Multi-objective Optimal Control Research Articles

A multi-objective optimal control approach to motor strategy changes in older people with mild cognitive impairment during obstacle crossing.

Mild cognitive impairment (MCI) may lead to difficulty maintaining postural stability and balance during locomotion. This heightened susceptibility to falls is particularly evident during tasks such as obstacle negotiation, which demands efficient motor planning and reallocation of attentional resources. This study proposed a multi-objective optimal control (MOOC) technique to assess the changes in motor control strategies during obstacle negotiation in older people affected by amnestic MCI. Motion data from 12 older adults with MCI and 12 controls when crossing obstacles were measured using a motion capture system, and used to obtain the control strategy of obstacle-crossing as the best compromise between the conflicting objectives of the MOOC problem, i.e., minimising mechanical energy expenditure and maximising foot-obstacle clearance. Comparisons of the weighting sets between groups and obstacle heights were performed using a two-way analysis of variance with a significance level of 0.05. Compared to the controls, the MCI group showed significantly lower best-compromise weightings for mechanical energy expenditure but greater best-compromise weightings for both heel- and toe-obstacle clearances. This altered strategy involved a trade-off, prioritising maximising foot-obstacle clearance at the expense of increased mechanical energy expenditure. The MCI group could successfully navigate obstacles with a normal foot-obstacle clearance but at the cost of higher mechanical energy expenditure. MCI alters the best-compromise strategy between minimising mechanical energy expenditure and maximising foot-obstacle clearances for obstacle-crossing in older people. These findings provide valuable insights into how MCI impacts motor tasks and offer potential strategies for mitigating fall risks in individuals with MCI. Moreover, this approach could serve as an assessment tool for early diagnosis and a more precise evaluation of disease progression. It may also have applications for individuals with impairments in other cognitive domains.

Multi-objective optimal control of a hybrid offshore wind turbine platform integrated with multi-float wave energy converters

Offshore floating wind turbines will play a pivotal role in achieving net-zero emissions. This study explores a hybrid platform combining an offshore floating wind turbine with wave energy converters (WECs) from an active control perspective to mitigate turbine damage risk while maximizing wave energy conversion. Initially, the control-oriented state-space modelling of the hybrid platform and the validation of the time-domain Cummins-type models of different orders are performed by the Eulerian-Lagrangian method with model linearization and downscaling. Then, a multi-objective non-causal optimal controller is introduced, balancing wave energy capture and penalizing the nacelle acceleration. When wave energy capture maximization is set as the control target, the proposed optimal controller can improve energy output by 184% as compared against a well-tuned passive damper across all peak periods tested. However this causes peak hub acceleration to increase marginally beyond the desirable limits of 3–4 m/s2 for wind turbine operation. When hub acceleration is penalized, the multi-objective optimal controller can reduce peak values below limits by between 40% and 61% with trivial loss of wave energy capture.

Validation of a Model Predictive Control Strategy on a High Fidelity Building Emulator

In recent years, advanced controllers, including Model Predictive Control (MPC), have emerged as promising solutions to improve the efficiency of building energy systems. This paper explores the capabilities of MPC in handling multiple control objectives and constraints. A first MPC controller focuses on the task of ensuring thermal comfort in a residential house served by a heat pump while minimizing the operating costs when subject to different pricing schedules. A second MPC controller working on the same system tests the ability of MPC to deal with demand response events by enforcing a time-varying maximum power usage limitation signal from the electric grid. Furthermore, multiple combinations of the control parameters are tested in order to assess their influence on the controller performance. The controllers are tested on the BOPTEST framework, which offers standardized test cases in high-fidelity emulation models, and pre-defined baseline control strategies to allow fair comparisons also across different studies. Results show that MPC is able to handle multi-objective optimal control problems, reducing thermal comfort violations by between 66.9% and 82% and operational costs between 15.8% up to 20.1%, depending on the specific scenario analyzed. Moreover, MPC proves its capability to exploit the building thermal mass to shift heating power consumption, allowing the latter to adapt its time profile to time-varying constraints. The proposed methodology is based on technologically feasible steps that are intended to be easily transferred to large scale, in-field applications.

Solving Multi-Objective Optimal Control Problems Using a Multiresolution Approach

This paper presents an adaptive multiresolution strategy for multi-objective optimal control problems. The optimal control problem is solved using a direct approach, with individualistic grid adaptation facilitated by a local error analysis at element boundaries. Multiple objectives are considered using a dominance-based approach applying both local and global search methods to a collaborative population of unique solutions. These aspects are simultaneously incorporated via a novel application of evolutionary algorithms for adaptive optimal control problems. Together, this avoids the need for a priori specification of the quantity and temporal location of element boundaries and the set of scalarization weights defining the multi-objective descent directions. Solution fidelity can thus increase concurrently with the exploration of the design space, which leads to increased numerical efficiency while propagating and maintaining population diversity. The benefits of the proposed approach over traditional uniform-grid implementations are demonstrated. Results show that the multiresolution approach is capable of striking an effective balance between solution fidelity, population diversity, and computational cost unachievable using uniform grids.

Interval riccati equation-based and non-probabilistic dynamic reliability-constrained multi-objective optimal vibration control with multi-source uncertainties

Structural vibration control is used to ensure the safety of structures in service and has become an active research area in the past few years. In this study, uncertainties in structural dynamics are considered to propose an interval linear quadratic regulator (LQR) method based on an interval Riccati equation. Multi-objective optimization with non-probabilistic dynamic reliability as a constraint is performed to design an optimal uncertain vibration control system. To alleviate the difficulty of quantifying the probabilistic uncertainty and accurately characterize uncertainty information for small samples, multi-source uncertainties are regarded as interval parameters. The bounds on these uncertainties are determined, and the deterministic and uncertain parts of an interval state-space equation for vibration control are then formulated using an expanded-order matrix and the interval analysis method. Next, the interval perturbation method with a matrix series is used to develop a novel solution method for the linear inhomogeneous time-invariant equation in the interval state-space equation for the vibration control system and is used to accurately predict the interval bounds of the state responses. The conventional LQR method from modern control theory is used to propose a novel optimal control method based on a novel interval Riccati equation using the Lyapunov equation and interval uncertainty propagation. The proposed interval control method can be used to estimate the uncertain bounds of the controlled gain and cost function. A non-probabilistic dynamic reliability model is established to evaluate the reliability index of the system, which can overcome the limitations of the large computational cost of determining the probabilistic reliability. The deterministic controlled cost and uncertain states are considered as two optimization objectives with the proposed reliability constraint. The resulting constrained multi-objective optimal vibration control problem is designed and solved using c-DPEA. A flowchart is presented as a clear overview of the uncertain vibration control method, and the effectiveness of the proposed method is validated using two numerical examples. Different optimal control designs are obtained using different reliability constraints for quantitatively analyzing the safety of the control system.

A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces

The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from Gebken and Peitz (J Optim Theory Appl 188:696–723, 2021) is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the Clarke subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem.

Data-driven multi-objective intelligent optimal control of municipal solid waste incineration process

The municipal solid waste incineration (MSWI) process has become the primary technology for municipal solid waste (MSW) treatment worldwide due to its advantages of harmlessness, reduction, and resource recovery. However, the automatic combustion control (ACC) system developed in developed countries are often not effectively applicable to other countries, particularly China, due to regional differences in MSW composition. To achieve intelligent development of MSWI plants, it is crucial to develop intelligent optimal control technology tailored to national conditions to reduce comprehensive pollutant emission concentration (CPEC) and improve combustion efficiency (CE). This article proposes a data-driven multi-objective intelligent optimal control strategy. Firstly, based on the analysis of the whole process, the Tikhonov regularization-least regression decision tree (TR-LRDT) algorithm is used to establish a MSWI whole process model, incorporating serial controlled objects and parallel pollutant indicators, to support a multi-objective optimization model. Then, leveraging the ACC system and expert experience, a multi-input multi-output loop controller is established using the single neuron adaptive PID (SNA-PID) algorithm to achieve stable control of key controlled variables. Next, a mutation crossover strategy and termination condition are integrated with the multi-objective particle swarm optimization (MOPSO) algorithm to solve the multi-objective optimization model, and domain expert rules are applied to determine the optimal setpoints for key controlled variables in the Pareto front, aiming to reduce CPEC and improve CE. Finally, the effectiveness of the proposed intelligent optimal control strategy is validated using actual data. The experimental results demonstrate that this strategy not only maintains the stability of key controlled variables but also decreases CPEC by 1.82% and increases CE by 2.38%, laying a foundation for further research into intelligent optimization control of the MSWI process. Further, the software system based on the proposed strategy is developed and validated on a hardware-in-loop simulation platform.

Multiobjective optimal control problems. Stationary Navier–Stokes equations

This paper deals with the solution of some multi-objective optimal control problems for stationary Navier–Stokes equations. More precisely, we look for Pareto and Nash equilibria associated to standard cost functionals. First, we prove the existence of equilibria and we deduce appropriate optimality systems. Then, we analyse the existence and characterization of Pareto and Nash equilibria for the Navier–Stokes equations. Here, we use the formalism of Dubovitskii and Milyoutin., see [Girsanov FV. Lectures on mathematical theory of extremum problems. Berlin: Springer-Verlag; 1972. (Notes in economics and mathematical systems; vol. 67)]. Finally, we also present a finite element approximation of the bi-objective problem, we illustrate the techniques with several numerical experiments and we compare the Pareto and Nash equilibria.

Distributed and Multi-Agent Reinforcement Learning Framework for Optimal Electric Vehicle Charging Scheduling

The increasing number of electric vehicles (EVs) necessitates the installation of more charging stations. The challenge of managing these grid-connected charging stations leads to a multi-objective optimal control problem where station profitability, user preferences, grid requirements and stability should be optimized. However, it is challenging to determine the optimal charging/discharging EV schedule, since the controller should exploit fluctuations in the electricity prices, available renewable resources and available stored energy of other vehicles and cope with the uncertainty of EV arrival/departure scheduling. In addition, the growing number of connected vehicles results in a complex state and action vectors, making it difficult for centralized and single-agent controllers to handle the problem. In this paper, we propose a novel Multi-Agent and distributed Reinforcement Learning (MARL) framework that tackles the challenges mentioned above, producing controllers that achieve high performance levels under diverse conditions. In the proposed distributed framework, each charging spot makes its own charging/discharging decisions toward a cumulative cost reduction without sharing any type of private information, such as the arrival/departure time of a vehicle and its state of charge, addressing the problem of cost minimization and user satisfaction. The framework significantly improves the scalability and sample efficiency of the underlying Deep Deterministic Policy Gradient (DDPG) algorithm. Extensive numerical studies and simulations demonstrate the efficacy of the proposed approach compared with Rule-Based Controllers (RBCs) and well-established, state-of-the-art centralized RL (Reinforcement Learning) algorithms, offering performance improvements of up to 25% and 20% in reducing the energy cost and increasing user satisfaction, respectively.

Energy hub management for integrated energy systems: A multi-objective optimization control strategy based on distributed output and energy conversion characteristics

To improve the comprehensive utilization efficiency of energy, a multi-objective optimization control strategy applied to the energy hub (EH) within the system is proposed to address the electrical and thermal load distribution of the integrated energy system (IES) and the low-carbon economic operation. First, a model of the electrical and thermal energy outputs is established based on the characteristics of the IES network and the multidimensional “load parameter” evolution law. Moreover, a distributed control strategy is proposed that utilizes the information interaction between neighboring EHs to accurately share the electrical and thermal loads, which reduces the communication burden of the system while avoiding overloads. Furthermore, to coordinate the optimal operation of the devices within the hub, based on the energy conversion characteristics of the EH, a multi-objective optimization model is proposed that considers low-carbon and economic aspects to realize efficient energy use. Simulation results show that the proposed strategy effectively improves the robustness of the system while realizing proportional load distribution and low-carbon economic operation. Under the same load, when focusing on system economics, the operating cost is 2.182/¥ lower than when focusing on low-carbon systems, but carbon emission is 1.6753/kg CO2 higher.

Multi-Objective Optimization and Stable Operation Control Strategy for Fractional Frequency Transmission System Based on Large Signal Stability Analysis

Multi-Objective Optimization and Stable Operation Control Strategy for Fractional Frequency Transmission System Based on Large Signal Stability Analysis

Decoupled MPC Power Balancing Strategy for Coupled Inductor Flying Capacitor DC–DC Converter

A decoupled model predictive control (MPC) power balancing strategy for a coupled inductor-based flying capacitor DC–DC converter (FCDC) is a proposed to solve the power imbalance caused by the parameter differences in the coupled inductor. The decoupled mathematical model of coupled inductor FCDC is firstly derived by analyzing the converter operation state under various modes. On this basis, the control relationship between inductor current and flying capacitor (FC) voltage is redefined and an MPC power balance strategy based on the inductor current with single-step optimization is proposed. The proposed MPC strategy not only achieves decoupled power balancing control but also solves multi-objective dynamic optimization control of the inductor current and FC voltage, greatly reducing the computation load. A detailed theoretical analysis of the proposed strategy is presented and the balancing performance is effectively verified through the experiments.

Research on multi-condition and multi-objective control of pumped storage unit optimized by improved multi-objective particle swarm optimization algorithm

Abstract In order to maintain good control quality of the pumped storage unit regulation system during the switching of operating conditions, a multi-objective optimization framework based on improved multi-objective particle swarm optimization algorithm is proposed, which takes into account the control stability, rapidity and robustness under multiple working conditions. Firstly, the fractional order PID controller with higher applicability and flexibility is introduced to replace the traditional PID controller. Then, an objective function considering the ITAE index of low-head and medium-high-head conditions is constructed. On this basis, the multi-objective particle swarm optimization algorithm with pigeon swarm search operator, adaptive Cauchy mutation strategy and improved initialization method is used to optimize the controller parameters, and the multi-condition and multi-objective fractional order PID optimal control of pumped storage unit regulation system is realized. Through simulation, it is proved that the controller parameters based on the framework optimization proposed in this paper have strong adaptability and robustness under different working conditions, which provides a new idea for the optimal control of pumped storage unit regulation system.

Health-conscious optimal control of Li-ion cell using simplified full homogenized macro-scale model

This article presents the optimal charging of a Li-ion cell based on a simplified full homogenized macro-scale (FHM) model. A solid electrolyte interface (SEI) layer model is included in the simplified FHM model to quantify cell degradation. With these models, a multi-objective optimal control problem subject to constraints from safety concerns is formulated to achieve health-conscious optimal charging. This constrained optimal control problem is converted to a nonlinear programming problem (NLP). A nonlinear model predictive control (NMPC) strategy is adopted by solving the NLP at each sampling time using the pseudo-spectral optimization method. The effect of the input current upper bound on the cell film resistance Rfilm and state of health (SoH) reveals that Rfilm and SoH are more sensitive to input current upper bound at lower values of input current upper bound. Simulation results show that the simplified model and pseudo-spectral method are crucial for reducing the computational load of the model. The proposed algorithm is more efficient in reducing health degradation than the conventional constant current constant voltage (CCCV) charging algorithm since it can explicitly handle the film resistance and capacity as health parameters. Multiple cycle charging simulations revealed that the health-conscious algorithm decreases health degradation and increases battery life.

Quantum-inspired deep reinforcement learning for adaptive frequency control of low carbon park island microgrid considering renewable energy sources

The low carbon park islanded microgrid faces operational challenges due to the high variability and uncertainty of distributed renewable energy sources. These sources cause severe random disturbances that impair the frequency control performance and increase the regulation cost of the islanded microgrid, jeopardizing its safety and stability. This paper presents a data-driven intelligent load frequency control (DDI-LFC) method to address this problem. The method replaces the conventional LFC controller with an intelligent agent based on a deep reinforcement learning algorithm. To adapt to the complex islanded microgrid environment and achieve adaptive multi-objective optimal frequency control, this paper proposes the quantum-inspired maximum entropy actor-critic (QIS-MEAC) algorithm, which incorporates the quantum-inspired principle and the maximum entropy exploration strategy into the actor-critic algorithm. The algorithm transforms the experience into a quantum state and leverages the quantum features to improve the deep reinforcement learning’s experience replay mechanism, enhancing the data efficiency and robustness of the algorithm and thus the quality of DDI-LFC. The validation on the Yongxing Island isolated microgrid model of China Southern Grid (CSG) demonstrates that the proposed method utilizes the frequency regulation potential of distributed generation, and reduces the frequency deviation and generation cost.

Modeling and Multi-objective Optimal Control of Thedynamics of Counterterrorism in the Sahel Region in Africa

Terrorist activity in the Sahel region has been on the increase for almost a decade. Groups advocating extremist ideologies with a political or religious base are carrying out attacks against states with the aim of imposing a totalitarian ideology, sometimes against a backdrop of political crisis and famine. In this state of crisis and sometimes communal conflict, it is questionable whether ideological terrorism can really be eradicated in the Sahel. In this study, we develop a model of the dynamics of ideological terrorism based on the terrorism situation in the Sahel. In particular, this model incorporates popular resistance to terrorism through the class of volunteers for the defense of the homeland, but we also take into account the indoctrination of certain sections of the population vulnerable to fanatical ideology. We estimate $\mathcal{R}_0$ , the number of elementary replications of extremist behavior, which enables us to predict the evolution of extremism. We also identify four thresholds $\mathcal{R}_1$, $\mathcal{R}_2$, $\mathcal{R}_3$ and $\mathcal{R}_4$ of sufficient conditions for the eradication of ideological terrorism and brigandage. A multi-objective optimal control of a counter-terrorism strategy is also presented. Finally, we perform a numerical simulation of the analysis and control results to test our hypotheses.

Optimization of energy efficiency for offshore wind farms via wake modeling-free NMPC

This paper presents an energy efficiency improvement scheme for offshore wind farms. This scheme uses learning-based nonlinear model predictive control (NMPC) and does not require wake modeling. The main feature is that each wind turbine can independently complete all optimal control, without the need for wind farm wake model calculation and iterative optimization. Specifically, this paper studies the critical factors for increasing the active power of wind farms and reducing the structural load of wind turbines, and reconstructs the optimal control objectives of wind turbines. Furthermore, combined with the nonlinear model of wind turbines containing uncertainty, a nonlinear model predictive control algorithm based on deep neural networks was designed, which can achieve multi-objective optimal control at the wind turbine level. The simulation results show that the uncertainty estimation method can effectively improve the nonlinear control performance, achieve an increase in the active power of the wind farm without wake iterative optimization, and at the same time suppress the structural loads of all wind turbines.

Adaptive Reactive Power Optimization in Offshore Wind Farms Based on an Improved Particle Swarm Algorithm

To address the reactive power optimization control problem in offshore wind farms (OWFs), this paper proposes an adaptive reactive power optimization control strategy based on an improved Particle Swarm Optimization (PSO) algorithm. Firstly, an OWF multi-objective optimization control model is established, with the total sum of voltage deviations at wind turbine (WT) terminals, active power network losses, and reactive power margin of WTs as comprehensive optimization objectives. Innovatively, adaptive weighting coefficients are introduced for the three sub-objectives, enabling the weights of each optimization objective to be adaptively adjusted based on real-time operating conditions, thus enhancing the adaptability of the reactive power optimization model to changes in operating conditions. Secondly, a Uniform Adaptive Particle Swarm Optimization (UAPSO) algorithm is proposed. On one hand, the algorithm initializes the particle swarm using a uniform initialization method; on the other hand, it improves the particle velocity update formula, allowing the inertia coefficient to adaptively adjust based on the number of iterations and the fitness ranking of particles. Simulation results demonstrate the following: (1) Under various operating conditions, the proposed adaptive multi-objective reactive power optimization strategy can ensure the stability of node voltages in offshore wind farms, reduce active power losses, and simultaneously improve reactive power margins. (2) Compared with the traditional PSO algorithm, UAPSO exhibits an approximately 10% improvement in solution speed and enhanced solution accuracy.

Application of Deep Learning Algorithm in Optimization of Engineering Intelligent Management Control

Currently, there are a series of problems in the management of the construction industry, such as resource waste, substandard quality, and low construction efficiency. In response to this phenomenon, the author proposes a multi-objective optimization control method for construction engineering management projects using deep learning algorithms. This method analyzes the relationship between cost, duration, and quality, and constructs an optimization management model for these three factors. At the same time, the improved SULSTM neural network algorithm is used to optimize the model parameters. The experimental results indicate that, when the value coefficient is 0.2211, the total investment cost and quality coefficient are 412700 yuan and 0.99496 yuan, respectively. When the value coefficient is 0.1976, the total cost and quality coefficient are 456300 yuan and 0.98798 yuan, respectively. When the value coefficient is 0.1990, the total cost and quality coefficient are 456300 yuan and 0.99496 yuan, respectively. Proved that the SUSTM neural network algorithm has faster convergence speed and lower loss values compared to the improved LSTM neural network algorithm. The cost of improving quality has a greater impact on the quality coefficient than the duration, and the total investment cost has a greater impact on the value coefficient than the quality coefficient.

A Multi-Objective Optimal Control Method for Navigating Connected and Automated Vehicles at Signalized Intersections Based on Reinforcement Learning

The emergence and application of connected and automated vehicles (CAVs) have played a positive role in improving the efficiency of urban transportation and achieving sustainable development. To improve the traffic efficiency at signalized intersections in a connected environment while simultaneously reducing energy consumption and ensuring a more comfortable driving experience, this study investigates a flexible and real-time control method to navigate the CAVs at signalized intersections utilizing reinforcement learning (RL). Initially, control of CAVs at intersections is formulated as a Markov Decision Process (MDP) based on the vehicles’ motion state and the intersection environment. Subsequently, a comprehensive reward function is formulated considering energy consumption, efficiency, comfort, and safety. Then, based on the established environment and the twin delayed deep deterministic policy gradient (TD3) algorithm, a control algorithm for CAVs is designed. Finally, a simulation study is conducted using SUMO, with Lankershim Boulevard as the research scenario. Results indicate that the proposed methods yield a 13.77% reduction in energy consumption and a notable 18.26% decrease in travel time. Vehicles controlled by the proposed method also exhibit smoother driving trajectories.