Identification of linear continuous-time system using wavelet modulating filters

An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filters have been analyzed. Using linear modulating filters, we can obtain an identification model that is parameterized directly in continuous-time model parameters. By applying the results from discrete-time model identification to the obtained identification model, a continuous-time estimation method is developed. Considering the accuracy of parameter estimates, an instrumental variable (Ⅳ) method is proposed, and the design of modulating integral filter is discussed. The relationship between the accuracy of identification and the parameter of modulating filter is investigated, and some points about designing Gaussian wavelet modulating function are outlined. Finally, a simulation study is also included to verify the theoretical results.

Continuous-time System Identification with Nuclear Norm Minimization and GPMF-based Subspace Method

To improve the accuracy and effectiveness of continuous-time(CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization(NNM) with the generalized Poisson moment functional(GPMF)based subspace method. The GPMF algorithm provides a simple linear mapping for subspace identification without the timederivatives of the input and output measurements to avoid amplification of measurement noise, and the NNM is a heuristic convex relaxation of the rank minimization. The Hankel matrix with minimized nuclear norm is used to determine the model order and to avoid the over-parameterization in subspace identification method(SIM). Furthermore, the algorithm to solve the NNM problem in CT case is also deduced with alternating direction methods of multipliers(ADMM). Lastly, two numerical examples are presented to evaluate the performance of the proposed method and to show the advantages of the proposed method over the existing methods.

Enhanced LMI Representations for H2 Performance of Polytopic Uncertain Systems: Continuous-time Case

Based on two recent results, several new criteria of H2 performance for continuous-time linear systems are established by introducing two slack matrices. When used in robust analysis of systems with polytopic uncertainties, they can reduce conservatism inherent in the earlier quadratic method and the established parameter-dependent Lyapunov function approach. Two numerical examples are included to illustrate the feasibility and advantage of the proposed representations.

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.

RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT

This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.

Continuous-time chaotic systems: Arbitrary full-state hybrid projective synchronization via a scalar signal

Relerrlng to contlnuous-Ume claaotlc systems, tills paper presents a new projective syncnromzatlon scheme, wnlcn enables each drive system state to be synchronized with a linear combination of response system states for any arbitrary scaling matrix. The proposed method, based on a structural condition related to the uncontrollable eigenvalues of the error system, can be applied to a wide class of continuous-time chaotic （hyperchaotic） systems and represents a general framework that includes any type of synchronization defined to date. An example involving a hyperchaotic oscillator is reported, with the aim of showing how a response system attractor is arbitrarily shaped using a scalar synchronizing signal only. Finally, it is shown that the recently introduced dislocated synchronization can be readily achieved using the conceived scheme.

Stackelberg Game Approach to Mixed H2/H∞ Problem for Continuous-Time System

This paper studies the mixed H2/H∞ control for continuous-time linear dynamic systems.By applying Stackelberg game approach, the control input is treated as the leader and the disturbance is treated as the follower, respectively. Under standard assumptions and maximum principle, a necessary and sufficient existence condition which is based on three decoupled Riccati equations is obtained.Explicit expression of controllers and solutions to forward backward differential equations(FBDES)are obtained by homogeneous analysis of variables. A numerical example is finally given to verify the efficiency of the proposed approach.

Variance minimization for continuous-time Markov decision processes: two approaches

This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.

A continuous-time formulation for refinery production scheduling problems involving operational transitions in mode switching

In the refinery scheduling, operational transitions in mode switching are of great significance to formulate dynamic nature of production and obtain efficient schedules. The discrete-time formulation meets two main challenges in modeling: discrete approximation of time and large size of mixed-integer linear problem(MILP).In this article, a continuous-time refinery scheduling model, which involves transitions of mode switching, is presented due to these challenges. To reduce the difficulty in solving large scale MILPs resulting from the sequencing constraints, the global event-based formulation is chosen. Both transition constraints and production transitions are introduced and the numbers of key variables and constraints in both of the discrete-time and continuous-time formulations are analyzed and compared. Three cases with different lengths of time horizons and different numbers of orders are studied to show the efficiency of the proposed model.

A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

We develop an online adaptive dynamic programming （ADP） based optimal control scheme for continuous-time chaotic systems. The idea is to use the ADP algorithm to obtain the optimal control input that makes the performance index function reach an optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to achieve optimal control. In the ADP structure, neural networks are used to construct a critic network and an action network, which can obtain an approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Our simulation results illustrate the performance of the established optimal control method.

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).

Parameters Identification of Continuous-Time Hammerstein System with Advanced Gauss Pseudo spectral Method

An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approximation method.The linear part was written as a controllable canonical form to circumvent the high order time-derivative of the input and output(I/O) signals,which could multiply the measurement noise in the identification procession.Furthermore,an output error minimization was constructed for the CT Hammerstein model identification,which was then transcribed into a nonlinear programming(NLP) problem by AGPM.AGPM could converge to the true values of the CT Hammerstein model with few interpolated Legendre-Gauss(LG) nodes.Lastly,two illustrative examples were proposed to verify the accuracy and efficiency of the method.

Identification of Continuous-Time Hammerstein System with Nuclear Norm Convex Relaxation

The nuclear norm convex relaxation method is proposed to force the rank constraint in the identification of the continuous-time( CT) Hammerstein system. The CT Hammerstein system is composed of a linear time invariant( LTI) system and a static nonlinear function( the linear part is followed by the nonlinear part). The nonlinear function is approximated by the pseudospectral basis functions, which have a better performance than Hinge functions and Radial Basis functions. After the approximation on the nonlinear function, the CT Hammerstein system has been transformed into a multiple-input single-output( MISO) linear model system with the differential pre-filters. However, the coefficients of static nonlinearity and the numerators of the linear transfer function are coupled together to challenge the parameters identification of the Hammerstein system. This problem is solved by replacing the one-rank constraint of the regularization optimization with the nuclear norm convex relaxation. Finally, a numerical example is given to verify the accuracy and the efficiency of the method.

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.

Variance Optimization for Continuous-Time Markov Decision Processes

This paper considers the variance optimization problem of average reward in continuous-time Markov decision process (MDP). It is assumed that the state space is countable and the action space is Borel measurable space. The main purpose of this paper is to find the policy with the minimal variance in the deterministic stationary policy space. Unlike the traditional Markov decision process, the cost function in the variance criterion will be affected by future actions. To this end, we convert the variance minimization problem into a standard (MDP) by introducing a concept called pseudo-variance. Further, by giving the policy iterative algorithm of pseudo-variance optimization problem, the optimal policy of the original variance optimization problem is derived, and a sufficient condition for the variance optimal policy is given. Finally, we use an example to illustrate the conclusion of this paper.

Zero-Sum Continuous-Time Markov Games with One-Side Stopping

The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates,while only one player can choose a stopping time.The dynamic programming principle reduces this problem to a system of ODEs with unilateral constraints.This system plays the role of the Bellman equation.We show that its solution provides the optimal strategies of the players.Additionally,the existence and uniqueness theorem for the deduced system of ODEs with unilateral constraints is derived.

A Stackelberg strategy for continuous-time mixed H2/H∞ control problem with time delay

This paper is concerned with the mixed H2/H∞ control with linear continuous time system and time delay. To deal with this, we presents a Stackelberg strategy by treating the control input and the disturbance as leader and follower, respectively. The leader＇s control strategy minimizes the cost function which is in H2 norm and the follower＇s control strategy maximizes the cost function which is in H∞ norm. The main technique of this paper is deal with the noncausal relationship of the variables caused by time delay in the control input by introducing two costates to capture the future information and one state to capture the past information. Through theory analyzing, the Stackelberg strategy exists uniquely. Moreover, with the assistance of the extended state space expression, the explicit expression of the strategy is obtained.

On iterative learning control design for tracking iteration-varying trajectories with high-order internal model

In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOlM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOlM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.

A continuous-time/discrete-time mixed audio-band sigma delta ADC

This paper introduces a mixed continuous-time/discrete-time, single-loop, fourth-order, 4-bit audioband sigma delta ADC that combines the benefits of continuous-time and discrete-time circuits, while mitigating the challenges associated with continuous-time design. Measurement results show that the peak SNR of this ADC reaches 100 dB and the total power consumption is less than 30 mW.

Integral-type functionals of first hitting times for continuous-time Markov chains

We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.