Dynamic Optimal Control Strategy Research Articles

Synthesis of dynamic modelling framework and optimal control strategy for virtually coupled train sets with guaranteed safety

Virtual coupling represents a novel railway operational mechanism, wherein several trains share state information and adjust their behaviours based on control objectives, which include safety (collision avoidance) assurance and stability (uniform velocity and constant spacing between trains) maintenance. However, the conflict between safety and stability requirements becomes more apparent, as the closer spacing between trains. Moreover, the hybrid nature of the train platoon operation, which involves both discrete events and continuous dynamics, also poses a significant barrier to the control strategy synthesis. This paper presents the Virtually Coupled Train Sets (VCTS) dynamic modelling framework and strategy synthesis approach to address these problems. A Hybrid Markov Decision Process (HMDP) is adopted for relative longitudinal dynamics modelling of trains, considering the influence of the uncertainty dynamic of trains ahead. A Stackelberg game-based strategy synthesis algorithm is applied for the safe guarantee by overcoming the uncertainty, and a Q-learning method is used for stability strategy selection from the safe strategy. The results showed a 17.95% expansion in the safe state space when compared to the general relative braking scheme (which assumes maximal acceleration during the delay horizon). In a four-train tracking operation scenario, compared with Q-learning without safe constraints, our approach gives similar stability performance; compared with Q-learning with general relative braking safe constraints, our approach not only assurance safety but has a better stability performance.

Dynamic analysis and optimal control strategies of a predator–prey mathematical model for the pest eradication in oil palm plantation

Oil palm cultivation stands as a crucial industry in Indonesia, significantly contributing to the nation’s economy by generating employment opportunities and fostering social welfare for communities residing near plantations. Despite its economic importance, oil palm plantations face various challenges, with one prominent issue being the infestation of nettle caterpillar pests. These pests cause leaf skeletonization, resulting in a staggering 36% reduction in oil palm productivity over a two-year period. This paper explores diverse strategies for pest management in oil palm plantations, encompassing biological control through the stimulation of natural predators, mechanical control involving the collection and incineration of cocoons, and chemical control through pesticide application. The research introduces a predator–prey mathematical model for oil palm plantation pests, where the leaf area serves as the primary food source for caterpillars, acting as prey. Through dynamic model analysis, four equilibrium points are identified, with interconnected conditions dictating their existence and stability. These conditions are visually represented in a bifurcation plane, providing concise information. The study further includes bifurcation diagrams of equilibrium points to elucidate the influence of each parameter on pests, predators, and the leaf area of oil palm plants. Additionally, sensitivity analysis of the stable interior equilibrium point is conducted to understand the impact of individual parameters. The paper extends its investigation to optimal control strategies, evaluating six scenarios categorized into two population conditions: with predators and without predators. Within each population condition, three control strategies are considered—chemical control only, mechanical control only, and a combination of chemical and mechanical control. Simulation results from the optimal control study reveal that the presence of natural predators emerges as a pivotal strategy in effectively managing nettle caterpillars. Notably, the control of resistant pests through pupa incineration has a substantial impact on reducing the caterpillar population in subsequent life cycles.

Dynamic optimal control strategy for distributed electric heating system under electricity pricing lever

To address wind curtailment, a method is proposed to improve wind power consumption by controlling user demand response. Considering residents’ comfort demand for heating in winter, a distributed electric heating system is established and an optimal control model is established to enhance wind power consumption capacity. By considering the influence of electricity price and comparing the optimal model under basic tariffs, time-of-use and real-time tariffs, a dynamic optimal control method for distributed electric heating systems driven by electricity price leverage is proposed. The simulation results show that the method can effectively guide electric heating users to actively participate in load regulation, significantly improve wind curtailment and ensure economic and stable power grid operation. Using different electricity prices as leverage can systematically incorporate a large number of distributed electric heating users into the controllable load of wind power consumption, providing a new method for large-scale wind power consumption.

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.

Droop control strategy for microgrid inverters: A deep reinforcement learning enhanced approach

To better tap into the potential of distributed renewable energy generation, microgrid system has become an emerging technology. As the bridge of microgrids, the inverters can flexibly convert distributed DC power input into AC power output. It is verified that the traditional droop control strategy for microgrid inverters has inherent defects of uneven reactive power distribution. To this end, this paper proposes a droop control strategy as a multi-objective optimization problem while considering the deviations of bus voltage and reactive power distributions of microgrids. Then, the optimization problem is further formulated as a Markov decision process and solved by a deep reinforcement learning (DRL) algorithm called deep deterministic policy gradient to obtain a dynamic optimal droop coefficient control strategy. Simulation results demonstrated that our DRL-based strategy eliminates the uneven reactive power distribution without voltage drop.

Two-level optimal scheduling method for a renewable microgrid considering charging performances of heat pump with thermal storages

Combining compression heat pump with thermal energy storage (HPTES) allows the shifting of heat demand to off peak periods or periods with surplus renewable electricity. However, it is not clear that how the charging performances (efficiency, charging time and supply water temperature) of HPTES affect the optimal coordinated scheduling of a renewable microgrid. In this study, we proposed a two-level scheduling optimization method for a renewable grid-connected microgrid considering charging performances of heat pump with thermal storages. This method is based on an integrated nonlinear dynamic model of a renewable microgrid including photovoltaic/wind power generator, buildings and HPTES; and the time lag in energy conversion and transport process was considered. Level I in this method is for the scheduling optimization of HPTES, three different model-based dynamic optimal control strategies were developed for the charging process of HPTES to supply domestic hot water and floor radiant heating in buildings. It's found that coefficient of performance (COP) of HPTES during charging varies with the charging time and the supply water temperature. Thus at the level II, a half-hourly time interval was proposed for the optimal scheduling of microgrid, through which a hybrid charging time scheduling can be applied to the optimal control of HPTES for different supply water temperatures. Based on the microgrid model integrating different optimal control strategies of HPTES, different dynamic optimal coordinated scheduling were developed for the microgrid in three scenarios. It can be found that the charging performances of HPTES affect the optimal coordinated scheduling of heat supplies from heat pump and TES in a microgrid significantly, and heat production rates vary with time differently under different operation scheduling of a microgrid. The proposed optimal half-hourly scheduling method with hybrid charging time of HPTES leads to the reduction of the overall operating cost including the penalty cost for the microgrid, and the increase of domestic hot water temperature up to the required value. This study would be useful for the optimal scheduling of a renewable microgrid containing HPTES at a low cost in practice.

Fault-Tolerant Optimal Control for Discrete-Time Nonlinear System Subjected to Input Saturation: A Dynamic Event-Triggered Approach.

This paper investigates the dynamic event-triggered fault-tolerant optimal control strategy for a class of output feedback nonlinear discrete-time systems subject to actuator faults and input saturations. To save the communication resources between the sensor and the controller, the so-called dynamic event-triggered mechanism is adopted to schedule the measurement signal. A neural network-based observer is first designed to provide both the system states and fault information. Then, with consideration of the actuator saturation phenomenon, the adaptive dynamic programming (ADP) algorithm is designed based on the estimates provided by the observer. To reduce the computational burden, the optimal control strategy is implemented via the single network adaptive critic architecture. The sufficient conditions are provided to guarantee the boundedness of the overall closed-loop systems. Finally, the numerical simulations on a two-link flexible manipulator system are provided to verify the validity of the proposed control strategy.

Structure and control co-optimization for an ejector expansion heat pump coupled with thermal storages

Optimal design and control are often coupled tasks for improving energy system performances. There is a lack of study on the structure and control co-optimization of heat pump coupled with thermal energy storages, which can enhance the penetration levels of intermittent renewables in integrated energy systems, thus we proposed a coupled dynamic optimization method for the structure and control co-optimization of this kind of dynamic energy system, and applied it successfully to a transcritical CO2 ejector expansion heat pump coupled with hot and cold water storages for thermal energy charging. Based on a complicated nonlinear dynamic system model considering thermal stratification in thermal energy storages, the structure and control co-optimization solutions were obtained for this coupled system during energy charging by using the co-optimization method with genetic algorithm. The detailed structures of gas cooler, evaporator, hot and cold energy storage tanks were optimized, then a dynamic optimal control strategy was developed for the whole charging process. The overall coefficient of performance can be increased by 23.2% and the total power consumption can be reduced by 17.6% using this newly developed co-optimization strategy, compared to the constant control parameter strategy. This study would be helpful for a structure and control co-optimization of other dynamic or stable energy systems.

Multi-objective non-simultaneous dynamic optimal control for an ejector expansion heat pump with thermal storages

This study is to enhance the overall performances of a transcritical CO2 heat pump coupled with hot and cold thermal energy storages (HPTES) during energy charging by using a controllable ejector to replace an expansion valve (ExV) in heat pump and a new multi-objective non-simultaneous dynamic optimization strategy. A Modelica-based dynamic simulation model was developed and validated for an ejector expansion CO2 heat pump with thermal storages during charging process, and a model-based multi-objective non-simultaneous dynamic optimization strategy was proposed. Under a single-objective dynamic optimal control strategy, the overall coefficient of performance (COP) can be increased 22.0%, energy consumption can be reduced 17.3%, and charging time can be reduced significantly during charging process of thermal storages by using an ejector expansion heat pump compared to an ExV heat pump. Charging performances of the ejector HPTES system can be enhanced further by using a multi-objective non-simultaneous dynamic optimal control strategy, in which multiple transient performance parameters of the HPTES system, instead of energy consumption and cost as in the literature, were used as multi-objective functions. The mechanisms of dynamic performance enhancements of an ejector HPTES were revealed. This study would be useful for a dynamic optimal control of other coupled energy systems under unsteady conditions.

Dynamic modelling and optimal control strategies for chemical-looping combustion in an industrial-scale packed bed reactor

The transient operation of a Chemical-looping Combustion (CLC) process in a large-scale packed bed reactor (PBR) unit is presented in this study. This work adapts 1-D heterogeneous dynamic model that considers mass and heat transport resistances in the oxygen carrier particle and the bulk fluid phase. The proposed industrial-scale model was compared using data available in the open literature and was used to study optimal control strategies that can increase power production and reduce fuel slip during the oxidation and reduction stages of this process, respectively. Moreover, promising (optimistic) and pessimistic (worst-case) scenarios were considered for this process and used to demonstrate the operational flexibility of the packed bed reactor under different process operating conditions. Results from these scenarios show an extensive recovery heat process and a near full methane conversion into CO2 and H2O during the oxidation and reduction stages, respectively. Similarly, the purge stages were performed relatively fast using low amounts of purge gas. Therefore, the present study bolsters the importance of the CLC PBR process as an attractive carbon capture and sequestration (CCS) technology that can potentially reduce the energy penalty often entailed in CO2 capture and sequestration.

A differential game approach to dynamic optimal control strategies for watershed pollution across regional boundaries under eco-compensation criterion

In recent years, transboundary pollution reflected by watershed pollution has emerged in an endless stream, manifesting as the overflow phenomenon of one-way or crossing between river basins. Such pollution significantly seriously affects the inherent requirements for achieving regional sustainable and coordinated development in China. By introducing the eco-compensation criterion, a cross-regional boundaries pollution abatement differential game model covering upstream and downstream regions in a continuous time is established. Subsequently, the optimal control theory is adopted by maximizing the net present value of river basin welfare to explore relevant optimal feedback equilibriums on the overall watershed environmental quality under the Stackelberg and cooperative game contracts. Eventually, a case study of Xiang Jiang River Basin (XJRB) in Hunan Province of China serves to verify the practicable effectiveness of the foregoing model combined with numerical simulation and support key insights as below: (i) the watershed environmental degradation cost factor as well as the payoff factor possess significant impact on emission capacities of upstream and downstream; (ii) the optimal trajectory of pollutant stock in the downstream affected by the upstream pollutant stock and pollution transfer coefficient is higher than that in the upstream; (iii) the setting of eco-compensation criterion can effectively stimulate upstream governments to invest more in environmentally friendly technologies; and (iv) the joint decisions of the two game parties improve the total welfare level of both river basin regions. Findings present an efficient approach for the design of environmental policies addressing conflicts over water pollution across regional boundaries.

Research on dynamic optimal control strategy of distributed super capacitor energy storage system based on convolution neural network

SummaryCompared with other modes of transport, urban rail transit has significant advantages such as large capacity, punctual safety, energy saving, and environmental protection. For pure electric buses, the problem of slow start, large battery energy loss, short battery life, and insufficient recovery of braking energy is caused by the use of single energy only. The power battery and super capacitor are combined to form a compound power supply to solve the problem. In order to improve the feature extraction ability of convolution neural networks, a deep convolution neural network model based on continuous convolution is designed. The model uses small scale convolution kernel to extract local features more carefully, and increases the nonlinear expression ability of the model by means of two continuous coiling layers. Dropout technology is used to reduce the interdependence between neurons, and the model is optimized by suppressing network overfitting. If the battery and the supercapacitor are combined to form a dual energy source system, it can not only meet the instantaneous high power demand of the electric vehicle but also prolong the life of the battery. Increasing the mileage of electric vehicles has become the development direction of pure electric vehicles. Due to its fast charging and discharging speed, long cycle life, and friendly environment, supercapacitor has unique advantages and development prospects in solving the problem of urban rail transit regeneration failure, performance analysis, modeling, and parameter identification of ultracapacitor. The performance of ultracapacitor is analyzed, and an improved dynamic equivalent circuit model of ultracapacitor is established. Therefore, this paper studies the control strategy of dual energy source storage system and the driving range of the dual energy source pure electric vehicle, which has a broad application prospect and practical significance.

Sensitivity of joint contagiousness and susceptibility-based dynamic optimal control strategies for HIV prevention.

Predicting the population-level effects of an infectious disease intervention that incorporate multiple modes of intervention is complicated by the joint non-linear dynamics of both infection transmission and the intervention itself. In this paper, we consider the sensitivity of Dynamic Optimal Control Profiles (DOCPs) for the optimal joint investment in both a contagiousness and susceptibility-based control of HIV to bio-behavioral, economic, and programmatic assumptions. The DOCP is calculated using recently developed numerical algorithms that allow controls to be represented by a set of piecewise constant functions that maintain a constant yearly budget. Our transmission model assumes multiple stages of HIV infection corresponding to acute and chronic infection and both within- and between-individual behavioral heterogeneity. We parameterize a baseline scenario from a longitudinal study of sexual behavior in MSM and consider sensitivity of the DOCPs to deviations from that baseline scenario. In the baseline scenario, the primary determinant of the dominant control were programmatic factors, regardless of budget. In sensitivity analyses, the qualitative aspects of the optimal control policy were often robust to significant deviation in assumptions regarding transmission dynamics. In addition, we found several conditions in which long-term joint investment in both interventions was optimal. Our results suggest that modeling in the service of decision support for intervention design can improve population-level effects of a limited set of economic resources. We found that economic and programmatic factors were as important as the inherent transmission dynamics in determining population-level intervention effects. Given our finding that the DOCPs were robust to alternative biological and behavioral assumptions it may be possible to identify DOCPs even when the data are not sufficient to identify a transmission model.

Model-based Dynamic Optimal Control of an Ejector Expansion CO2 Heat Pump Coupled with Thermal Storages

This study presents a model-based dynamic optimization strategy for charging of hot and cold thermal storages with a dual-mode CO2 ejector expansion heat pump, which could be used as a high-efficiency smart grid enabling option in heating and cooling services for buildings or industry. The dynamic model of this coupled system was developed by Modelica. The outlet water temperatures of hot and cold tanks are used as indicators in dynamic optimal control strategy. To optimize the overall performances during energy process, the transient performances are optimized by genetic algorithm based on dynamic model of system. Single-objective and multi-objective dynamic optimal control strategies were developed and applied for this system. Study results show that these two developed model-based dynamic optimal control strategies can optimize the overall performances of such coupled systems during energy charging. Compared with the control strategy with constant control parameters, these two dynamic optimal control strategies can be useful in the coordinative optimization of multiple control parameters, and multi-objective dynamic optimal control strategy is superior to the single-objective one.

Model-based dynamic optimal control of a CO2 heat pump coupled with hot and cold thermal storages

This study presents a model-based dynamic optimization strategy for a dual-mode CO2 heat pump coupled with hot and cold thermal storages, which was proposed as a high-efficiency smart grid enabling option in heating and cooling services for buildings or industry. Dynamic optimal control for simultaneously charging of hot and cold thermal storages is very delicate. The optimal control of compressor discharge pressure were commonly used for optimal control of heat pump systems. In this study, the outlet water temperatures of hot and cold tanks are used as indicators in the dynamic optimal strategy for charging of hot and cold storages using a dual-mode heat pump. The Modelica based dynamic model of the coupled system was developed and validated. To optimize the overall coefficient of performance (COP) during energy process, the transient total COP is optimized by genetic algorithm based on Modelica-based modeling of dynamic system. A dynamic optimal control strategy was developed and implemented into an experimental system. Test results show that this developed model-based dynamic optimal control strategy is able to search the optimal transient total COP and optimize the overall COP of such coupled systems during energy charging; and the optimal results is better than those obtained using another two experiment-based methods.

Control Strategy of BESS in Photovoltaic Station based on Power Forecasting

With the improvement of the very short term photovoltaic power forecasting, a new dynamic optimal control strategy for BESS based on the photovoltaic power forecasting is proposed to smooth photovoltaic power fluctuations. The operating rules are proposed based on the forecasted photovoltaic power information to minimize the offset of SOC as well as considering the performance of the energy storage to get the optimal control for the next control step, which result in a progressive control principle. The proposed method is verified by the actual data from photovoltaic station.

A Dynamic Programming-Based Control Strategy with Optimum Efficiency of Hybrid Energy Storage System for HEV

A reasonable and effective control strategy for HEV (Hybrid Electric Vehicle) with HESS (Hybrid Energy Storage System) can improve the system efficiency and battery service life. A dynamic programming-based global optimal control strategy which fully considered the efficiency of each component in HEV is presented. To compare with the nonlinear proportion factor dynamic coordination strategy, the fuel consumption is not increased. The cycle numbers of battery are further decreased which benefits its cycle life improvement. The regenerative energy callback ratio improves 3% under the shanghai drive cycle as an example. Since this optimization algorithm considers efficiency of each subsystem, the efficiency optimum under the selected driving cycle was realized. It can also provide a reference for the non-linear scaling factor allocation strategies to determine the scale factors.

Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles

Organic Rankine Cycles (ORCs) are particularly suitable for recovering energy from low-grade heat sources. This paper describes the behavior of a small-scale ORC used to recover energy from a variable flow rate and temperature waste heat source. A traditional static model is unable to predict transient behavior in a cycle with a varying thermal source, whereas this capability is essential for simulating an appropriate cycle control strategy during part-load operation and start and stop procedures. A dynamic model of the ORC is therefore proposed focusing specifically on the time-varying performance of the heat exchangers, the dynamics of the other components being of minor importance. Three different control strategies are proposed and compared. The simulation results show that a model predictive control strategy based on the steady-state optimization of the cycle under various conditions is the one showing the best results.

Cost-effective management of invasive species using linear-quadratic control

Abstract The removal of invasive species is the first step toward restoring an ecosystem following invasion. We develop spatially-explicit, dynamic optimal control strategies for a large class of invasion problems using linear-quadratic control. This approach allows us to produce new insights that help guide policy that could not have emerged from existing models. We assume adults are sedentary, and heterogeneous patches are connected via dispersal of offspring. We develop a generalized approach to optimally manage species across time and space and apply the framework to several examples, primarily based on Spartina alterniflora . General conclusions are drawn and we show that strong connectivity makes invasive control much more costly, demonstrating that reducing connectivity can be a cost-effective part of invasive species control.

System dynamic modeling and optimal torque control strategy for E.T.Driver based on AMT

Hybrid power system is one of the kernel technologies of hybrid electric vehicles (HEV). The performance of HEV is determined greatly by the hybrid power system. The integrative hybrid power system...