Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programmin...Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined.展开更多
A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker ty...A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions.展开更多
Persistent low temperatures in autumn and winter have a huge impact on crops,and greenhouses rely on solar radiation and heating equipment to meet the required indoor temperature.But the energy cost of frequent operat...Persistent low temperatures in autumn and winter have a huge impact on crops,and greenhouses rely on solar radiation and heating equipment to meet the required indoor temperature.But the energy cost of frequent operation of the actuators is exceptionally high.The relationship between greenhouse environmental control accuracy and energy consumption is one of the key issues faced in greenhouse research.In this study,a non-linear model predictive control method with an improved objective function was proposed.The improved objective function used tolerance intervals and boundary constraints to optimize the objective evaluation.The nonlinear model predictive control(NMPC)controller design was based on the wavelet neural network(WNN)data-driven model and applied the interior point method to solve the optimal solution of the objective function control,thus balancing the contradiction between energy consumption and control precision.The simulation results showed that the improved NMPC method reduced energy consumption by 21.02%and 9.54%compared with the model predictive control and regular NMPC,which proved the method achieved good results in a low-temperature environment.This research can provide an important reference for the field as it offers a more efficient approach to managing greenhouse climates,potentially leading to substantial energy savings and enhanced sustainability in agricultural practices.展开更多
This paper provides a solution to generalize the integrator and the integral control action. It is achieved by defining two function sets to generalize the integrator and the integral control action, respectively, res...This paper provides a solution to generalize the integrator and the integral control action. It is achieved by defining two function sets to generalize the integrator and the integral control action, respectively, resorting to a stabilizing controller and adopting Lyapunov method to analyze the stability of the closed-loop system. By originating a powerful Lyapunov function, a universal theorem to ensure regionally as well as semi-globally asymptotic stability is established by some bounded information. Consequently, the justification of two propositions on the generalization of integrator and integral control action is verified. Moreover, the conditions used to define the function sets can be viewed as a class of sufficient conditions to design the integrator and the integral control action, respectively.展开更多
In this paper, a class of fire-new general integral control, named general concave integral control, is proposed. It is derived by normalizing the bounded integral control action and concave function gain integrator, ...In this paper, a class of fire-new general integral control, named general concave integral control, is proposed. It is derived by normalizing the bounded integral control action and concave function gain integrator, introducing the partial derivative of Lyapunov function into the integrator and originating a class of new strategy to transform ordinary control into general integral control. By using Lyapunov method along with LaSalle’s invariance principle, the theorem to ensure regionally as well as semi-globally asymptotic stability is established only by some bounded information. Moreover, the highlight point of this integral control strategy is that the integrator output could tend to infinity but the integral control action is finite. Therefore, a simple and ingenious method to design general integral control is founded. Simulation results showed that under the normal and perturbed cases, the optimum response in the whole domain of interest can all be achieved by a set of the same control gains, even under the case that the payload is changed abruptly.展开更多
文摘Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined.
文摘A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions.
基金supported by the National Natural Science Foundation of China(Grant.No.31901400)the Fundamental Research Funds for the Provincial Universities of Zhejiang(Grant.No.2023YW09).
文摘Persistent low temperatures in autumn and winter have a huge impact on crops,and greenhouses rely on solar radiation and heating equipment to meet the required indoor temperature.But the energy cost of frequent operation of the actuators is exceptionally high.The relationship between greenhouse environmental control accuracy and energy consumption is one of the key issues faced in greenhouse research.In this study,a non-linear model predictive control method with an improved objective function was proposed.The improved objective function used tolerance intervals and boundary constraints to optimize the objective evaluation.The nonlinear model predictive control(NMPC)controller design was based on the wavelet neural network(WNN)data-driven model and applied the interior point method to solve the optimal solution of the objective function control,thus balancing the contradiction between energy consumption and control precision.The simulation results showed that the improved NMPC method reduced energy consumption by 21.02%and 9.54%compared with the model predictive control and regular NMPC,which proved the method achieved good results in a low-temperature environment.This research can provide an important reference for the field as it offers a more efficient approach to managing greenhouse climates,potentially leading to substantial energy savings and enhanced sustainability in agricultural practices.
文摘This paper provides a solution to generalize the integrator and the integral control action. It is achieved by defining two function sets to generalize the integrator and the integral control action, respectively, resorting to a stabilizing controller and adopting Lyapunov method to analyze the stability of the closed-loop system. By originating a powerful Lyapunov function, a universal theorem to ensure regionally as well as semi-globally asymptotic stability is established by some bounded information. Consequently, the justification of two propositions on the generalization of integrator and integral control action is verified. Moreover, the conditions used to define the function sets can be viewed as a class of sufficient conditions to design the integrator and the integral control action, respectively.
文摘In this paper, a class of fire-new general integral control, named general concave integral control, is proposed. It is derived by normalizing the bounded integral control action and concave function gain integrator, introducing the partial derivative of Lyapunov function into the integrator and originating a class of new strategy to transform ordinary control into general integral control. By using Lyapunov method along with LaSalle’s invariance principle, the theorem to ensure regionally as well as semi-globally asymptotic stability is established only by some bounded information. Moreover, the highlight point of this integral control strategy is that the integrator output could tend to infinity but the integral control action is finite. Therefore, a simple and ingenious method to design general integral control is founded. Simulation results showed that under the normal and perturbed cases, the optimum response in the whole domain of interest can all be achieved by a set of the same control gains, even under the case that the payload is changed abruptly.
