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.

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.

Compressive Measurement Identification of Linear Time-Invariant System Application in DC Motor

In traditional system identification (SI), actual values of system parameters are concealed in the input and output data;hence, it is necessary to apply estimation methods to determine the parameters. In signal processing, a signal with N elements must be sampled at least N times. Thus, most SI methods use N or more sample data to identify a model with N parameters;however, this can be improved by a new sampling theory called compressive sensing (CS). Based on CS, an SI method called compressive measurement identification (CMI) is proposed for reducing the data needed for estimation, by measuring the parameters using a series of linear measurements, rather than the measurements in sequence. In addition, the accuracy of the measurement process is guaranteed by a criterion called the restrict isometric principle. Simulations demonstrate the accuracy and robustness of CMI in an underdetermined case. Further, the dynamic process of a DC motor is identified experimentally, establishing that CMI can shorten the identification process and increase the prediction accuracy.

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).

A Model-free Approach to Fault Detection of Continuous-time Systems Based on Time Domain Data

In this paper, a model-free approach is presented to design an observer-based fault detection system of linear continuoustime systems based on input and output data in the time domain. The core of the approach is to directly identify parameters of the observer-based residual generator based on a numerically reliable data equation obtained by filtering and sampling the input and output signals.

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.

COMPREHENSIVE DAMPING COEFFICIENT——A NEW DEFINITION TO DAMPING EFFECT OF LINEAR TIME-INVARIANT SYSTEMS

A new concept is presented to express the damping property of linear time-invariant systems, by the Lyapunov theorem in view of quadratic form-defined energy. Two definitions are introduced: damping energy function D（X0, X）=Ci∫x0, x xidxi-1and comprehensive damping coefficient η-min(Ci/an-i). It is concluded that （ⅰ） of the Hurwitz determinants, △x-1 is proportional to the damping effect of oscillating systems, （ⅱ） the comprehensive damping coefficients of linear time-invariant systems are derived as. piecewise rational fractions which can be easily calculated and （ⅲ） the damping torque coefficient obtained for synchronous machines is independent of ω.

Improved algebraic method for linear continuous-time model identification

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.

QUALITATIVE BEHAVIORS OF LINEAR TIME-INVARIANT DYNAMIC EQUATIONS ON TIME SCALES

We investigate the type of singularity and qualitative structure of solutions to a time-invariant linear dynamic system on time scales. The results truly unify the qualitative behaviors of the system on the continuous and discrete times with any step size.

Eigenstructure Assignment Method and Its Applications to the Constrained Problem

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.

An overview on the designs of distributed observers in LTI multi-agent systems

With the rapid development of information technologies and cloud computing, sensor networks play an increasingly important role in our society. Over the past few decades, distributed observer theory has attracted unprecedented attention due to its wide potential applications in different areas. Meanwhile, various approaches and algorithms have been proposed and investigated. The design of distributed observers is one of the frontier topics of system and control research, which has the significant theoretical values and broad application prospects. This paper attempts to review the representative models and the corresponding approaches for distributed observer design in linear time-invariant(LTI) systems. Firstly, the research backgrounds and main advances of distributed observer designs are briefly reviewed. Then, recent results of distributed observer designs for discrete-time and continuous-time LTI multi-agent systems(MASs) are introduced in detail, respectively. Finally, the prospects and the future work directions of the design of distributed observers are put forward. The main purpose of this paper is to promote the emerging topic on the designs of distributed observers, with focuses on the interdisciplinary interest from technological sciences.

DISTURBANCE ATTENUATION VIA STATE-FEEDBACK CONTROLLERS

This paper focuses on the H optimal control problem in which the wholestate is available for feedback. We show that in attenuating the disturbance, the Hoptimal performance of dynamic state-feedback is no better than that of static state-feedback, which generalizes current results for linear time-invariant systems with no directtransmission from the disturbance and control input to the controlled output.

IDENTIFICATION OF TIME-VARIANT CONTINUOUS SYSTEM BY A QUASI-NEWTON METHOD

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.

LS-Based Parameter Estimation of DARMA Systems with Uniformly Quantized Observations

This paper is concerned with the parameter estimation of deterministic autoregressive moving average(DARMA)systems with quantization data.The estimation algorithms adopted here are the least squares(LS)and the forgetting factor LS,and the signal quantizer is of uniform,that is,with uniform quantization error.The authors analyse the properties of the LS and the forgetting factor LS,and establish the boundedness of the estimation errors and a relationship of the estimation errors with the size of quantization error,which implies that the smaller the quantization error is,the smaller the estimation error is.A numerical example is given to demonstrate theorems.