Discrete Optimal Control Model Research Articles

Hurwicz criterion based optimal control model for uncertain descriptor systems with an application to industrial management

In this work, optimal control models subject to discrete and continuous uncertain descriptor systems are both investigated under Hurwicz criterion. At first, by employing dynamic programming method, a recurrence equation is obtained to simplify the discrete optimal control model, and a bang-bang control problem is settled according to this equation. Then, for the continuous optimal control model, an equation of optimality is proposed and testified with the help of uncertainty theory and the principle of optimality, revealing the internal connection between optimal control and optimal value. Finally, a numerical example and an industrial management model are provided to illustrate the validness of above results.

A discrete optimal control model for the distributed energy system considering multiple disturbance inputs

Distributed energy systems with the characteristics of flexible scheduling, high reliability, and high efficiency have been widely studied because it can absorb abundant renewable energy and solve long-distance energy transmission loss. Wind power, photovoltaic power, and user load power have obvious intermittently and volatility, which brings difficulties to the dispatching and control of distributed energy systems. This work focuses on the optimal control problem of a distributed energy system considering multiple disturbance inputs. A discrete system model suitable for developing optimal control is established and solved by minimizing performance function in the process of iterating disturbance inputs and its function vector. Based on the optimal control results, a method for stabilizing the output power is designed to consider operating cost and loss. The effectiveness of the proposed method is verified by different disturbance inputs and compared with the classical optimization algorithm. The results indicate that the optimal control model can effectively suppress disturbance influences and obtain a fast and satisfactory control effect. The output stabilization method can save operating costs and reduce equipment loss. Compared with the optimization algorithm, the proposed method is more stable and reliable. This work provides a new insight into multi-disturbance suppression of the distributed energy systems.

Digital twin of mechatronic drive based on the optimal control model of BLDC motor

This paper presents a digital twin of a mechatronic drive based on a brushless DC (BLDC) motor model based on a nonlinear discrete optimal control model. Some parameters of a BLDC motor, such as resistance and inductance of windings, magnetic flux, viscous friction coefficient in bearings, angular velocity and electromagnetic moment, can change due to both degradation of structural elements and external forces. Simulation by a complete enumeration of the values of the parameters of the mechatronic device with a certain step will make it possible to adapt the program of the control device to changing operating conditions according to the criterion of minimizing the control energy by changing the parameters of the state matrices and control of the digital twin. As a result, the accuracy of the movement of the mechatronic device along the given trajectory will increase due to the greater correspondence of the control parameters to the real object.

Optimizing the management of uneven-aged Pinus nigra stands between two stable positions

This study proposes a discrete optimal control model to obtain harvest strategies that maximize the net present value (NPV) of the timber harvested from uneven-aged Pinus nigra stands located in the Spanish Iberian System, between two stable positions. The model was constructed using an objective function that integrates financial data on the harvesting operations with a matrix model describing the population dynamics. The initial and final states are given by the stable diameter distribution of the stand, and the planning horizon is 70 years. The scenario analysis corresponding to the optimal solutions revealed that the stand diameter distribution does not deviate substantially from the equilibrium position over time and that the NPV for the optimal harvesting schedule was always greater than the NPV for the “sustainable/stable” harvesting strategy. The NPV increase for the different scenarios is between 5.36% and 14.43%, showing a greater increase in higher site index scenarios and higher recruitments.

Are the Economically Optimal Harvesting Strategies of Uneven-Aged Pinus nigra Stands Always Sustainable and Stabilizing?

Traditional uneven-aged forest management seeks a balance between equilibrium stand structure and economic profitability, which often leads to harvesting strategies concentrated in the larger diameter classes. The sustainability (i.e., population persistence over time) and influence of such economically optimal strategies on the equilibrium position of a stand (given by the stable diameter distribution) have not been sufficiently investigated in prior forest literature. This article therefore proposes a discrete optimal control model to analyze the sustainability and stability of the economically optimal harvesting strategies of uneven-aged Pinus nigra stands. For this model, we rely on an objective function that integrates financial data of harvesting operations with a projection matrix model that can describe the population dynamics. The model solution reveals the optimal management schedules for a wide variety of scenarios. To measure the distance between the stable diameter distribution and the economically optimal harvesting strategy distribution, the model uses Keyfitz’s delta, which returns high values for all the scenarios and, thus, suggests that those economically optimal harvesting strategies have an unstabilizing influence on the equilibrium positions. Moreover, the economically optimal harvesting strategies were unsustainable for all the scenarios.

Discrete optimal control model and bound error for microbial continuous fermentation

A discrete optimal control model is given according to the discrete nonlinear dynamic system of continuous fermentations of glycerol to 1,3-propanediol (1,3-PD). The property of some major functions and their bounds on approximation errors are studied in this paper. Then, the conclusion that the optimality function of discrete optimal control model is the consistent approximation to one of the continuous optimal control model is proved. The results presented in this work can be used as guidelines for the optimal algorithm and its convergence.

OPTIMAL INJECTION STRATEGIES FOR POLYMER FLOODING USING IMPLICIT DISCRETE MAXIMUM PRINCIPLE

In order to maximize the profits gained from oil recovery of polymer flooding, a discrete optimal control model is established for determining the best injection concentrate of polymer solution.The discrete states equations are obtained from continuous model of polymer flooding by full implicit difference schemes.The necessary conditions of the optimal control problem are derived from implicit discrete maximum principle.A gradient based algorithm is presented to solve the problem numerically,in which the coefficient matrices of adjoint equations are directly constructed during the solution of states equations.A polymer flooding simula- tion example of three-dimensional model shows the practicality and efficiency of the proposed approach.

A Discrete Optimal Control Model of Human Response

A quantitative discrete optimal control model is developed for the response characteristics of the human operator. This model considered human’s inherent psychogical refractory and sampling behavior that reflects intelligent feature. It is an open–loop, closed–loop control system. This control behavior is in accordance with human’s physiology and psychology characteristics. So it has strong explanation ability. Comparison is made between the model predictions and experimental data. The result shows that the model agrees with the experiment It is shown the discrete model is the same as the continuous model when sampling intervals tend to zero.

Economics of water allocation to instream uses in a fully appropriated river basin: Evidence from a New Mexico wild river

In fully appropriated multiple‐use river basins, a major potential competitor for a share of water may be publicly sponsored appropriations to supplement low streamflows for fish, wildlife, and recreation, which generates economic values not revealed in the marketplace. Based on a survey of instream recreationists on New Mexico's Rio Chama a travel cost model is developed to identify the potential recreation demand for instream flows. A discrete optimal control model is formulated that solves for the intraseasonal allocation of reservoir releases which maximizes the yearly value of instream recreation benefits, net of values of competing uses in the basin. Results indicate that in New Mexico, reservoir releases which augment low streamflows can return gross recreation benefits in the range of $900 to $1100 per acre‐foot (ac ft) of water consumed (1 ac ft = 1.233 × 10 3 m3). This compares to a $40/ac ft cost of using the water. Consequently, results strongly support the hypothesis of potential economic payoff from public investments in and management of instream flow reservations.