Multi-objective Optimal Control Research Articles

Comprehensive Performance Evaluation of Earthquake Search and Rescue Robots Based on Improved FAHP and Radar Chart

To effectively enhance the adaptability of earthquake rescue robots in dynamic environments and complex tasks, there is an urgent need for an evaluation method that quantifies their performance and facilitates the selection of rescue robots with optimal overall capabilities. In this paper, twenty-two evaluation criteria are proposed based on a comprehensive review of existing evaluation criteria for rescue robots across various domains. The evaluation criteria are tested using the test modules developed by the National Earthquake Response support service, obtaining the corresponding values for each criterion. Then, the weights of the criterion layer and comprehensive evaluation index are determined based on the analytical hierarch process and trapezoidal fuzzy number complementary judgment matrix, and a new consistency test method is proposed. The qualitative evaluation and quantitative analysis are effectively combined to overcome the subjective influence of expert decision-making. Additionally, the performance of three earthquake search and rescue robots is comprehensively evaluated and ranked using the improved radar chart method as an empirical example. Finally, the robustness of the ranking results is examined using a weight sensitivity analysis. The results of the sensitivity analysis demonstrate the effectiveness and feasibility of the proposed method, thereby providing valuable insights for developing multi-objective optimization control strategies and structural designs for earthquake search and rescue robots.

Multi-Objective set point optimization control of grate cooler considering energy efficiency evaluation

The grate cooler is a key piece of equipment for cooling cement clinker, whose parameter adjustment has a notable influence on energy consumption and equipment operation. This article proposes a multi-objective set-point optimization control method for the grate cooler control system, which takes into account energy efficiency evaluation. Based on the energy efficiency analysis of the grate cooler, the secondary air temperature, tertiary air temperature, and outlet clinker temperature are used as energy efficiency evaluation indicators, and a grate cooler energy efficiency evaluation model is established to construct a multi-objective function. After that, the grate pressure set point and fan current set point are optimized by utilizing the MOEA/D algorithm, and the predictive control method is combined to perform rolling optimization of the control parameters. Eventually, a simulation experiment is conducted based on the actual production data, and the simulation results demonstrate the feasibility and effectiveness of the optimized control method.

Multi-Objective Integrated Robust Optimal Control for Wastewater Treatment Processes

Multi-objective optimal control is widely applied in wastewater treatment processes (WWTPs) to ensure the security and stability of the operation processes. However, for the existing stepwise multi-objective optimal control (SMOC) algorithms, the unknown disturbances will further influence the obtain of set-points and the design of control laws, which may degrade the control performance and operation performance of WWTPs. Aim at the above-mentioned problem, this study presents a multi-objective integrated robust optimal control (MIROC) method for WWTPs. The merits of MIROC are three folds. First, a model approximator is designed to capture the nonlinear dynamics of WWTPs. Second, a disturbance observer is utilized to describe the disturbances of WWTPs. Then, based on the model approximator and disturbance observer, a more accurate prediction model of WWTPs with disturbances is established. Third, under the framework of multi-objective model predictive control (MMPC), a MIROC structure with a cooperative cost function (CCF) and a gradient-based multi-objective optimization algorithm (GMOA) is developed to coordinate optimization and control solution of WWTPs with unknown disturbances. Finally, the stability analysis of MIROC is provided in theory. Meanwhile, the results on the benchmark simulation platform demonstrate that MIROC can improve the performance of WWTPs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The SMOC algorithms may degrade the performance of WWTPs with the unknown disturbances. In the paper, a MIROC scheme is presented for WWTPs with the unknown disturbances. Three key parts are contained, the model approximator, the disturbance observer and the MIROC structure. A prediction model of WWTPs with disturbances is established with the model approximator and the disturbance observer. Then, the model approximator and the disturbance observer are applied to improve modeling accuracy of MIROC. Based on the prediction model of WWTPs, a MIROC structure is designed to comprehensively analyze the optimization process and control process of WWTPs with the unknown disturbances. Then, MIROC structure is composed of a CCF and a GMOA. Finally, the results on an industrial application of WWTPs demonstrate that MIROC can achieve optimal operation of WWTPs.

Multiple classical noise mitigation by multiobjective robust quantum optimal control

Multiple classical noise mitigation by multiobjective robust quantum optimal control

Optimizing chemotherapy treatment outcomes using metaheuristic optimization algorithms: A case study.

This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability of the equilibrium points in the model is analysed using the Jacobian matrix and eigenvalues. Additionally, bifurcation analysis is conducted to determine the optimal values for the control parameters. To evaluate the performance of the model and control strategies, benchmarking simulations are performed using the PlatEMO platform. The Pure Multi-objective Optimal Control Problem (PMOCP) and the Hybrid Multi-objective Optimal Control Problem (HMOCP) are two different forms of optimal control problems that are solved using revolutionary metaheuristic optimisation algorithms. The utilization of the Hypervolume (HV) performance indicator allows for the comparison of various metaheuristic optimization algorithms in their efficacy for solving the PMOCP and HMOCP. Results indicate that the MOPSO algorithm excels in solving the HMOCP, with M-MOPSO outperforming for PMOCP in HV analysis. Despite not directly addressing immediate clinical concerns, these findings indicates that the stability shifts at critical thresholds may impact treatment efficacy.

Control Strategy for Building Air Conditioning Cluster Loads Participating in Demand Response Based on Cyber-Physical System

In recent years, with rising urbanization and ongoing adjustments in industrial structures, there has been a growing dependence on public buildings. The load of public buildings gradually becomes the main component of the peak load in summer, among which the load of air conditioning is particularly prominent. To clarify the key problems and solutions to these challenges, this study proposes a multi-objective optimization control strategy for building air conditioning cluster participation in demand response based on Cyber-Physical System (CPS) architecture. In a three-layer typical CPS architecture, the unit level of the CPS achieves dynamic information perception of air conditioning clusters through smart energy terminals. An air conditioning load model based on the multiple parameter types of air conditioning compressors is presented. Then, the system level of the CPS fuses multiple pieces of information through smart energy gateways, analyzing the potential for air conditioning clusters when they participate in demand response. The system of system level (SoS level) of the CPS deploys a multi-objective optimization control strategy which includes the uncertainty of the initial states of air conditioning clusters within the intelligent building energy management system. The optimal model takes into account the differences in the environmental conditions of each individual air conditioning unit within the cluster and sets different operating modes for each unit to achieve load reduction while maintaining temperatures within a comfortable range for the human body. The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm based on Pareto frontiers is applied to solve this optimization control strategy and to optimize the operational parameters of the air conditioning clusters. A comparative analysis is conducted with single-objective optimization results obtained using the traditional Particle Swarm Optimization (PSO) algorithm. The case study results indicate that the proposed multi-objective optimization control strategy can effectively improve the thermal comfort of the human body towards the controlled temperatures of air conditioning clusters while meeting the accuracy of demand response. In the solution phase, the highest temperature within the air conditioning clusters is 24 °C and the lowest temperature is 23 °C. Adopting the proposed multi-objective optimization control strategy, the highest temperature is 26 °C and the lowest temperature is 23.5 °C within the clusters and the accuracy of demand response is up to 92%. Compared to the traditional PSO algorithm, the MOPSO algorithm has advantages in convergence and optimization precision for solving the proposed multi-objective optimization control strategy.

A Multi-objective Optimization Control Strategy of a Range-Extended Electric Vehicle for the Trip Range and Road Gradient Adaption

A Multi-objective Optimization Control Strategy of a Range-Extended Electric Vehicle for the Trip Range and Road Gradient Adaption

Koopman-based surrogate models for multi-objective optimization of agent-based systems

Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend potentially nonlinearly on control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.

A multi-objective optimization method for enclosed-space lighting design based on MOPSO

With the rapid development of underground spaces and manned cabins, the design of enclose-space has received attention. Humans working in enclosed-space for a long period of time are prone to fatigue, which in serious cases can lead to human errors and major accidents. Therefore, the optimized design of enclosed-space is of great research significance to enhance the efficiency and comfort of workers. The lighting environment is one of the important objectives of the optimized design of enclosed-space, and the current research on lighting design often focuses on single-objective reduction of energy consumption or improvement of visual effects, and lacks attention to non-visual effects. We propose multi-objective optimal control strategy for enclosed-space lighting systems, taking the visual effects, non-visual effects, and energy efficiency of lighting as the optimization objectives and constraints, combined with multi-objective particle swarm optimization algorithm. Firstly, we obtain a set of optimal Pareto front solution for the dimming level by improving the algorithm. Secondly, to select appropriate lighting strategies according to different working scenarios, we introduce the fuzzy integrated evaluation method of experts to find the best compromise. Finally, we used a manned simulated enclosed cabin based on DIALux evo for a case study to compare the optimization results with baseline solutions. The results show that when we employed the improved dimming strategy, the energy efficiency and visual comfort were significantly improved compared with the baseline lighting design. The proposed method can satisfy human non-visual effects requirements, providing a research reference for future enclosed-space lighting optimization.

Closed-form Solution for Multi-Objective Optimal Analytical Balance Control for a Single-Stage Isolated MVAC-LVDC Converter in an Electric-Vehicle Ultra-Fast Charging-Station

Closed-form Solution for Multi-Objective Optimal Analytical Balance Control for a Single-Stage Isolated MVAC-LVDC Converter in an Electric-Vehicle Ultra-Fast Charging-Station

Pontryagin’s Minimum Principle-Based Power Management of Plug-In Hybrid Electric Vehicles to Enhance the Battery Durability and Thermal Safety

Temperature affects the battery aging and stability, bringing about significant effects on the electric vehicle&#x2019;s economy, reliability, and safety. Therefore, it is necessary to consider the battery thermal condition when designing the power management scheme. In this paper, an optimal power management strategy for plug-in hybrid electric vehicles is proposed based on Pontryagin&#x2019;s Minimum Principle (PMP). Two situations, normal operation and cooling system failure, are considered. The impacts of battery aging and temperature rise are characterized based on durability analysis model and thermal model. The temperature variation rate of the battery is incorporated into the Hamiltonian function, and the correlation between the cost optimization and temperature rise is disclosed by shooting method. Then the optimal co-state variables in different cases are determined. Based on above efforts, the PMP-based multi-objective optimal control strategy is proposed and evaluated based on the temperature statistical data in Shenyang, China. The results show that the proposed method can improve the durability of the battery and inhibit the excessive temperature rise. In case of the cooling system failure, it can realize the trade-off between safety and economy to reduce the risk of battery thermal runaway.

Distributed Optimal Consensus Control of Multiagent Systems Involving State and Control Dependent Multiplicative Noise

This paper aims to solve the multi-objective optimization control problem by investigating the consensus problem of multi-agent simultaneous optimization with state and control dependent multiplicative noise. The main contributions of this work are two-fold. First, the optimal consensus control problem is solved by designing the free item of an optimal controller, and the coefficient of the feedback gain is obtained based on analyzing a parameterized generalized algebraic Riccati equation. Second, we derive a new consensus controller that comprises two parts different from the current consensus. One part minimizes a linear quadratic index with a singular control weighting matrix, and the other affords the multi-agent systems to achieve mean square consensus.

Multiobjective Integrated Optimal Control for Nonlinear Systems.

The multiobjective optimal control method optimizes the performance indexes of nonlinear systems to obtain setpoints, and designs a controller to track the setpoints. However, the stepwise optimal control method that independently analyzes the optimization process may obtain unfeasible and difficult to track setpoints, which will reduce the operation and control performance of the systems. To solve this problem, a multiobjective integrated optimal control (MIOC) strategy is proposed for nonlinear systems in this article. The main contributions of MIOC are threefold. First, in the framework of multiobjective model predictive control, an integrated control structure with a comprehensive cost function and a collaborative optimization algorithm is designed to achieve the coordinate optimal control. Second, for the time inconformity of setpoints and control laws caused by the characteristic of tracking control, the different prediction horizons are designed for the comprehensive cost function. Then, the collaborative optimization algorithm is proposed for the comprehensive cost function to achieve the integrated solution of setpoints and control laws to enhance the operation and control performance of nonlinear systems. Third, the stability and control performance analysis of MIOC is provided. Finally, the proposed MIOC method is applied for a nonlinear system to demonstrate its effectiveness.

Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set

Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set

Application of cell mapping to control optimization for an antenna servo system on a disturbed carrier

Abstract. The cell-mapping method, due to its global optimality, has been applied to solve multi-objective optimization problems (MOPs) and optimal control problems. However, the curse of dimensionality limits its application in high-dimensional systems. In this paper, the multi-parameter sensitivity analysis is investigated to reduce the parameter space dimension, which broadens the application of cell mapping to MOPs in high-dimensional parameter space. A post-processing algorithm for MOPs is introduced to help choose proper control parameters from the Pareto set. The proposed scheme is applied successfully in the control parameter optimization of an adaptive nonsingular terminal sliding-mode control for an antenna servo system on a disturbed carrier. Moreover, as the existing global optimal tracking control with an adjoining cell-mapping method may generate tracking-phase differences, an optimal-sliding-mode combined-control strategy is proposed. By using the combined-control strategy, the azimuth and pitch angles of the antenna system are controlled to catch up to a target trajectory with the minimum cost function and to keep high-precision tracking after that.

Optimizing breast cancer treatment using hyperthermia: A single and multi-objective optimal control approach

In recent decades, the study and development of numerical strategies for cancer treatment have become increasingly feasible, thanks to the advancement of numerical techniques and the increased availability of higher-performance computers. This has enabled researchers to tackle more complex and realistic problems associated with cancer treatment. Among the deadliest types of carcinomas, breast cancer is one of the most extensively studied, primarily due to its high annual incidence and mortality rate. From a medical standpoint, hyperthermia has emerged as one of the most promising treatment modalities. In general, this procedure involves applying heat to the tumor using an applicator over a period of time in order to destroy pathological cells. The applicator provides a source of energy that is used to raise the temperature inside the tumor. Traditionally, a constant heat source has been utilized during the treatment period. This article proposes single and multi-objective optimal control problems for breast cancer treatment by hyperthermia, and solutions for these problems are provided. In this instance, the heat source is treated as a control variable considering two types of strategies: i) increasing monotone control and ii) non-monotone control. For this purpose, the extent of tissue damage is considered a constraint in each application to ensure the degree of tissue damage. As expected, the findings demonstrate that the best result was achieved when employing a strategy that considers only the lateral limits, without any additional constraints. In addition, for every case study, a more appropriate optimal strategy can be employed for cancer treatment. Moreover, for the multi-objective optimal control problem, a satisfactory balance between the objectives can be selected such that a specific optimal strategy can be established for each patient.

Evaluating the choice of radial basis functions in multiobjective optimal control applications

Evolutionary Multi-Objective Direct Policy Search (EMODPS) is a prominent framework for designing control policies in multi-purpose environmental systems, combining direct policy search with multi-objective evolutionary algorithms (MOEAs) to identify Pareto approximate control policies. While EMODPS is effective, the choice of functions within its global approximator networks remains underexplored, despite their potential to significantly influence both solution quality and MOEA performance. This study conducts a rigorous assessment of a suite of Radial Basis Functions (RBFs) as candidates for these networks. We critically evaluate their ability to map system states to control actions, and assess their influence on Pareto efficient control policies. We apply this analysis to two contrasting case studies: the Conowingo Reservoir System, which balances competing water demands including hydropower, environmental flows, urban supply, power plant cooling, and recreation; and The Shallow Lake Problem, where a city navigates the trade-off between environmental and economic objectives when releasing anthropogenic phosphorus. Our findings reveal that the choice of RBF functions substantially impacts model outcomes. In complex scenarios like multi-objective reservoir control, this choice is critical, while in simpler contexts, such as the Shallow Lake Problem, the influence is less pronounced, though distinctive differences emerge in the characteristics of the prescribed control strategies.

Robust Constrained Multi-Objective Guidance of Supersonic Transport Landing Using Evolutionary Algorithm and Polynomial Chaos

Landing of supersonic transport (SST) suffers from a large uncertainty due to its highly sensitive aerodynamic properties in the subsonic domain, as well as the wind gusts around runways. At the vehicle design stage, a landing trajectory optimization under wind uncertainty in a multi-objective solution space is desired to explore the possible trade-off in its key flight performance metrics. The proposed algorithm solves this robust constrained multi-objective optimal control problem by integrating non-intrusive polynomial chaos expansion into a constrained evolutionary algorithm. The computationally tractable optimization is made possible through the conversion of a probabilistic problem into an equivalent deterministic representation while maintaining a form of the multi-objective problem. The generated guidance trajectories achieve a significant reduction of the uncertainty in their terminal states with a marginal modification in the control history of the deterministic solutions, validating the importance of the consideration of robustness in trajectory optimization.

Hierarchical distributed MPC method for hybrid energy management: A case study of ship with variable operating conditions

The energy management (EM) strategy, power controller, and local controller of the EM system are coupled, and together affect hybrid power system performance. To achieve coordinated control and multi-objective optimisation of a hybrid power system, a hierarchical distributed control method was proposed, and a validation study was conducted based on model-in-the-loop simulations (MILs) and hardware-in-the-loop simulations (HILs). First, a real-time EM strategy based on a combination of forward dynamic programming (FDP) and model predictive control (MPC) methods was proposed to optimise the power allocation for multiple energy sources. Second, a distributed controller based on a consistency algorithm was proposed to coordinate the differences in the characteristics of multiple energy sources. A dynamic virtual impedance-based droop controller was designed for dynamic tracking of the reference power. The performance of the three-layer control structure was comprehensively validated through MILs and HILs. The results show that the dynamic virtual impedance-based droop control method can track the nonlinear reference power with control deviation within 5 %. The distributed controller is able to keep the bus voltage stable. The global control accuracy of the DC bus voltage is improved by 18.08 %, and the battery current global fluctuations is reduced by 17.4 %. The real-time FDP-MPC-based EM strategy can achieve 99.89 % energy savings and emissions reduction compared to the global DP-MPC-based method, with greater robustness, real-time performance. The results demonstrate that the proposed method is effective for real-time applications and can achieve hierarchical and multi-objective optimal control of the hybrid power system.

Optimization over the Pareto front of nonconvex multi-objective optimal control problems

Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives the Pareto front is usually difficult to view, if not impossible, and even in the case of just two objectives constructing the whole Pareto front so as to visually inspect it might be very costly. Therefore, optimization over the Pareto (or efficient) set has been an active area of research. Although there is a wealth of literature involving finite dimensional optimization problems in this area, there is a lack of problem formulation and numerical methods for optimal control problems, except for the convex case. In this paper, we formulate the problem of optimizing over the Pareto front of nonconvex constrained and time-delayed optimal control problems as a bi-level optimization problem. Motivated by existing solution differentiability results, we propose an algorithm incorporating (i) the Chebyshev scalarization, (ii) a concept of the essential interval of weights, and (iii) the simple but effective bisection method, for optimal control problems with two objectives. We illustrate the working of the algorithm on two example problems involving an electric circuit and treatment of tuberculosis and discuss future lines of research for new computational methods.