequency bands.Thus,only one-stage CTLE is sufficient to achieve an over-20-dB boost at Nyquist frequency to save power.The VGA adopts an enhanced structure based on the Gilbert cell,where the gain is manipulated by controlling the gate voltage of MOS transistors.The CTLE undergoes variations in its DC gain during the adjustment process to equalize channel losses.The role of the VGA is to stable the DC gain changes induced by the adjustment of the CTLE.The output buffer adopts two stages,aiming to ensure that the gain does not attenuate excessively while maintaining output impedance matching.The AFE consumes 21.1 mW with a supply voltage of 1.5/1 V.It can provide a maximum boost of 22.5 dB,and the data rate reaches up to 64 Gb/s.Additionally,it features peaking adjustment capabilities in the low,mid,and high-frequency bands.Finally,the measurement demonstrates its ability to effectively equalize a channel with a 12-dB loss at the Nyquist frequency of 16 GHz.
