SIAM Conf. on Control and its Applications最新文献

{"title":"Study of Certain Stochastic Predator-Prey Models","authors":"N. Du, N. H. Dang, G. Yin","doi":"10.1137/1.9781611974072.56","DOIUrl":"https://doi.org/10.1137/1.9781611974072.56","url":null,"abstract":"In this paper, we provide sufficient conditions for the permanence and ergodicity of a stochastic predator-prey model with Beddington-DeAngelis functional response. These sufficient conditions are sharp and close to the necessary conditions as well. In addition to the nondegenerate diffusion, degenerate cases are also treated. In the degenerate case, our results characterize the support of the associated unique invariant probability measure. Convergence in total variation of the transition probability to the invariant measures is given. We also consider a stochastic model with regime-switching. Our results are demonstrated by several examples.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127388937","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}

{"title":"Optimal Control of Crop Irrigation based on the Hamilton-Jacobi-Bellman Equation","authors":"J. Ramanathan, Yuting Chen, P. Cournède","doi":"10.1137/1.9781611973273.4","DOIUrl":"https://doi.org/10.1137/1.9781611973273.4","url":null,"abstract":"Water management in agriculture is a key issue due to the increasing problem of water scarcity worldwide. Based on the recent progress in the dynamic modeling of plant growth in interaction with the water resource, our objective is to study the optimal control problem of crop irrigation. For this purpose, we first describe the LNAS model for sugar beet growth, driving the dynamics of both plant biomass and soil water reserve. We then introduce the utility function corresponding to the farmer’s profit and derive the value function from the Hamilton-Jacobi-Bellman (HJB) equation. Then a backward finite-difference scheme is implemented to solve the HJB equation. It is proved to converge under a proper Courant-Friedrichs-Lewy condition for the discretization step. A few numerical simulations are provided to illustrate the resolution.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129938368","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}

{"title":"Optimal Bidding Strategies for Wind Power Producers with Meteorological Forecasts","authors":"Antonio Giannitrapani, S. Paoletti, A. Vicino, Donato Zarrilli","doi":"10.1137/1.9781611973273.3","DOIUrl":"https://doi.org/10.1137/1.9781611973273.3","url":null,"abstract":"In recent years, the interest in clean renewable energy resources, such as wind and photovoltaic, has grown rapidly. It is well known that the inherent variability in wind power generation and the related difficulty in predicting future generation profiles, raise major challenges to wind power integration into the electricity grid. In this work we study the problem of optimizing energy bids for an independent Wind Power Producer (WPP) taking part into a competitive electricity market. It is assumed that the WPP is subject to financial penalties for generation shortfall and surplus. This means that, if the energy delivered over a given time slot is different from that subscribed in the bid, the WPP will be penalized, the monetary entity of the penalty depending on the wholesale market behavior, the day of the year and the time slot involved. An optimization procedure is devised to minimize this risk and maximize the expected profit of the seller. Specifically, each energy bid is computed by exploiting the forecast energy price for the day ahead market, the historical wind statistics at the plant site and the day-ahead wind speed forecasts provided by a meteorological service. We also examine and quantify the strategic role of an energy storage device in increasing reliability of bids and mitigating the financial risks of the WPP.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132278154","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}

{"title":"Computing the structured distance to instability","authors":"P. Apkarian, D. Noll, Laleh Ravanbod","doi":"10.1137/1.9781611974072.58","DOIUrl":"https://doi.org/10.1137/1.9781611974072.58","url":null,"abstract":"We analyze robust stability and performance of dynamical systems with real uncertain parameters. We compute criteria like the distance to instability, the worst-case spectral abscissa, or the worst-case H∞-norm, which quantify the degree of robustness of such a system when parameters vary in a given set ∆. As computing these indices is NP-hard, we present a heuristic which finds good lower bounds fast and reliably. Posterior certification is then obtained by an intelligent global strategy. A test bench of 87 systems with up to 70 states 39 uncertain parameters with up to 11 repetitions demonstrates the potential of our approach. 1 Problem Specification. Robustness specifications limit the loss of performance and stability in a system where differences between the mathematical model and reality crop up. Robustness against real parametric uncertainties is among the most challenging calls in this regard. Already deciding whether a given system with uncertain real parameters δ is robustly stable over a given parameter range δ ∈ ∆ is NP-hard, and this is aggravated when it comes to deciding whether a given level of H2or H∞-performance is guaranteed over that range. In this work we address this type of uncertainty by computing three key criteria, which quantify the degree of parametric robustness of a system. These are (a) the worst-case H∞-norm, and (b) the worst-case spectral abscissa over a given parameter range, and (c) the distance to instability, or stability margin, of a system with uncertain parameters. Consider a Linear Fractional Transform [23] with real parametric uncertainties as in Figure 1, where P (s) :    ẋ = Ax + Bpp + Bww q = Cqx + Dqpp + Dqww z = Czx + Dzpp + Dzww (1.1) and x ∈ R is the state, w ∈ R1 a vector of exogenous inputs, and z ∈ R1 a vector of regulated outputs. The uncertainty channel is defined as p = ∆q, where the time-invariant uncertain matrix ∆ has the blockdiagonal form ∆ = diag [δ1Ir1 , . . . , δmIrm ] , (1.2) ONERA, Control System Department, Toulouse, France Universite de Toulouse, Institut de Mathematiques with δ1, . . . , δm representing real uncertain parameters, and ri giving the number of repetitions of δi. Here we assume without loss that δ = 0 ∈ ∆ represents the nominal parameter value, and we consider δ ∈ ∆ in one-to-one correspondence with the matrix ∆ in (1.2). For practical applications it is generally sufficient to consider the case ∆ = [−1, 1]. To analyze the performance of (1.1) in the presence of the uncertain δ ∈ R we compute the worst-case H∞-performance h = max{‖Twz(δ)‖∞ : δ ∈ ∆}, (1.3) where ‖·‖∞ is the H∞-norm, and where Twz(s, δ) is the transfer function z(s) = Fu(P (s), ∆)w(s), obtained by closing the loop between (1.1) and p = ∆q with (1.2) in Figure 1. The solution δ ∈ ∆ of (1.3) represents a worst possible choice of the parameters δ ∈ ∆, which may be an important element in analyzing performance and robustness of the system, see e.g. [1]. Our second criterion is similar in nature, as it ","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129227168","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}

{"title":"Convexity + curvature: Tools for the global stabilization of nonlinear systems with control inputs subject to magnitude and rate bounds","authors":"J. Solís-Daun","doi":"10.1137/1.9781611974072.19","DOIUrl":"https://doi.org/10.1137/1.9781611974072.19","url":null,"abstract":"The aim of this paper is to address the global asymptotic stabilization (gas) of affine systems with control inputs subject to magnitude and rate bounds, in the framework of ArtsteinSontag’s control Lyapunov function (clf) approach. These bounds are defined by compact (convex) control value sets (cvs) U with 0 ∈ intU . Convex Analysis together with Differential Geometry allow us to reveal the intrinsic geometry involved in the clf stabilization problem, and to solve it, if an optimal control ω(x) exists. The existence and uniqueness of ω(x) depends on convexity properties of cvs U ; whereas its regularity and boundedness of its differential is achieved in terms of the curvature of U . However, in view that control ω(x) is singular, we redesign it to derive an explicit formula for regular damping feedback controls fulfilling magnitude and rate bounds that render gas a class of affine systems.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120926371","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}

{"title":"Periodic Control System Stabilization on Time Scales","authors":"Francisco Miranda","doi":"10.1137/1.9781611973273.14","DOIUrl":"https://doi.org/10.1137/1.9781611973273.14","url":null,"abstract":"The stabilization of periodic control systems using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we suggest an alternative way to solve stabilization problems. This method is based on a combination of the Lyapunov functions method with local controllability conditions. In many situations this method admits a rigorous mathematical justification and leads to effective numerical methods. Applications to mechanical problems are provided here.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116092447","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}

{"title":"New Results On Stochastic Consensus Networks","authors":"C. Somarakis, J. Baras","doi":"10.1137/1.9781611974072.17","DOIUrl":"https://doi.org/10.1137/1.9781611974072.17","url":null,"abstract":"We revisit the general linear consensus problem and provide new conditions for asymptotic consensus on two types of stochastic versions of the algorithm, in discrete and continuous time. We show that our method unifies a number of proposed models in the literature as well as it extends and generalizes existing results.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127706303","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}

{"title":"Adaptive Polynomial Identification and Optimal Tracking Control for Nonlinear Systems","authors":"Fernando Ornelas, A. Villafuerte","doi":"10.1137/1.9781611974072.36","DOIUrl":"https://doi.org/10.1137/1.9781611974072.36","url":null,"abstract":"The paper proposes an adaptive polynomial identifier and a robust nonlinear optimal tracking control scheme for polynomial systems. The identifier approximates an uncertain nonlinear system, where its parameters are on-line adapted using a Kalman-Bucy filter. Then, based on the identifier an optimal tracking controller is synthesized, including an integral term to provide it robustness. The identification and control scheme is illustrated via simulations for the control of the blood glucose level in diabetic patients.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"258 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114261715","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}

{"title":"Modeling and Analysis of Adaptive-Conversion-Ratio-Based Bidirectional Switched-Capacitor Converter","authors":"Yuen-Haw Chang, Kun-Wei Wu","doi":"10.1137/1.9781611973273.21","DOIUrl":"https://doi.org/10.1137/1.9781611973273.21","url":null,"abstract":"","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"193 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123176362","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}

{"title":"A max-plus fundamental solution semigroup for a class of lossless wave equations","authors":"P. Dower, W. McEneaney","doi":"10.1137/1.9781611974072.55","DOIUrl":"https://doi.org/10.1137/1.9781611974072.55","url":null,"abstract":"A new max-plus fundamental solution semigroup is presented for a class of lossless wave equations. This new semigroup is developed by employing the action principle to encapsulate the propagation of all possible solutions of a given wave equation in the evolution of the value function of an associated optimal control problem. The max-plus fundamental solution semigroup for this optimal control problem is then constructed via dynamic programming, and used to formulate the fundamental solution semigroup for the original wave equation. An application of this semigroup to solving twopoint boundary value problems is discussed via an example.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125311726","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}