Pub Date : 2020-10-14DOI: 10.56082/annalsarscimath.2020.1-2.553
T. Damm, B. Jacob
We introduce a coercivity condition as a time domain analogue of the frequency criterion provided by the famous Kalman-YakubovichPopov lemma. For a simple stochastic linear quadratic control problem we show how the coercivity condition characterizes the solvability of Riccati equations.
{"title":"ON COERCIVITY AND THE FREQUENCY DOMAIN CONDITION IN INDEFINITE LQ-CONTROL","authors":"T. Damm, B. Jacob","doi":"10.56082/annalsarscimath.2020.1-2.553","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.553","url":null,"abstract":"We introduce a coercivity condition as a time domain analogue of the frequency criterion provided by the famous Kalman-YakubovichPopov lemma. For a simple stochastic linear quadratic control problem we show how the coercivity condition characterizes the solvability of Riccati equations.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77217476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-02DOI: 10.56082/annalsarscimath.2022.1-2.216
A. Stoica, I. Yaesh
The synthesis problem of static output feedback controllers within the anisotropic-norm setup is revisited. A tractable synthesis approach involving iterations over a convex optimisation problem is suggested, similarly to existing results for the H∞-norm minimisation case. The results are formulated by a couple of Linear Matrix Inequalities coupled via a bilinear equality, revealing, as in the H∞ case the duality of between the control-type and filtering type LMIs and allowing a tractable iterative method to cope with practical static output feedback synthesis problems. The resulting optimisation scheme is then applied to a flight control problem, where the merit of the anisotropic norm setup is shown to provide a useful trade-off between closed loop response and feedback gains
{"title":"STATIC OUTPUT FEEDBACK REVISITED","authors":"A. Stoica, I. Yaesh","doi":"10.56082/annalsarscimath.2022.1-2.216","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2022.1-2.216","url":null,"abstract":"The synthesis problem of static output feedback controllers within the anisotropic-norm setup is revisited. A tractable synthesis approach involving iterations over a convex optimisation problem is suggested, similarly to existing results for the H∞-norm minimisation case. The results are formulated by a couple of Linear Matrix Inequalities coupled via a bilinear equality, revealing, as in the H∞ case the duality of between the control-type and filtering type LMIs and allowing a tractable iterative method to cope with practical static output feedback synthesis problems. The resulting optimisation scheme is then applied to a flight control problem, where the merit of the anisotropic norm setup is shown to provide a useful trade-off between closed loop response and feedback gains","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"215 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72834124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.142
E. Kaslik, M. Neamţu, L. F. Vesa
This paper analyses a mathematical model with time delay for the labor force on a market. Three variables are taken into account: the number of unemployed and employed persons in the market and the number of new vacancies created by the government and the private sector, which is based on a past value of the unemployment number in the creation of new vacancies. The positivity of the solutions is examined and the existence of a unique equilibrium point of the mathematical model is proved. A local stability analysis is undertaken, showing that the unique equilibrium is locally asymptotically stable, for any value of the time delay. Numerical simulations are carried out which substantiate the theoretical statements and suggest that the positive equilibrium point is globally asymptotically stable.
{"title":"AN UNEMPLOYMENT MODEL WITH TIME DELAY","authors":"E. Kaslik, M. Neamţu, L. F. Vesa","doi":"10.56082/annalsarscimath.2020.1-2.142","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.142","url":null,"abstract":"This paper analyses a mathematical model with time delay for the labor force on a market. Three variables are taken into account: the number of unemployed and employed persons in the market and the number of new vacancies created by the government and the private sector, which is based on a past value of the unemployment number in the creation of new vacancies. The positivity of the solutions is examined and the existence of a unique equilibrium point of the mathematical model is proved. A local stability analysis is undertaken, showing that the unique equilibrium is locally asymptotically stable, for any value of the time delay. Numerical simulations are carried out which substantiate the theoretical statements and suggest that the positive equilibrium point is globally asymptotically stable.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73440513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.382
V. Răsvan
The present paper starts from a model with distributed parameters (i.e. described by hyperbolic partial differential equations with nonstandard (derivative) boundary conditions) of a hydroelectric power plant with tunnel, surge tank and penstock. The association of a system of functional differential equations of neutral type and the oneto-one correspondence between the solutions of the two mathematical objects is given. Further, it is given the deduction - via singular perturbations - of the nonlinear ordinary differential equations for modeling the surge tank in order to discuss its stability under constant power delivery of the hydraulic turbine. Some other unsolved problems are pointed out.
{"title":"NEW RESULTS ON WATER HAMMER STABILITY","authors":"V. Răsvan","doi":"10.56082/annalsarscimath.2020.1-2.382","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.382","url":null,"abstract":"The present paper starts from a model with distributed parameters (i.e. described by hyperbolic partial differential equations with nonstandard (derivative) boundary conditions) of a hydroelectric power plant with tunnel, surge tank and penstock. The association of a system of functional differential equations of neutral type and the oneto-one correspondence between the solutions of the two mathematical objects is given. Further, it is given the deduction - via singular perturbations - of the nonlinear ordinary differential equations for modeling the surge tank in order to discuss its stability under constant power delivery of the hydraulic turbine. Some other unsolved problems are pointed out.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75408189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.439
V. Ungureanu
This paper considers stability problems for discrete-time linear fractional -order systems (LFOSs) with Markovian jumps and/ or multiplicative noise. For the case of LFOSs with finite delays and Markovian jumps, we provide sufficient conditions for the mean-square asymptotic (MSA) stability or instability of the system by using Lyapunov type equations. In the absence of the Markovian perturbations, we use Ztransform and operator spectral properties to derive instability criteria for fractional-order systems with multiplicative random perturbations and either finite or infinite delays. Four numerical results accompanied by computer simulations illustrate the effectiveness of the theoretical results.
{"title":"MEAN SQUARE ASYMPTOTIC STABILITY OF DISCRETE-TIME LINEAR FRACTIONAL ORDER SYSTEMS","authors":"V. Ungureanu","doi":"10.56082/annalsarscimath.2020.1-2.439","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.439","url":null,"abstract":"This paper considers stability problems for discrete-time linear fractional -order systems (LFOSs) with Markovian jumps and/ or multiplicative noise. For the case of LFOSs with finite delays and Markovian jumps, we provide sufficient conditions for the mean-square asymptotic (MSA) stability or instability of the system by using Lyapunov type equations. In the absence of the Markovian perturbations, we use Ztransform and operator spectral properties to derive instability criteria for fractional-order systems with multiplicative random perturbations and either finite or infinite delays. Four numerical results accompanied by computer simulations illustrate the effectiveness of the theoretical results.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"196 1-6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72494108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.246
B. Stoyanov
We propose a novel self-shrinking chaos based pseudo-random number output algorithm. The result of the analysis shows that the presented generator ensures a secure way for sending electronic information with critical applications in data encryption.
{"title":"SELF-SHRINKING CHAOS BASED PSEUDO-RANDOM ALGORITHM","authors":"B. Stoyanov","doi":"10.56082/annalsarscimath.2020.1-2.246","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.246","url":null,"abstract":"We propose a novel self-shrinking chaos based pseudo-random number output algorithm. The result of the analysis shows that the presented generator ensures a secure way for sending electronic information with critical applications in data encryption.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85214465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.179
Silvia Baeva, Vasil A. Shterev, Nikolay Hinov
In this paper is presented comparative analysis between two cases of risk assessment for e-bike cycling in urban area. The input parameters taken into account in first case are the number of obstacles in each alternative branch of the route and in second case - the number of obstacles and road surface. Under obstacle in this study is considered any object that could either threaten the life of cyclist or present an obstacle in his way (potholes on the road or dangerous terrain, stray animals, hooligans, incompetent car drivers etc.). The researches is made as a stochastic problem with two stages. The first stage consists of a calculation of the average risk in each branch of the route. The input parameters are stochastic and discretized, preprocessed by statistic methodology. In the second stage the optimal route is found by application of the Bellman’s optimally principle.
{"title":"COMPARATIVE ANALYSIS BETWEEN TWO CASES OF RISK ASSESSMENT FOR E-BIKE CYCLING IN URBAN AREA","authors":"Silvia Baeva, Vasil A. Shterev, Nikolay Hinov","doi":"10.56082/annalsarscimath.2020.1-2.179","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.179","url":null,"abstract":"In this paper is presented comparative analysis between two cases of risk assessment for e-bike cycling in urban area. The input parameters taken into account in first case are the number of obstacles in each alternative branch of the route and in second case - the number of obstacles and road surface. Under obstacle in this study is considered any object that could either threaten the life of cyclist or present an obstacle in his way (potholes on the road or dangerous terrain, stray animals, hooligans, incompetent car drivers etc.). The researches is made as a stochastic problem with two stages. The first stage consists of a calculation of the average risk in each branch of the route. The input parameters are stochastic and discretized, preprocessed by statistic methodology. In the second stage the optimal route is found by application of the Bellman’s optimally principle.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88910011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.24
Irina Badralexi, S. Balea, A. Halanay, D. Jardan, R. Rădulescu
The model studied in this paper describes the competitive interaction between healthy and malignant cells in leukemia with the involvement of the immune system. The model consists of 9 delay-differential equations with 9 delays. Local stability is investigated for the equilibrium points of the system. Lyapunov-Krasovskii functionals related
{"title":"A COMPLEX MODEL OF CELL EVOLUTION IN LEUKEMIA INCLUDING COMPETITION AND THE ACTION OF THE IMMUNE SYSTEM","authors":"Irina Badralexi, S. Balea, A. Halanay, D. Jardan, R. Rădulescu","doi":"10.56082/annalsarscimath.2020.1-2.24","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.24","url":null,"abstract":"The model studied in this paper describes the competitive interaction between healthy and malignant cells in leukemia with the involvement of the immune system. The model consists of 9 delay-differential equations with 9 delays. Local stability is investigated for the equilibrium points of the system. Lyapunov-Krasovskii functionals related","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90709588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.198
A. Famà, L. Restuccia, H. Kanchev
"In previous papers in the linear and anisotropic case, constitutive relations, rate equations, temperature and energy equations were derived by the authors to describe the mechanical, thermal and transport properties of fluid-saturated crystals with porous channels defects, using a model developed by one of us (L. R.) in the framework of nonequilibrium thermodynamics. A structural permeability tensor `a la Kubik, rij , its gradient and its flux Vijk were introduced as internal variables in the thermodynamic state vector. Here, we work out in the isotropic and perfect isotropic linear cases the constitutive functions for the stress tensor, the entropy density, the chemical potentials, and also the rate equations for rij , Vijk, the fluid-concentration and the heat fluxes, describing disturbances propagating with finite velocity and presenting a relaxation time. The porous defects modify the thermal conductivity and when they have a density higher than a suitable characteristic value the thermal conductivity decreases. Furthermore, the closure of the system of equations, describing the media under consideration and linearized around a thermodynamic equilibrium state is obtained. The derived results may have great relevance in biology, medical sciences and in several technological sectors, like seismic engineering and nanotechnology (where high-frequency waves propagation is present and the properties variation rate of the considered medium is faster than the relaxation times of the fluxes towards their equilibrium value)."
在以前的论文中，作者在线性和各向异性的情况下，推导了本构关系、速率方程、温度和能量方程来描述具有多孔通道缺陷的饱和流体晶体的力学、热学和输运性质，使用的是我们中的一个人(L. R.)在非平衡热力学框架下建立的模型。引入结构渗透率张量' A la Kubik, rij及其梯度和通量Vijk作为热力学状态向量的内变量。在各向同性和完全各向同性线性情况下，我们得到了应力张量、熵密度、化学势的本构函数，以及rij、Vijk、流体浓度和热通量的速率方程，描述了以有限速度传播的扰动，并给出了松弛时间。多孔缺陷改变了热导率，当它们的密度高于合适的特征值时，热导率降低。此外，还得到了方程组的闭包，该方程组描述了所考虑的介质，并围绕热力学平衡状态线性化。所得结果可能在生物学、医学以及地震工程和纳米技术等若干技术领域具有重大意义(在这些领域，存在高频波传播，所考虑的介质的性质变化率快于通量向其平衡值的松弛时间)。”
{"title":"NON-EQUILIBRIUM THERMODYNAMICS FRAMEWORK FOR FLUID FLOW AND POROSITY DYNAMICS IN POROUS ISOTROPIC MEDIA","authors":"A. Famà, L. Restuccia, H. Kanchev","doi":"10.56082/annalsarscimath.2020.1-2.198","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.198","url":null,"abstract":"\"In previous papers in the linear and anisotropic case, constitutive relations, rate equations, temperature and energy equations were derived by the authors to describe the mechanical, thermal and transport properties of fluid-saturated crystals with porous channels defects, using a model developed by one of us (L. R.) in the framework of nonequilibrium thermodynamics. A structural permeability tensor `a la Kubik, rij , its gradient and its flux Vijk were introduced as internal variables in the thermodynamic state vector. Here, we work out in the isotropic and perfect isotropic linear cases the constitutive functions for the stress tensor, the entropy density, the chemical potentials, and also the rate equations for rij , Vijk, the fluid-concentration and the heat fluxes, describing disturbances propagating with finite velocity and presenting a relaxation time. The porous defects modify the thermal conductivity and when they have a density higher than a suitable characteristic value the thermal conductivity decreases. Furthermore, the closure of the system of equations, describing the media under consideration and linearized around a thermodynamic equilibrium state is obtained. The derived results may have great relevance in biology, medical sciences and in several technological sectors, like seismic engineering and nanotechnology (where high-frequency waves propagation is present and the properties variation rate of the considered medium is faster than the relaxation times of the fluxes towards their equilibrium value).\"","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91174051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.62
G. Yin, Zhexin Wen
In our recent work, in lieu of using white noise, we examined Kolmogorov systems driven by wideband noise. Such systems naturally arise in statistical physics, biological and ecological systems, and many related fields. One of the motivations of our study is to treat more realistic models than the usually assumed stochastic differential equation models. The rationale is that a Brownian motion is an idealization used in a wide range of models, whereas wideband noise processes are much easier to be realized in the actual applications. This paper further investigates the case that in addition to the wideband noise process, there is a singularly perturbed Markov chain. The added Markov chain is used to model discrete events. Although it is a more realistic formulation, because of the non-Markovian formulation due to the wideband noise and the singularly perturbed Markov chain, the analysis is more difficult. Using weak convergence methods, we obtain a limit result. Then we provide several examples for the utility of our findings.
{"title":"TWO-TIME-SCALE REGIME-SWITCHING STOCHASTIC KOLGOMOROV SYSTEMS WITH WIDEBAND NOISES","authors":"G. Yin, Zhexin Wen","doi":"10.56082/annalsarscimath.2020.1-2.62","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.62","url":null,"abstract":"In our recent work, in lieu of using white noise, we examined Kolmogorov systems driven by wideband noise. Such systems naturally arise in statistical physics, biological and ecological systems, and many related fields. One of the motivations of our study is to treat more realistic models than the usually assumed stochastic differential equation models. The rationale is that a Brownian motion is an idealization used in a wide range of models, whereas wideband noise processes are much easier to be realized in the actual applications. This paper further investigates the case that in addition to the wideband noise process, there is a singularly perturbed Markov chain. The added Markov chain is used to model discrete events. Although it is a more realistic formulation, because of the non-Markovian formulation due to the wideband noise and the singularly perturbed Markov chain, the analysis is more difficult. Using weak convergence methods, we obtain a limit result. Then we provide several examples for the utility of our findings.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76651590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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