Time-Varying Neural Networks for Dynamical Systems Modeling with Application to Image Compression

Kwang Cheul Shin 보안공학연구지원센터 2016 International Journal of Security and Its Applicat Vol.10 No.12

The architecture of a class of time-varying neural networks can be determined by simply adopting that of the conventional neural networks, while the weights are allowed to vary with time. The challenge lies how to select the weights, when applying a time-varying neural network. In this paper, we use the iterative learning methodology for training time-varying neural networks, and the neural networks are proposed for modeling and identification of discrete-time time-varying nonlinear systems. Time-varying dynamical neural networks (DNNs) are presented by the architecture of conventional high-order DNNs with connection weights varying with time. Both conventional DNNs and time-varying DNNs are used to identify time-varying systems. The weights are updated by least squares integral learning algorithm with dead-zones. For time-varying case, iterative learning and its improved algorithms are used to update connection weights. The identification error is ensured to converge to the bound, which is proportional to the approximation error.

시변 지연시간을 갖는 이산 구간 시변 시스템의 시변 불확실성의 안정범위

한형석 ( Hyung-seok Han ) 한국항행학회 2017 韓國航行學會論文誌 Vol.21 No.6

본 논문에서는 시변 지연시간이 있는 선형 이산 구간 시변 시스템의 지연 상태변수에 존재하는 불확실성 안정범위에 관한 것을 다룬다. 고려된 시스템은 지연 없는 상태변수에 대한 시스템 행렬이 구간범위에서 시변으로 변동하고, 지연 시간이 구간범위 내에서 시변인 지연 상태변수에 대하여 비구조화된 불확실성이 시변으로 존재하는 시스템이다. 기존의 많은 연구들이 시변에 대한 부분을 고려하지 못하고 시불변 경우에 대하여 얻어진 것에 반하여, 본 논문에서는 모든 요소를 시변으로 고려하여 새로운 안정범위를 도출하였다. 새로운 안정범위는 적용 가능한 시스템에 대한 제한이 없는 것으로 그 효용성이 기존의 결과 보다 우수하다. 제안된 범위는 복잡한 선형행렬부등식 혹은 리아프노프 방정식의 상한 해 한계를 이용하는 복잡한 과정이 필요하지 않다. 수치예제를 통하여 제안된 결과가 기존의 결과들을 포함할 수 있음을 보이고, 이들 보다 확장성과 효용성이 우수함을 확인한다. In this paper, we consider the stability bound for uncertainty of delayed state variables in the linear discrete interval time-varying systems with time-varying delay time. The considered system has an interval time-varying system matrix for non-delayed states and is perturbed by the unstructured time-varying uncertainty in delayed states with time-varying delay time within fixed interval. Compared to the previous results which are derived for time-invariant cases and can not be extended to time-varying cases, the new stability bound in this paper is applicable to time-varying systems in which every factors are considered as time-varying variables. The proposed result has no limitation in applicable systems and is very powerful in the aspects of feasibility compared to the previous. Furthermore. the new bound needs no complex numerical algorithms such as LMI(Linear Matrix Inequality) equation or upper solution bound of Lyapunov equation. By numerical examples, it is shown that the proposed bound is able to include the many existing results in the previous literatures and has better performances in the aspects of expandability and effectiveness.

시변 지연시간을 갖는 이산 구간 시변 시스템의 안정조건

한형석 ( Hyung-seok Han ) 한국항행학회 2016 韓國航行學會論文誌 Vol.20 No.5

본 논문에서는 상태변수에 시변 지연시간이 있는 선형 이산 구간 시변 시스템의 안정조건을 새롭게 제안한다. 고려한 시스템은 지연 없는 상태변수에 대한 시스템 행렬과 지연 상태변수에 대한 시스템 행렬이 시변 구간 행렬로 표현되며, 지연시간도 구간에 대하여 시변인 특성을 갖는다. 제안된 안정조건은 리아프노프 안정 이론을 이용하여 유도되며, 매우 간단한 부등식의 형태로 표현된다. 본 논문에서는 기존의 시불변 구간 행렬의 안정성 문제를 시변 구간 행렬의 안정성 문제로 확장하고, 기존에 발표된 결과를 포함하는 강력한 안정조건이 유도된다. 이 안정조건의 유도과정에서는 복잡한 선형행렬부등식 혹은 리아프노프 방정식의 상한 해 한계를 구하지 않아도 된다. 또한, 기존의 결과들과의 비교를 통하여 제안된 안정조건이 많은 기존 안정 조건들을 포함할 수 있음을 보인다. 기존 수치예제를 일반적인 형태로 확장하였고 이에 대하여 새로운 안정조건의 확장성과 효용성을 확인한다. In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.

Adaptive Fuzzy Controller Design for Unstable Nonlinear Time-varying System

Kim, In Hwan,Hur, Nam Soo 진주산업대학교 1998 산업과학기술연구소보 Vol.- No.5

A new adaptive controller is developed for unstable nonlinear time-varying systems which combines a model reference adaptive controller (MRAC) and a fuzzy controller. The fuzzy controller is used to analyze and to compensate the nonlinerar time-varying characteristics of the plant. The MRAC is applied to control the linear time-invariant subsystem of the unknown plant, where the nonlinear time-varying plant is supposed to comprise a nonlinear time-varying subsystem and a linear time-invariant subsystem. It is assumed that the steady state output error of the MRAC system is caused by the nonlinear time-varying subsystem. The nonlinear time-varying subsystem, which is assumed to be an error generator, can then be modelled using fuzzy theory by using input/output data from the unknown plant in the MRAC. A fuzzy control system with state feedback is therefore designed in order to make the output of the error generator converge to zero asymototically. The stability analysis for the overall system is discussed in view of global asymptotic stability. In conclusion, the unknown nonlinear time-varying plant can be controlled by the new adaptive control theory such that the output error of the given plant converges to zero asymptotically.

Design of Supervisory Model Predictive Control for Building HVAC System Subject to Time-Varying Operating Points

Sitthiphat Promchaiwattana,David Banjerdpongchai 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11

This paper presents the design of supervisory model predictive control for HVAC systems with consideration of peak demand shaving and thermal comfort. In this work, we analyze the operating points with the thermal comfort requirement. Afterwards, we linearize the nonlinear dynamic model to a linear time-varying model. In particular, we specify that the operating point of the open-loop HVAC system satisfies the thermal comfort condition. This makes the predicted mean vote (PMV) equal to zero or nearly to zero. Subsequently, we calculate the zone temperature, the zone humidity ratio, and the volumetric flow rate. When considering the time-varying disturbance profiles, it appears that the operating points are time-varying. We observe that the coefficient of performance (COP) and the operating points are time-varying which lead to time-varying model. Moreover, we design supervisory control (SC) and model predictive control (MPC) for linear time-varying model. In the SC design, we aim to find the optimal reference zone temperature which is used as the reference signal for MPC. In the MPC design, the objectives are twofold. First, the zone temperature tracks the reference signal. Second, both electrical energy cost and deviation of desired thermal comfort are minimized. The computer simulation shows that MPC of time-varying HVAC system yields the best reference tracking. In addition, it reduces total electrical energy cost the most. We conclude that the optimal temperature reference can be effectively applied to the building HVAC systems while the occupants feel comfortable and the total electrical energy cost is the lowest.

한국 주택시장의 시간가변적 베타: 적합성과 예측력 분석

김중득,이영수 한국부동산연구원 2016 부동산연구 Vol.26 No.4

This paper investigates the time-varying behavior of beta for Korea housing market using monthly housing pricing indices of borough in Seoul and Busan over the period 2003-2014. In this paper, we focus on tests based on Kalman filter. First, in order to know whether betas have varied substantially over time, this paper estimates time-varying betas using the Kalman filter algorithm in the framework of a state-space model. Second, we compare the fitting and forecast ability of two different time-varying beta models(using AR(1) and random walk process) and use the constant beta of the single factor model as a benchmark. Our results find that in time-series test, measures of forecast errors overwhelmingly support the Kalman filter method implying betas are time-varying substantially over time. In comparison of time-varying betas, Betas of AR(1) process are preferred to random walk process in sample fitting performances and betas of random walk process provide more accurate forecast. 서울과 부산의 월간 구별 아파트 가격지수로 우리나라 주택시장의 시간가변적인 베타의 행태를 분석하였다. 이를 위해 위험과 수익의 관계를 대표하는 CAPM을 정태적 베타모형과 칼만필터 방법으로 추정한 임의보행과정 시변베타모형, AR(1)과정 시변베타모형으로 분석하고 모형의 적합성(fitting)과 예측력(forecast)을 검정하였다. 분석결과를 요약하면, 첫째, 시간가변적 베타()모형이 정태적베타()모형보다 적합성에서 월등하였으며 시간가변적 베타모형 중에서는 시간가변적 베타 AR(1)모형이 적합성에서 우수하였다. 둘째, 모형의 예측력의 검정에서 정태적 모형과 시간가변적 베타 AR(1)모형 보다 시간가변적 베타 임의보행모형이 예측력에서 가장 우수하였다. 이로써 우리나라 주택시장의 베타는 불안정적이며 시간 가변적임을 확인하였다.

Time-varying physical parameter identification of shear type structures based on discrete wavelet transform

Wang, Chao,Ren, Wei-Xin,Wang, Zuo-Cai,Zhu, Hong-Ping Techno-Press 2014 Smart Structures and Systems, An International Jou Vol.14 No.5

This paper proposed a discrete wavelet transform based method for time-varying physical parameter identification of shear type structures. The time-varying physical parameters are dispersed and expanded at multi-scale as profile and detail signal using discrete wavelet basis. To reduce the number of unknown quantity, the wavelet coefficients that reflect the detail signal are ignored by setting as zero value. Consequently, the time-varying parameter can be approximately estimated only using the scale coefficients that reflect the profile signal, and the identification task is transformed to an equivalent time-invariant scale coefficient estimation. The time-invariant scale coefficients can be simply estimated using regular least-squares methods, and then the original time-varying physical parameters can be reconstructed by using the identified time-invariant scale coefficients. To reduce the influence of the ill-posed problem of equation resolving caused by noise, the Tikhonov regularization method instead of regular least-squares method is used in the paper to estimate the scale coefficients. A two-story shear type frame structure with time-varying stiffness and damping are simulated to validate the effectiveness and accuracy of the proposed method. It is demonstrated that the identified time-varying stiffness is with a good accuracy, while the identified damping is sensitive to noise.

Finite-time Consensus of Leader-following Multi-agent Systems with Multiple Time Delays over Time-varying Topology

Fenglan Sun,Mingyan Tuo,Jürgen Kurths,Wei Zhu 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.8

This paper studies the finite-time consensus of leader-following multi-agent systems with multiple time delays over time-varying topology. The finite-time consensus protocol based on the agents’ states and the communication topology is designed. By adopting the algebraic graph theory, Lyapunov stability theory and pinning control method, some sufficient conditions for the finite-time consensus are given. It is proved that the system can reach consensus in a finite time both over the connected and disconnected topology. Moreover, the upper bound of the convergence time is given. Several simulations are presented to verify the effectiveness of the adopted method.

근육의 활성화 시 상관관계를 반영한 Target Cascading 기반 머슬시너지 추출 기법

김장현(Janghyeon Kim),윤한얼(Han Ul Yoon) 한국지능시스템학회 2022 한국지능시스템학회논문지 Vol.32 No.3

머슬시너지는 중추신경계가 동작을 수행할 때, 근육에 전달되는 모듈화된 제어 신호이다. 일반적으로, 머슬시너지는 근전도 신호로부터 최적화 기반 알고리즘인 비부정 행렬 인수분해를 통해 추출할 수 있다. Time-varying 머슬시너지 추출의 경우 머슬시너지의 수, 근육의 수, 타임 스텝의 길이가 최적화 성능에 영향을 끼친다. 또한, 비현실적인 머슬시너지 추출을 방지하기 위해 생체역학적 제약조건을 부과한다면 최적화 수행 시간 및 복원율이 더욱 저하된다. 따라서 본 논문에서는 target cascading을 적용하여 위 문제를 해결하는 방법론을 제안한다. Target cascading은 하나의 프로세스를 메인/서브 시스템으로 나누어 최적화를 수행하므로 빠르게 최적해를 구한다. 단일 머슬시너지는 독립된 하나의 서브 시스템으로 간주할 수 있으므로, 머슬시너지를 서브 시스템으로 설정하여 target cascading을 진행하면 최적화 성능의 향상을 기대할 수 있다. Target cascading을 적용했을 때와 적용하지 않았을 때 추출하는 각각의 머슬시너지를 최적화 소요 시간 및 복원율 관점에서 비교 분석한다. 그 결과, 생체역학적 제약조건이 부과된 time-varying 머슬시너지 추출에 제안한 방법론을 적용했을 때 평균적으로 3배 빠른 속도로 최적화하며, 복원율도 평균적으로 약 1.6배 높았다. Muscle synergy is a modularized control signal transmitted by the central neural system to control muscles when we perform specific tasks. After measuring surface electromyography, generally, muscle synergy is used to be extracted by employing the non-negative matrix factorization which is an optimization-based algorithm. When we extract time-varying muscle synergy, the number of synergies, the number of muscles involved in a synergy, and the length of time step are crucial hyper parameters which have an effect on optimization performance. Moreover, the aforementioned optimization performance might be severely deteriorated when biomechanical constraints are imposed to avoid extracting unrealistic muscle synergy. In this paper, we propose a method in which a target cascading plays a key role to solve the issues above. Under the target cascading, the entire process is divided into main-/sub-system and each process is then optimized individually, which in turn, accelerates the optimization process. A single muscle synergy conceptually corresponds to an independent sub-system; accordingly, we can expect better performance by adopting the target cascading for the muscle synergy extraction process. In the experiment, we extract time-varying muscle synergies under two conditions - to whether a target cascading is applied or not - and compare the outcomes in perspectives of an elapsed time as well as a reconstruction ratio. The results show, for the given constrained time-varying muscle synergy extraction problem, that the optimization process can be improved by 3 times and 1.6 times in terms of an elapsed time and as a reconstruction ratio, respectively, when the target cascading is applied.

Time-Varying Line-of-Sight Rate Estimator with a Single Modified Tracking Index for RF Homing Guidance

나원상,황익호 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.5

A practical time-varying line-of-sight (LOS) rate estimator is proposed for surface-to-air missile (SAM) guidance using an RF seeker. The range-dependant LOS rate dynamics and variances of boresight error (BSE) measurements constitute the Kalman filtering problem associated with the time-varying matrix differential Riccati equation (DRE). Since the conventional gain-scheduled steady-state Kalman filter derived by solving an algebraic Riccati equation (ARE) cannot fully consider the time-varying nature of LOS rate dynamics, it might not be appropriate for volatile missile-target engage-ment scenarios. This motivates us to investigate a pseudo-analytic solution to the time-varying Kalman filtering problem based on the algebraic transform of the given DRE. Apart from the previous works, the explicit form of time-varying Kalman gain is expressed in terms of a single filter design parameter, called modified tracking index. The proposed time-varying filter is not only able to effectively handle the time-varying LOS rate dynamics but is also affordable for real-time implementation. Adjoint analysis results for a homing guidance loop show that the proposed LOS rate estimator could improve guidance performance and be an excellent choice for SAM applications.