Equilibrium Control Strategies Research Articles

Adversarial Multiagent Output Containment Graphical Game With Local and Global Objectives for UAVs

Multiple leader and follower graphical games constitute challenging problems for aerospace and robotics applications. One of the challenges is to address the mutual interests among the followers with an optimal control point of view. In particular, the traditional approaches treat the output containment problem by introducing selfish followers where each follower only considers their own utility. In this article, we propose a differential output containment game over directed graphs where the mutual interests among the followers are addressed with an objective functional that also considers the neighboring agents. The obtained output containment error system results in a formulation where outputs of all followers prove to converge to the convex hull spanned by the outputs of leaders in a game optimal manner. The output containment problem is solved using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr{H}_\infty$</tex-math></inline-formula> output feedback method, where the new necessary and sufficient conditions are presented. Another challenge is to design distributed Nash equilibrium control strategies for such games, which cannot be achieved with the traditional quadratic cost functional formulation. Therefore, a modified cost functional that provides both Nash and distributed control strategies in the sense that each follower uses the state information of its own and neighbors is presented. Furthermore, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr{L}_{2}$</tex-math></inline-formula> gain bound of the output containment error system that experiences worst-case disturbances with respect to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr{H}_\infty$</tex-math></inline-formula> criterion is investigated. The proposed methods are validated by means of multiagent quadrotor unmanned aerial vehicles output containment game simulations.

Coupling analysis between cost and carbon emission of bamboo building materials: A perspective of supply chain

Bamboo building materials with carbon storage potential are considered to be the key to low carbon emissions and sustainable development in the construction industry. However, the willingness to pay and the carbon storage effect of bamboo materials still face major obstacles, and the supply chain needs to be optimised as it affects the economic and green benefits of bamboo building materials. This study aims to investigate the carbon emission and cost distribution of bamboo building materials, analyse the key influencing factors and propose an equilibrium optimisation strategy. Results indicate that ‘Carbonisation’, ‘Glue application’ and ‘anti-mould, anti-corrosion and drying’ in the production phase are the major contributors to carbon emissions, which are mainly generated by biomass fuel carbonisation kiln, adhesives and anti-mould preservatives. ‘Transportation from front-end factory to back-end factory” and ‘Transportation from back-end factory to construction site” in the supply phase are the largest obstacles to cost, and transportation distance is the key factor. The results were accepted by the manufacturer and facilitated the screening of the best equilibrium control strategy: clean energy replacement, use of new adhesives and anti-mould products and adjustment of transport distances. After the implementation of the optimisation strategy, carbon emissions were reduced by 40.10% and costs were reduced by 35.31%, indicating that the effect of the optimisation strategy is obvious. This study explores the carbon reduction potential of bamboo building materials, provides actionable guidance for producers of building materials and architects, and promotes the willingness of society to accept payment.

Research on Equalization Control Strategy of Marine Lithium Battery Pack

With the widespread use of clean energy in ship electric power systems, marine lithium battery systems are becoming more and more popular. Aiming at the problems between the individual cells in the lithium battery pack, such as inconsistency in voltage, capacity, and internal resistance, the state of charge (SOC) of battery is selected as the equalization control variable, an equalization topology structure based on SOC for battery connecting or bypassing is designed. The equilibrium control strategy fusing model predictive control (MPC) algorithm and time-sequence control algorithm is adopted. The simulation model is built on the MATLAB/Simulink platform, and the different value combinations of two equalization parameters (i.e., equalization period T and number of batteries connected to the battery pack q) were simulated and analyzed. The results show that the designed equalization control strategy can quickly and accurately achieve SOC equalization, by optimizing two key parameters, the equalization accuracy and equalization speed of the marine lithium battery pack can be improved, also the energy loss in the equalization process can be reduced.

Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network

Abstract The heating pipe network system with such dynamic characteristics as nonlinearity and large time lag may cause hydraulic disorder. To solve this problem, this paper proposes a unit control-based hydraulic equilibrium control strategy, which constructs an equilibrium regulation system for heating pipe networks by optimising the inlet device of each unit and using a novel control theory. By developing a cascade control system to control the return water temperature and the pressure difference between supply and return water of the branches at each unit of the pipe network, we were able to stabilise the pressure and control the temperature. Then, we used the averaging control theory to set the parameters of regulation systems between each unit. The research results indicate that, compared to the traditional single-loop negative-feedback return water temperature control system, the cascade averaging controller has a better control effect than the single-loop PID controller. This is because it has a smaller overshoot and can cope with system interference factors quickly. Therefore, the temperature of return water between each unit can be coordinated and fluctuation is within a smaller range. This effectively eliminates the influence of static and dynamic hydraulic disorder on entire system stability.

Research on M-SMES Temperature Equilibrium Control Strategies Considering State Assessment

In the future, superconducting magnetic energy storage (SMES) technology will be developed toward large capacity. Among them, a single magnet is expensive and technically challenging. The integration of multiple SMES (M-SMES) is a feasible technical route. But there is coordination among multimodule energy storage magnets, so the formulation of its control strategy is very important. In this article, based on the toroidal magnet, a state evaluation method of toroidal magnet considering the withstand voltage and temperature of the magnet is proposed. To solve the problem of power distribution caused by the difference in initial capacity, initial temperature, and maximum output power during the cooperative control of multiple SMES, a temperature equilibrium control strategy for energy storage magnets combined with state assessment is proposed. System simulation results showed that this strategy could effectively balance the working state of each module and maximize the power output capability of the energy storage magnet by ensuring the safety of the magnet.

Differential game learning approach for multiple microsatellites takeover of the attitude movement of failed spacecraft

Takeover of the attitude control function of a failed spacecraft suffering from fuel exhaustion or actuator failures enables recycling of on-board valuable reusable payloads. Microsatellites can provide cost-efficient ways for the attitude takeover control through coordination. Differential games are used to study the individual optimal decision problem, where each player optimizes their local performance index function to obtain the control policy, and the games predefined global objective can be achieved. In this paper, the failed spacecraft attitude takeover control problem is transformed into a multi-microsatellite differential game problem. First, the multi-microsatellite differential game model is established, the performance index function is designed for each microsatellite, and the mathematical description of the multi-microsatellite differential game problem is realized. Second, the Hamilton-Jacobi (HJ) equations are provided and solved through the single neural network (NN) based policy iteration (PI) algorithm to learn the multi-microsatellite game equilibrium control strategies. Finally, numerical simulations are carried out to validate the effectiveness of the multi-microsatellite differential game learning method. The results have shown that the predefined global objective of the takeover of the attitude control of the failed spacecraft can be realized through the approximate game equilibrium control strategies of multiple microsatellites.

Constrained Utility Deviation-Risk Optimization and Time-consistent HJB Equation

In this paper we propose a unified utility deviation-risk model which covers both utility maximization and mean-variance analysis as special cases. We derive the time-consistent Hamilton-Jacobi-Bellman (HJB) equation for the equilibrium value function and significantly reduce the number of state variables, which makes the HJB equation derived in this paper much easier to solve than the extended HJB equation in the literature. We illustrate the usefulness of the time-consistent HJB equation with several examples which recover the known results in the literature and go beyond, including a mean-variance model with stochastic volatility dependent risk aversion, a utility deviation-risk model with state dependent risk aversion and control constraint, and a constrained portfolio selection model. The numerical and statistical tests show that the utility and deviation-risk have a significant impact on the equilibrium control strategy and the distribution of the terminal wealth.

Constrained Utility Deviation-Risk Optimization and Time-Consistent HJB Equation

In this paper we propose a unified utility deviation-risk model which covers both utility maximization and mean-variance analysis as special cases. We derive the time-consistent Hamilton--Jacobi--Bellman (HJB) equation for the equilibrium value function and significantly reduce the number of state variables, which makes the HJB equation derived in this paper much easier to solve than the extended HJB equation in the literature. We illustrate the usefulness of the time-consistent HJB equation with several examples which recover the known results in the literature and go beyond, including a mean-variance model with stochastic volatility dependent risk aversion, a utility deviation-risk model with state dependent risk aversion and control constraint, and a constrained portfolio selection model. The numerical and statistical tests show that the utility and deviation-risk have a significant impact on the equilibrium control strategy and the distribution of the terminal wealth.

A High-Efficiency Bidirectional Active Balance for Electric Vehicle Battery Packs Based on Model Predictive Control

This study designs an active equilibrium control strategy based on model predictive control (MPC) for series battery packs. To shorten equalisation time and reduce unnecessary energy consumption, bidirectional active equalisation is modelled and analysed, and the model predictive control algorithm is then applied to the established state space equation. The optimisation problem that minimises the equilibrium time is transformed to a linear programming form in each cycle. By solving the linear programming problem online, a group of control optimal solutions is found and the series equalisation problem is decoupled. The equalisation time is shortened by dynamically adjusting the equalisation current. Simulation results show that the MPC algorithm can avoid unnecessary energy transfer and shorten equalisation time. The bench experimental result shows that the equilibrium time is reduced by 31%, verifying the rationality of the MPC strategy.

State-of-Charge Balancing Control of a Modular Multilevel Converter with an Integrated Battery Energy Storage

With the fast development of the electric vehicle industry, the reuse of second-life batteries in vehicles are becoming more attractive, however, both the state-of-charge (SOC) inconsistency and the capacity inconsistency of second-life batteries have limits in their utilization. This paper focuses on the second-life batteries applied battery energy storage system (BESS) based on modular multilevel converter (MMC). By analyzing the power flow characteristics among all sources within the MMC-BESS, a three-level SOC equilibrium control strategy aiming to battery capacity inconsistency is proposed to balance the energy of batteries, which includes SOC balance among three-phase legs, SOC balance between the upper and lower arms of each phase, and SOC balance of submodules within each arm. In battery charging and discharging control, by introducing power regulations based on battery capacity proportion of three-phase legs, capacity deviation between the upper and lower’s arm, and the capacity coefficient of the submodule into the SOC feedback control loop, SOC balance of all battery modules is accomplished, thus effectively improving the energy utilization of second-life battery energy storage system. Finally, the effectiveness and feasibility of the proposed methods are verified by results obtained from simulations and the experimental platform.

Effect of fatigue on the precision of a whole-body pointing task

We addressed the issue of the possible degradation of the aiming precision of a whole-body pointing task, when movement coordination is deranged by selective fatigue of the postural task component. The protocol involved continuous repetition (0.1 Hz frequency) of rapid whole-body pointing trials toward a target located beyond arm length, starting from stance and requiring knee flexion. Six healthy human subjects repeated the trials until exhaustion. Such repetition led to electromyography signs of fatigue in rectus femoris (active in body lowering and raising), but not in deltoid (prime mover for arm reaching component). Rectus femoris fatigue affected the equilibrium control strategy, since the anteroposterior displacement of the center of foot pressure was reduced during the fatigued compared with the initial trials. Conversely, the precision of the aiming movement was unaffected by the rectus femoris fatigue in spite of changes in finger trajectory. Trunk inclination at the end of whole-body pointing task and hip and shoulder marker trajectories were unaffected by rectus femoris fatigue. Control experiments were made, whereby fatiguing repetitions of the postural component of the task were performed without finger pointing, except in the first and last five complete whole-body pointing trials. The results were not different from those of the main protocol, except for a transient change in finger trajectory in the very first trial after fatigue. The CNS takes into account the state of postural muscles’ fatigue and the concurrently ensuing equilibrium constraints in order to appropriately modify whole-body pointing strategy and keep pointing precision at the target.