This paper has investigated best tracking performance for linear feedback control systems in the case that plant uncertainty and control effort need to be considered simultaneously. Firstly, an average integral square...This paper has investigated best tracking performance for linear feedback control systems in the case that plant uncertainty and control effort need to be considered simultaneously. Firstly, an average integral square criterion of the tracking error and the plant input energy over a class of additive model errors is defined. Then, utilizing spectral factorization to minimize the performance index, we obtain an optimal controller design method, and furthermore study optimal tracking performance under plant uncertainty and control energy constraint. The results can be used to evaluate optimal average tracking performance and control energy in designing practical control systems.展开更多
In the paper the proposition of a discrete, robust, minimal energetic P servo controller for second order plant is presented. The plant under consideration is described with the use of a state space equation and a tra...In the paper the proposition of a discrete, robust, minimal energetic P servo controller for second order plant is presented. The plant under consideration is described with the use of a state space equation and a transfer function with interval parameters. The considered model describes for example an oriented PV （photovoltaic） system. As a controller a P （proportional） controller was applied. It is very simple and their application in the situation we deal with assures the suitable control performance. The controller is going to be implemented at digital platform. To construct the control system a cost function proposed by the authors was applied. It describes both the energy consumption and the sample time of controller. The proposed cost function is a function of plant parameters, describing the dynamics of the plant and controller parameters： proportional gain and sample time. For the cost function a simple geometric interpretation can be given： for fixed plant parameters and varying controller parameters it is a surface in the Ra plane. This fact can be applied to assign of optimal controller. Theoretical results were depicted by a numerical example.展开更多
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal ...This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein(2002). The price is determined by two optimal stochastic control problems(mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations.By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates.The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.展开更多
Considering the uncertainty of kelp-abalone-sea cucumber population, an interval model of carbon sink fisheries with multi-trophic levels is proposed. The equilibria of the model are identified and the corresponding s...Considering the uncertainty of kelp-abalone-sea cucumber population, an interval model of carbon sink fisheries with multi-trophic levels is proposed. The equilibria of the model are identified and the corresponding stabilities are discussed. And the existence of bionomic equilibrium of the model is investigated. Next the optimal controller is designed to obtain the optimal harvest using Pontryagin＇s maximum principle. Numerical simulations are carried to prove the results.展开更多
基金High Technology Research and Development (863) Program(No.2003AA517020)
文摘This paper has investigated best tracking performance for linear feedback control systems in the case that plant uncertainty and control effort need to be considered simultaneously. Firstly, an average integral square criterion of the tracking error and the plant input energy over a class of additive model errors is defined. Then, utilizing spectral factorization to minimize the performance index, we obtain an optimal controller design method, and furthermore study optimal tracking performance under plant uncertainty and control energy constraint. The results can be used to evaluate optimal average tracking performance and control energy in designing practical control systems.
文摘In the paper the proposition of a discrete, robust, minimal energetic P servo controller for second order plant is presented. The plant under consideration is described with the use of a state space equation and a transfer function with interval parameters. The considered model describes for example an oriented PV （photovoltaic） system. As a controller a P （proportional） controller was applied. It is very simple and their application in the situation we deal with assures the suitable control performance. The controller is going to be implemented at digital platform. To construct the control system a cost function proposed by the authors was applied. It describes both the energy consumption and the sample time of controller. The proposed cost function is a function of plant parameters, describing the dynamics of the plant and controller parameters： proportional gain and sample time. For the cost function a simple geometric interpretation can be given： for fixed plant parameters and varying controller parameters it is a surface in the Ra plane. This fact can be applied to assign of optimal controller. Theoretical results were depicted by a numerical example.
基金supported by National Natural Science Foundation of China(Grant Nos.11271143,11371155 and 11326199)University Special Research Fund for Ph D Program(Grant No.20124407110001)+1 种基金National Natural Science Foundation of Zhejiang Province(Grant No.Y6110775)the Oxford-Man Institute of Quantitative Finance
文摘This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein(2002). The price is determined by two optimal stochastic control problems(mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations.By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates.The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.
文摘Considering the uncertainty of kelp-abalone-sea cucumber population, an interval model of carbon sink fisheries with multi-trophic levels is proposed. The equilibria of the model are identified and the corresponding stabilities are discussed. And the existence of bionomic equilibrium of the model is investigated. Next the optimal controller is designed to obtain the optimal harvest using Pontryagin＇s maximum principle. Numerical simulations are carried to prove the results.
