Dynamic Optimal Control Research Articles

Dynamic optimal control of flow front position in injection molding process: A control parameterization-based method

High dynamic and precise control of process variables within permissible limits is the key to high product quality in the injection molding industry. Among these variables, the injection flow rate of molten polymer is particularly significant. In this paper, an effective optimal open-loop and state feedback controller design method is designed to realize the optimal tracking control of the melt polymer flow front position flow of melt polymer fluid during injection molding. To this end, the dynamic model of the filling process is firstly established, taking into account the nonlinearity of hydraulic control system and the effect of molten polymer flow on the dynamics of the injection ram, and then the dynamic optimal tracking control problem of flow front position of molten polymer in injection molding machine is proposed. Then, an open-loop controller and a multi-level feedback control law are well designed, wherein the control signal and the control feedback kernels are parameterized by control parameterization. The controller design problems are transformed into sequential optimal parameter decision problems. The explicit expressions of the gradient information of the objective function and constraints on the parameters of the decision variables are solved by using the state sensitivity equation analysis method, and the gradient information is combined with the nonlinear programming algorithm to solve the optimization problems efficiently. Finally, the viability and effectiveness of the proposed design method are verified by numerical simulations.

Modeling and optimal control of the transmission dynamics of amebiasis

In this paper, the mathematical models for amebiasis are developed and presented. The first model considers the transmission dynamics of amebiasis coupled with two constant controls: treatment and sanitation. The next-generation matrix calculates the effective reproductive number, which is then used to assess model system stability. A sensitivity analysis is performed to determine the primary factors affecting disease transmission. Nonetheless, the results suggest that indirect transmission is more crucial than direct transmission in spreading disease. In addition, we extended the first model to incorporate time-dependent optimal control measures, namely community awareness, treatment, and sanitation. The aim was to reduce the number of infections emanating from interaction with carriers, infected people, and polluted environments while minimizing the expenses associated with adopting controls. The optimal control problem is solved by applying Pontryagin’s Maximum Principle and forward and backward-in-time fourth-order Runge–Kutta methods. The results indicate that an awareness program is optimal when a single control strategy is the only available option. However, when a combination of two controls is implemented, an approach combining awareness programs and treatment is shown to be optimal. Generally, the best strategy is implementing a combination of all three controls: awareness programs, sanitation, and treatment.

Adaptive signal light timing for regional traffic optimization based on graph convolutional network empowered traffic forecasting

With the acceleration of urbanization, urban traffic congestion is becoming more and more serious, in which the timing of signal lights for regional traffic optimization is particularly important. Since existing signal lights-based traffic optimization technologies, especially green wave, do not take the regional traffic follow into consideration, therefore not being efficient. Therefore, we propose Adaptive Signal Light Timing for Regional Traffic Optimization based on Graph Convolutional Network Empowered Traffic Forecasting. First, we propose a multi-intersection traffic flow prediction model, namely, A-GCN+ with an improved prediction accuracy of 6.3%, which utilizes the attention-aggregated graph convolutional neural networks (A-GCN) and temporal convolutional networks (TCN) to extract spatial and temporal features of the traffic flow. Second, we propose a dynamic regional traffic signal coordination optimization control method, which utilizes the predicted intersection approach traffic flow from A-GCN+ and combines it with the improved whale optimization algorithm (IWOA) to obtain the optimal solution for the regional average vehicle delay model. Finally, we propose a bidirectional green wave automatic control method for the main line, which utilizes the optimized results of dynamic regional traffic signal timing and employs a multi-strategy fusion graphical method to obtain the dynamic main line bidirectional green wave. Experimental results show that compared to the traditional graphical method, the multi-strategy fusion graphical method increases the green wave bandwidth by 20%. The mainline bidirectional green wave adaptive coordinated control method improves main line traffic efficiency by 32.3% and regional network traffic efficiency by 8.7%.

Dynamic behaviors and optimal control of a new delayed epidemic model

We are concerned in this paper with dynamic behaviors and an optimal control problem of a new delayed epidemic model. There are three major ingredients. The first one is the dynamic behaviors of the state system. The locally asymptotic stability of the disease-free equilibrium and the endemic equilibrium are investigated and the effect of time delay on stability is also discussed. It is also found that the Hopf bifurcation appears at a specific time delay. The second, which is the main new ingredient of this paper, is an optimal control problem. Applying vaccine strategy in the system, an optimal control problem is proposed to minimize the total number of infected individuals as much as possible, maximize the total number of the uninfected individuals, and reduce the total control cost. In view of Pontryagin’s maximum principle, the specific characteristics of the optimal control policy are given. The third ingredient is the numerical simulations of the theoretical results.

Dynamical behaviors and optimal control of delayed S2IS rumor propagation model with saturated conversion function over complex networks

Nowadays, online information is disseminated in multiple languages on different platforms, and research on the dissemination trend and control of online rumors is a topic worth discussing. In the bilingual environment, we study the S2IS rumor propagation model with time delay and saturated conversion function which implies the limitation of resources in homogeneous and heterogeneous networks. First and foremost, the analysis of the boundedness of the solutions and the existence of the rumor-spreading equilibrium points is given in our work, and we figure out the basic reproduction number. Next, we conduct the local stability analysis of the rumor-free equilibrium point and the rumor-spreading equilibrium points according to the characteristic equation. The global stability of the rumor-free equilibrium point is shown based on the Lyapunov stability theory. Besides, we study the forward and backward bifurcation phenomenon and optimal control problem in theory, which is seldom discussed in the bilingual environment. Finally, numerical simulations are performed to verify the correctness of our main results.

Promoting the Maneuverability and Fault-Tolerant Control Capabilities of Dual-System/Hybrid VTOL UAVs

This paper presents an active fault-tolerant flight control system (FCS) design for the dual-system/hybrid VTOL UAV configuration that maximally exploits its inherent over-actuation abilities to provide higher levels of fault-tolerance and reliability compared to that of the other VTOL UAVs configurations up to this point. The significance of this study is to convert the main drawback of having the vertical rotors as dead weights during the cruise to a key advantage where all the UAV's controls are kept active during all the flight phases raising the UAV's fault-tolerance and maneuverability abilities. The FCS proposed elaborates on a new architecture for the hierarchical automatic control loops using the dynamic inversion control to design the trajectory tracking virtual commands and employing optimal dynamic control allocation to optimally resolve the controls redundancy. Regarding fault-tolerance, the presented FCS handles simultaneous failures and jamming of all the control surfaces during flight where the control commands to the healthy controls (vertical rotors) were automatically adapted such that the trimming and trajectory tracking were successfully maintained till the mission end. Additionally, this paper addresses for the first time the employment of the controls redundancy to enhance the VTOL UAV's maneuverability in fault-free cases, where we present a study of reducing the minimum turn radius of the UAV when the vertical rotors are employed with the control surfaces during the maneuver. A reduction of 38% in the coordinated steady-level minimum turn radius turn at 35 m/sec flight speed was achieved.

Dynamical analysis and optimal control of a stochastic SIAR model for computer viruses

Dynamical analysis and optimal control of a stochastic SIAR model for computer viruses

Adaptive dynamic programming-based optimal control for nonlinear state constrained systems with input delay

Adaptive dynamic programming-based optimal control for nonlinear state constrained systems with input delay

Optimal Dynamic Control of an Epidemic

Optimal Dynamic Control of an Epidemic We analyze how to optimally engage in social distancing in order to minimize the spread of an infectious disease. We identify conditions under which any optimal policy first engages in increasingly more social distancing and subsequently decreases its intensity. We show that an optimal policy might substantially delay measures that decrease the transmission rate to create herd immunity and that engaging in social distancing suboptimally early can increase the number of fatalities. Finally, we find that optimal social distancing can be an effective measure to reduce the death rate of a disease.

Dynamic real-time energy saving control of pressure-swing distillation based on artificial neural networks

Parameter variation can increase economic costs and energy consumption in distillation process when disturbances occur. In this work, a dynamic optimization control model based on ANNs was developed. Composition disturbances in pressure-swing distillation with and without heat integration to separate isoamyl alcohol and toluene were regarded as the research object. The economic cost and energy consumption were effectively reduced by predicting the most optimal operating parameters during the disturbance process and controlling the process in real time. In the absence of heat integration, the energy consumption of the control structure based on ANNs (CS2) is reduced by 1.68% and 1.70% respectively compared to traditional control structure (CS1) during ± 20% composition disturbance. In partial heat integration, the energy consumption of the control structure based on ANNs (CS4) is reduced by 3.24% and 2.68% compared to traditional control structure (CS3). TAC is saved by 3.51% and 3.31% when reaching stability.

Dynamic game optimization control for shared energy storage in multiple application scenarios considering energy storage economy

In response to poor economic efficiency caused by the single service mode of energy storage stations, a double-level dynamic game optimization method for shared energy storage systems in multiple application scenarios considering economic efficiency is proposed in this paper. By analyzing the needs of multiple stakeholders involved in grid auxiliary services, fully tap into the profitability potential of energy storage stations. The capacity of the shared energy storage system is optimized by the non-dominant sorting beluga whale optimization algorithm (NSBWOA) in the upper level, and the operation strategy under multiple scenarios is optimized by the adaptive greedy search algorithm (AGSA) in the lower level. With the goal of maximizing the gross annual total income and high-value peak regulation ratio, and minimizing the cost- income ratio, the optimal capacity configuration and operation strategy of the shared energy storage system are obtained through collaborative optimization between upper and lower level models. The effectiveness of the proposed method is verified through the simulation testing of actual operating data of a certain power grid in China. Simulation results show that the gross annual income and high-value peak regulation ratio across multiple scenarios (Scenario III) are the highest, and the cost-income ratio is at an acceptable low level, which can provide a theoretical basis for the large-scale application of energy storage systems in new power systems.

Dynamic analysis and optimal control of a stochastic COVID-19 model

In this paper, we construct a stochastic SAIR (Susceptible–Asymptomatic–Infected–Removed) epidemic model to study the dynamic and control strategy of COVID-19. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. We prove the necessary conditions for the existence of extinction and ergodic stationary distribution by defining two new thresholds, respectively. Through the stochastic control theory, the optimal control strategy is obtained. Numerical simulations show the validity of stationary distribution and optimal control. The parameters of the model are estimated by a set of real COVID-19 data. And, the sensitivity of all parameters shows that decreasing physical interaction and screening the asymptomatic as swiftly as possible can prevent the wide spread of the virus in communities. Finally, we also display the trend of the epidemic without control strategies.

Dynamic multi-objective optimization and multi-units linear active disturbance rejection control for wastewater treatment processes

Wastewater treatment processes (WWTPs) are complex nonlinear systems with strong nonlinearity among many treatment units and disturbances including weather conditions, uncertainties, and time-varying dynamics. This paper studies the multi-objective and multi-units linear active disturbance rejection control for WWTPs to lower the overall cost index and enhance the effluent quality index simultaneously. A multi-objective optimization method using the multi-strategy mutation and the adaptive mechanism is employed to dynamically optimize set points. Then, multiple-units linear active disturbance rejection controllers are designed to achieve tracking control for dissolved oxygen concentration (including 3-5 units) and nitrate level with unmeasurable disturbances based on the optimal set points. The comparison experiments tested on the benchmark simulation model No. 1 demonstrate that the proposed method can improve the tracking performance and achieve a significant improvement in reducing the overall cost index and the effluent quality index.

Optimal operation of a process by integrating dynamic economic optimization and model predictive control formulated with empirical model

Optimal operation of a process by integrating dynamic economic optimization and model predictive control formulated with empirical model

Dynamic optimal control of coal chemical looping gasification based on process modeling and complex risk computation

The safe and steady running of coal chemical looping gasification system (CCLGS) is directly related to the whole production benefit. CCLGS is composed of dryer, pyrolyzer, decomposer, fuel reactor (FR), and air reactor (AR), which reflects the complexity of the entire production process. In this paper, a novel dynamic safety control strategy based on process modeling and complex risk computation is put forward to ensure the stable operation of CCLGS. First, the process modeling of CCLGS is carried out by Aspen Plus, and the obtained simulation results are in agreement with experimental results. Then, the CCLGS complex network is formed by constructing the adjacency matrix and calculating comprehensive indicator (Ci) value to evaluate the importance of the variables and support risk computation. Subsequently, the risk values of five units are computed based on the unit maximum material coefficient (UMMC), unit general risk coefficient (UGRC), and unit special risk coefficient (USRC). The results prove that FR and AR have higher risk grades than other units. Finally, dynamic control study for FR and AR processes is conducted with the aim of evaluating pressure controllers by safety integrity level. The research will provide beneficial approaches for the safety control of actual plant.

Optimal Determination and Dynamic Control Analysis of the Graded and Staged Drought Limit Water Level of Typical Plateau Lakes

The technical research on determining the drought limit water level can be used as an important basis for starting the emergency response of drought resistance in the basin and guiding the drought resistance scheduling of water conservancy projects. When the concept of drought limit water level was first proposed, the main research object was reservoirs, and the method for determining the lake drought limit water level was not established. Referring to the calculation method of reservoir drought limit water level, the drought limit water level is used as a single warning indicator throughout the year, which lacks graded and staged standards, and also lacks rationality and effectiveness in practical application. Therefore, this article has improved the concept of lake drought limit water level (flow). Under different degrees of drought and water use patterns during the drought period, combined with the characteristics of lake water inflow, considering the factors such as ecology, water supply, and demand, lake inflow, evapotranspiration loss, a graded and staged standard of lake drought limit water level has been developed. For different types of lakes, a general method for determining the lake’s graded and staged drought limit water level has been established. The SCSSA-Elman neural network is used to construct the medium and long-term water inflow prediction model for lakes, and the calculation results of this model are used for the warning and dynamic control analysis of the lake drought limit water level. The application of this method has the characteristics of strong applicability and high reliability. Finally, the determination method and dynamic control method of the lake’s graded and staged drought limit water level have been successfully applied at Dianchi Lake in Yunnan.

Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage.

African swine fever is a highly contagious virus that causes pig disease. Its onset process is short, but the mortality rate is as high as 100%. There are still no effective drugs that have been developed to treat African swine fever, and prevention and control measures are currently the best means to avoid infection in pig herds. In this paper, two fractional order mathematical models with media coverage are constructed to describe the transmission of African swine fever. The first model is a basic model with media coverage, and no control measures are considered. For this model, the reproduction number is obtained by using the next generation matrix method. Then, the sufficient conditions for the existence and stability of two equilibriums are obtained. Based on the first model, the second model is established incorporating two control measures. By using Pontryagin's maximal principle, the optimal control solution is derived. After that, some numerical simulations are performed for the two models to verify the theoretical results. Both the qualitative analysis and numerical results indicate that timely media coverage combined with disinfection control measures is crucial to preventing the spread of disease.

Dynamic Optimal Control for Wastewater Treatment Process Under Multiple Operating Conditions

Wastewater treatment process (WWTP) is operated with multiple conditions. Accurately identify these conditions and satisfy the different requirements are the keys to guarantee the optimal operation of WWTP. To solve this problem, a dynamic optimal control (DOC) strategy is designed in this paper. First, with the aid of the predicting models by adaptive fuzzy neural network for effluent nitrate and total nitrogen, different operating conditions can be identified. Corresponding to each condition, changing number of operating objectives are formulated to match the different requirements. Second, due to the changeable operating objectives can cause the expanded/contracted dimension of Pareto-optimal set, a dynamic multi-objective particle swarm optimization algorithm is developed. In this algorithm, self-adjusting mechanism of population size and global optimal solution are designed to derive the optimal solutions of control variables. Third, fuzzy controllers, matched with the different conditions, are designed to trace these optimal solutions. Finally, the effectiveness of DOC strategy is tested on a real WWTP. The results demonstrate that this proposed DOC strategy enables to achieve promising operating performance. <i>Note to Practitioners</i>&#x2014;This article aims to develop an optimal control strategy to match the multiple conditions and improve the operating performance. To achieve this goal, a dynamic optimal control (DOC) strategy, with the consideration of different operating conditions, is designed. Two key points are contained, the identification of multiple operating conditions and the satisfaction of different requirements. Due to each condition confronts with different requirements, it is important to accurately identify the conditions and construct the corresponding operating objectives. Based on the obtained operating data, changeable operating objectives are established to describe the different conditions. In addition, to satisfy the operating requirements, it is necessary to optimize the changeable objectives, but the changes in the number of objectives can cause the expanded/ contracted of Pareto-optimal set. A dynamic multi-objective particle swarm optimization algorithm, with self-adjusting mechanism of population size and global optimal solution, is designed to deal with this kind of optimization problem. The effectiveness and applicability of the proposed DOC strategy are evaluated on a pilot platform of a real WWTP, showing the improvement on the operating performance. These advantages can be valuable for transplanting this strategy to other real wastewater treatment plants to realize the optimal operation.

Mixed H 2/H ∞ Control With Dynamic Event-Triggered Mechanism for Partially Unknown Nonlinear Stochastic Systems

This technical note discusses the design process of dynamic event-triggered control (DETC) with the mixed <inline-formula> <tex-math notation="LaTeX">$H_2/H_\infty$</tex-math> </inline-formula> for partially unknown nonlinear stochastic systems. The purpose of this problem is to design a controller to make the closed-loop system achieve the expected <inline-formula> <tex-math notation="LaTeX">$H_2$</tex-math> </inline-formula> performance under the condition that the <inline-formula> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> continuous attenuation level is protected. Firstly, a two-player non-zero-sum game for stochastic system is given. Then we prove the optimal control strategy and the worst interference, which constitute the Nash equilibrium solution and can be derived from the corresponding Hamiltonian functions. Furthermore, two neural networks (NNs) are used to realize Nash equilibrium. Under the condition of dynamic event-triggered mechanism (DETM), the control strategy only is updated at the trigger moment. In addition, the stability and weights convergence of the system are proved mathematically. Finally, two numerical example are given to prove it. <i>Note to Practitioners</i>&#x2014;In the practice of control engineering, mixed <inline-formula> <tex-math notation="LaTeX">$H_2/H_\infty$</tex-math> </inline-formula> control can not only evaluate the <inline-formula> <tex-math notation="LaTeX">$H_2$</tex-math> </inline-formula> performance index of the transient behavior of the system, but also measure the <inline-formula> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> performance index of the system&#x2019;s robustness to external disturbances and parameter uncertainty. And many useful signals and interference vary randomly. Therefore, the optimal control of stochastic systems and dynamics play an important role in the modern industry. Saving control resources is very important for actual production. Therefore DETC is considered in this paper. On the other hand, in practice, accurate system models are difficult to obtain. In order to tackle this difficulty, by designing a novel scheme via integral reinforcement learning technique, the system relaxes the requirement of drift dynamic and Zeno behavior is avoided.

Dynamic analysis and optimal control of a novel fractional-order 2I2SR rumor spreading model

In this paper, a novel fractional-order 2I2SR rumor spreading model is investigated. Firstly, the boundedness and uniqueness of solutions are proved. Then the next-generation matrix method is used to calculate the threshold. Furthermore, the stability of rumor-free/spreading equilibrium is discussed based on fractional-order Routh–Hurwitz stability criterion, Lyapunov function method, and invariance principle. Next, the necessary conditions for fractional optimal control are obtained. Finally, some numerical simulations are given to verify the results.