Multi-objective Optimal Control Research Articles

Optimal path planning of unmanned surface vehicle under current environment

Path planning for unmanned surface vehicles (USVs) in the presence of ocean currents is a challenging task. Several relevant methods have been proposed, but they all assume a constant surge velocity for the whole path. This hypothesis makes it impossible to achieve the simultaneous optimization of speed and energy consumption. To deal with this issue, in this paper an optimal control path planning method that considers the currents’ characteristics is proposed. Unlike traditional algorithms such as the A* algorithm and genetic algorithm, the proposed Multi-domain Coupling Collocation (MDCC) method does not require a constant thrust assumption. In addition, it can obtain the Pareto optimal path under various current environments and optimize the sailing parameters. Specifically, first a multi-objective optimal control path planning model considering the kinematic characteristics of USVs is established. Second, the MDCC method is proposed to solve it, which includes dividing the time interval, subdomain collocation, and transformation optimization. Last, the optimality and high efficiency of the proposed method are proved theoretically. Simulation experiments show that the proposed method can provide solutions to this problem where existing algorithms fail, and has strong robustness and high efficiency. Furthermore, the obtained path is superior to those obtained using the existing algorithms in various scenarios.

Multi-objective optimal control of multi-zone VAV systems for adaptive switching between normal and pandemic modes

The recent COVID-19 pandemic has highlighted the need to adapt the control of building HVAC systems to limit disease transmission in indoor environments. However, such operational adjustments may significantly increase energy use, creating a complex trade-off problem between infection risk mitigation and energy efficiency. Moreover, practical constraints, such as maintaining comfortable temperature and humidity levels for occupants and limited system equipment capacity, can limit the flexibility of operational adjustments, further exacerbating the challenge of finding optimal operational solutions. This paper therefore proposes an optimal control strategy for multi-zone VAV systems that adapts to switching between normal and pandemic modes. The strategy considers dual optimization objectives: minimizing system energy use and disease transmission risk, while also considering all practical constraints. Optimal operational parameters can be determined to achieve the best trade-off between these objectives based on pandemic conditions. Additionally, a new metric called “effective fresh air factor” is proposed to quantify the impact of multi-zone VAV systems on disease transmission in building zones. The effectiveness of the proposed strategy is evaluated in a simulated building and air-conditioning environment. Results show that the VAV system has superior ability to reduce transmission risk through operational adjustments, achieving a decrease in disease transmission risk by 25%–75% compared to normal operation.

Tradeoffs in optimization of Active Insulation Systems and HVAC: A case study in residential buildings

Active insulation systems (AIS) have been conceptualized to make buildings more responsive to changing environmental conditions, creating energy efficiency and flexibility gains. Building flexibility and efficiency can be further improved if the building is also equipped with optimized HVAC system controls. Optimal control of AIS and HVAC systems can be used to activate thermal mass, and past work has quantified the potential benefits of jointly optimizing both systems. In this work, we more fully elucidate and evaluate the potential tradeoffs between optimal control of these technologies with respect to building energy use and peak demand–including different configurations of heat pump systems and integrated building thermal energy storage. Tradeoffs are revealed by applying a multi-objective optimal control framework and comparing the Pareto optimal sets across various system configurations. Discussion of the results provides insights into how buildings can be best designed and controlled to achieve both energy efficiency and flexibility.

Adaptive authority dynamic game for human-machine cooperative control

An adaptive dynamic allocation strategy for driving authority based on the non-cooperative game was designed to solve the decision conflict problem between the driver and automatic system in human-machine driving. The coupling dynamics model of human-machine interaction was established according to the coupling mechanism between the driver and the automatic system. Considering the driver’s driving status and the driving risk of vehicles, the driving authority dynamic allocation strategy was designed. On this basis, the human-machine cooperative multi-objective optimal control problem is constructed, and the dynamic allocation control system was designed based on the non-cooperative game theory. The optimal control method was used to solve the Nash equilibrium solution and achieve the optimal authority allocation. The effectiveness of the proposed adaptive authority dynamic allocation strategy was verified under normal and emergency conditions. Results showed that the proposed strategy can effectively reduce human-machine decision conflicts and achieve harmonious human–machine cooperative driving.

The Clarke Coderivative of the Frontier Map in a Multi-objective Optimal Control Problem

The Clarke Coderivative of the Frontier Map in a Multi-objective Optimal Control Problem

Direct Instantaneous Torque Control of SRM Based on a Novel Multilevel Converter for Low Torque Ripple

The torque ripple of a switched reluctance motor (SRM) limits its application in electric vehicles. This paper proposes a DITC system for SRMs based on a novel multilevel converter (MLC), which aims at the problem that the torque ripple cannot be effectively suppressed for the conventional direct instantaneous torque control (DITC) of an SRM due to the limitation of the DC bus voltage in the asymmetric half-bridge converter (AHBC) and the single control strategy formulated in the commutation region. Based on the advantages of fast excitation and fast demagnetization for the proposed MLC and the torque distribution characteristics for each phase winding in the commutation region, a novel torque hysteresis control strategy is developed to improve the torque-following ability of the DITC and achieve the purpose of minimizing the torque ripple in the commutation region. In addition, multiobjective optimization control of the motor is carried out to improve the efficiency of the DITC system while suppressing the torque ripple. The effectiveness of the proposed SRM drive scheme is verified by experiment, which is of great significance for the application of SRMs in electric vehicles.

Multi-objective optimal control of tungiasis diseases with terminal demands

In this paper, we aim to minimize the epidemic size of tungiasis disease and economic costs simultaneously, with terminal demands for infected humans. A human–jigger parasite control system with four control schemes for humans and jiggers is established. We propose a multi-objective optimal control problem with terminal constraints, in which the accumulated number of infected humans and control costs are involved. By applying the modified normal boundary intersection algorithm and the interior point scheme, numerical simulations for different combinations of control schemes are carried out, and actual data in Madagascar are used. Effective combination schemes are indicated from the perspectives of disease eradication, cost saving and time saving. Once these effective combinations are properly performed, the disease can be controlled. When only minimizing the epidemic size, the combination of the optimal treatments and adulticiding efforts is the best choice in the rainy season; the combination of the optimal personal protections and treatments is the preferential option in the dry season. When only minimizing the economical cost, the combination of the optimal adulticide and larvicide is the better selection in the rainy season; the combination of the optimal personal protections, treatments and adulticiding efforts is the prior choose in the dry season. Thus, there is a trade-off between the two objectives for all the effective combinations, decision-makers may choose an appropriate one to control the disease.

A novel engine and battery coupled thermal management strategy for connected HEVs based on switched model predictive control under low temperature

Under a low-temperature environment, electric vehicles face serious environmental adaptability problems, and efficient vehicle thermal management strategies are urgently needed. This paper presents a novel engine–battery coupled thermal management strategy for connected hybrid electric vehicles (HEVs). An improved system structure for an engine–battery coupled thermal management system (engine–battery CTMS) is designed to avoid unnecessary heat loss. The control requirements of the engine–battery CTMS include minimum engine fuel consumption, minimum power battery aging damage and minimum system energy consumption, which constitutes a multi-objective optimal control problem in a finite time domain. Based on model predictive control (MPC) theory, a switched nonlinear MPC (NMPC) control strategy is proposed to solve the optimal control problem of the complex coupled multi-input multi-output system. To verify the effectiveness of the proposed strategy, three comparative experiments of the centralized NMPC-based and rule-based methods combined with the improved system structure and the unimproved system structure are designed. The results of the cosimulation experiment between MATLAB/Simulink and AMEsim under various driving cycles and different ambient temperatures show that the improved structure and switched control strategy confer great advantages in reducing the controller computation burden, engine fuel consumption, and power battery aging damage.

Extending Life of Lithium-Ion Battery Systems by Embracing Heterogeneities via an Optimal Control-Based Active Balancing Strategy

This article formulates and solves a multiobjective fast charging-minimum degradation optimal control problem (OCP) for a lithium-ion battery module made of series-connected cells equipped with an active balancing circuitry. The cells in the module are subject to heterogeneity induced by manufacturing defects and nonuniform operating conditions. Each cell is expressed via a coupled nonlinear electrochemical, thermal, and aging model and the direct collocation approach is employed to transcribe the OCP into a nonlinear programming problem (NLP). The proposed OCP is formulated under two different schemes of charging operation: 1) same charging time (OCP-SCT) and 2) different charging time (OCP-DCT). The former assumes simultaneous charging of all cells irrespective of their initial conditions, whereas the latter allows for different charging times of the cells to account for heterogeneous initial conditions. The problem is solved for a module with two series-connected cells with intrinsic heterogeneity among them in terms of state of charge and state of health. Results show that the OCP-DCT scheme provides more flexibility to deal with heterogeneity, boasting of lower temperature increase, charging current amplitudes, and degradation. Finally, a comparison with the common practice of constant current (CC) charging over a long-term cycling operation shows that promising savings, in terms of retained capacity, are attainable under both control (OCP-SCT and OCP-DCT) schemes.

Time-Domain-Based Superposition Analysis for Triple Active Bridge and Its Application for ZVS and Current Stress Optimization

With the advantages of simple topology, voltage matching, electrical isolation, and bi-directional energy control, Triple Active Bridge (TAB) has become an active exploration and attempt for the flexible interconnection of DC ports. The high-frequency chain current (HFCC) calculation is the crucial step of zero voltage switching (ZVS) regions and current stresses, providing the basis for the subsequent performance optimization of TAB. Due to the number of switches increasing, TAB´s degrees of freedom (the phase shift angles and duty cycles) have multiplied compared with its two-port topology. The existing current calculation methods of TAB are challenging to balance accuracy and simplicity. Currently, the simple and accurate HFCC model considering all the TAB variables can hardly be found in the literature. This paper proposes a unified and novel solution for TAB HFCC calculation based on the superposition theorem, Thevenin theorem, and time domain method. It can get the uniform formula of the HFCC when all the control variables change. Based on the formula derived, this paper further presents the corresponding ZVS and current stress analysis of TAB. A multi-objective optimal control method is proposed, demonstrating efficiency improvement. Moreover, the trade-offs between the control simplicity and optimization effect are analyzed based on the proposed HFCC model. The modulation pattern with the least algorithmic complexity for efficiency maximization is found. The validity and accuracy of the proposed method have been verified experimentally.

Multi-Objective Control Strategy for Switched Reluctance Generators in Small-Scale Wind Power Generations

Switched reluctance generators (SRGs) are widely used in wind power generation. However, due to the natural tendency of SRG, there are always nonnegligible conflicts to achieve high efficiency and low output voltage ripple at the same time. This creates difficulties for the high-performance of SRG. Thus, a multi-objective optimization control strategy is proposed in this paper to improve the static performance of SRG. The proposed control strategy contains following steps. First, in order to gain the maximum output power range at different rotor speeds, the turn-off angle is optimized off-line by simulated annealing algorithm (SAA). The optimized results are fitted as a function of rotor speed for on-line regulating; then, a closed-loop controller is built, and the reference current is regulated according to the difference between actual output power and required output power. Second, a multi-objective function is constructed as the evaluation result of SRG performance, which takes system efficiency, output voltage ripple and power converter loss into consideration. In the end, the turn-on angle is tuned by SAA according to the real-time multi-objective evaluation result. The proposed control strategy can be flexibly applied to SRGs with different structures and avoids the disadvantage of single-objective optimization. The simulation and experiments results show that the overall performance of SRG is improved.

Identification of Motor Control Objectives in Human Locomotion via Multi-Objective Inverse Optimal Control

Abstract Predictive simulations of human motion are a precious resource for a deeper understanding of the motor control policies encoded by the central nervous system. They also have profound implications for the design and control of assistive and rehabilitation devices, for ergonomics, as well as for surgical planning. However, the potential of state-of-the-art predictive approaches is not fully realized yet, making it difficult to draw convincing conclusions about the actual optimality principles underlying human walking. In the present study, we propose a novel formulation of a bilevel, inverse optimal control strategy based on a full-body three-dimensional neuromusculoskeletal model. In the lower level, prediction of walking is formulated as a principled multi-objective optimal control problem based on a weighted Chebyshev metric, whereas the contributions of candidate control objectives are systematically and efficiently identified in the upper level. Our framework has proved to be effective in determining the contributions of the selected objectives and in reproducing salient features of human locomotion. Nonetheless, some deviations from the experimental kinematic and kinetic trajectories have emerged, suggesting directions for future research. The proposed framework can serve as an inverse optimal control platform for testing multiple optimality criteria, with the ultimate goal of learning the control objectives that best explain observed human motion.2

Multi-objective optimal droop control of solid oxide fuel cell based integrated energy system

Solid oxide fuel cell (SOFC) based integrated energy system (IES) is promising in the future low-carbon power generation market, due to the high efficiency and flexibility. However, it is challenging for the dynamic control design in dealing with the conflicting objectives in terms of fast power tracking and overall efficiency during the transient process of load response. To this end, this paper develops a multi-objective optimal droop control strategy for the real-time power dispatch of the IES. Firstly, a nonlinear implicit dynamic model consisting of SOFC, lithium-ion battery, photovoltaic array and DC-DC converter is developed. Then, a multi-objective optimization is formulated to balance the power tracking performance and transient efficiency. Non-dominated sorting genetic algorithm-II (NSGA-II) is adopted to search the optimal parameters for droop controller. Simulation results demonstrates that the electricity loss of the proposed method can be reduced by 96.26% with a slight compromise in power tracking performance.

Local stability of solutions to a parametric multi-objective optimal control problem

This paper studies local stability of solutions to a parametric multi-objective optimal control problem with constraints. By combining the scalarization method and non-scalarization methods, we show that if the unperturbed problem has a locally strong Pareto solution, then the Pareto solution set is locally Hölder continuous at a reference parameter.

A grid‐based searching algorithm for observer‐based multiobjective control of T–S fuzzy stochastic jump‐diffusion systems

Most studies on a multiobjective optimal control problem (MOCP) with nonlinear stochastic jump-diffusion system (NSJDS) constraints assume the state vector is available, but in practice, this is not necessarily the case. The observer-based MOCP is worthy of further research. Furthermore, the hybrid multiobjective differential evolution algorithm (HMODEA) is usually employed to help solve MOCPs with dynamical system constraints, and such problems often have a higher computational burden. To address these two issues, a grid-based front-squeezing searching algorithm (GBFSA) is proposed to solve the observer-based MOCP with NSJDS. Takagi-Sugeno (T-S) fuzzy model is used to approximate the NSJDS and convert the problem into an MOCP with linear matrix inequality (LMI) constraints. Then, the GBFSA efficiently searches for the Pareto front by merging the LMIs and the squeezing theorem. To automatically select a preferred Pareto controller, the minimum Manhattan distance (MMD) approch is applied. Mathematical proofs are given to show that the obtained Pareto optimal controller can concurrently stabilize the associated NSJDS and achieve the desired performance indices. In addition, computational complexity and convergence analysis are also provided.

Multi-objective optimal edge-drop control in tandem cold rolling of silicon steel strip

In cold rolling of silicon steel strip, edge drop directly affects the side cutting and yield of silicon steel. To improve the edge drop of silicon steel in the cold rolling process, a multi-stand coordinated control strategy and model based on multi-objective optimization are proposed. The first step is to analyze the influence of each control stand work roll shifting (WRS) on edge drop through the finite element model (FEM), then determine the edge drop control effectiveness of each work roll shifting actuator. Meanwhile, a fitting model is proposed to solve the limitation caused by the discrete change of efficiency factors in solving the optimal adjustments of each WRS. On this basis, the target model for silicon steel edge drop control is formulated, and the optimal adjustment model of WRS of each stand is established. To realize the optimal coordinated control among the rolling mill stands, a multi-objective optimal model of edge drop control has been established by the overall modeling method. The improved penalty function algorithm is developed to calculate the optimal adjustment of WRS for each stand. The experiments and application show that the proposed multi-objective optimal control strategy and model can effectively improve the accuracy of edge drop control in silicon steel continuous cold rolling.

Modeling and multi-objective optimal control of reaction-diffusion COVID-19 system due to vaccination and patient isolation

In this paper, a reaction-diffusion COVID-19 model is proposed to explore how vaccination-isolation strategies affect the development of the epidemic. First, the basic dynamical properties of the system are explored. Then, the system’s asymptotic distributions of endemic equilibrium under different conditions are studied. Further, the global sensitivity analysis of R0 is implemented with the aim of determining the sensitivity for these parameters. In addition, the optimal vaccination-isolation strategy based on the optimal path is proposed. Meantime, social cost C(m,σ), social benefit B(m,σ), threshold R0(m,σ) three objective optimization problem based on vaccination-isolation strategy is explored, and the maximum social cost (MSC) and maximum social benefit (MSB) are obtained. Finally, the instance prediction of the Lhasa epidemic in China on August 7, 2022, is made by using the piecewise infection rates β1(t), β2(t), and some key indicators are obtained as follows: (1) The basic reproduction numbers of each stage in Lhasa, China are R0(1:8)=0.4678,R0(9:20)=2.7655,R0(21:30)=0.3810 and R0(31:100)=0.7819; (2) The daily new cases of this epidemic will peak at 43 on the 20th day (August 26, 2022); (3) The cumulative cases in Lhasa, China will reach about 640 and be cleared about the 80th day (October 28, 2022). Our research will contribute to winning the war on epidemic prevention and control.

Optimal Lane-Free Crossing of CAVs Through Intersections

Connected and autonomous vehicles (CAVs), unlike conventional cars, will utilise the whole space of intersections and cross in a lane-free order. This article formulates such a lane-free crossing of intersections as a multi-objective optimal control problem (OCP) that minimises the overall crossing time, as well as the energy consumption due to the acceleration of CAVs. The constraints that avoid collision of vehicles with each other and with road boundaries are smoothed by applying the dual problem theory of convex optimisation. The developed algorithm is capable of finding the lower boundary of the crossing time of a junction which can be used as a benchmark for comparing other intersection crossing algorithms. Simulation results show that the lane-free crossing time is better by an average of 40% as compared to the state-of-the-art reservation-based method, whilst consuming the same amount of energy. Furthermore, it is shown that the lane-free crossing time through intersections is fixed to a constant value regardless of the number of CAVs.

Optimal design and stability control of an automotive magnetorheological brake considering the temperature effect

Magnetorheological brake (MRB) provide a potential alternative to traditional mechanical friction brakes in automobile applications owing to their technical advantages in terms of being compact yet powerful, having superior control performance, and wire-control features. However, the temperature effect has been an important issue that should be considered in the design and precise control of MRB. This paper presents the multi-objective optimal design and stability control of an automotive MRB considering the temperature effect. First, a description of the configuration design, magnetostatic field simulation, and mathematical modeling of the automotive MRB is presented in detail. Subsequently, design optimization of the MRB is carried out. The design of experiment method was adopted to screen out the major design variables, and the optimal solution was obtained using a multi-objective genetic algorithm (GA) non-dominated sorting genetic algorithm (NSGA-II). Thereafter, the torque output and response performance, as well as the temperature characteristics of the optimal MRB prototype are experimentally evaluated. The results indicate that the optimal design of the MRB was reasonable and effective. Finally, a GA-based back propagation neural network proportion integration differentiation controller is proposed for the stability control of the MRB during automobile braking. Its performance was verified to be satisfactory through both simulations and experiments.

Three-Level Inverter-PMSM Model Predictive Current Control Based on the Extended Control Set

In the neutral point clamped (NPC) three-level inverter-permanent magnet synchronous motor system, traditional model predictive current control (MPCC) uses the system predictive model to traverse the 27 basic voltage vectors, to achieve the d-q axis current component and neutral point voltage of the multi-objective optimal control. Finite control set model predictive control predicts the state change of the control target at future moments based on a finite number of switching states of the inverter. The control principle of this method is simple and easy to implement, but the control effectiveness of this control strategy is limited because only one basic vector can be selected as the optimum output per control period. In this paper, a model predictive current control strategy based on an extended control set (ECS-MPCC) is proposed, which can improve the control performance of the system by extending the control set to select multiple vectors in a single control period compared to the traditional strategy. In addition, to address the disadvantage of extending virtual space vectors leading to an increase in computation, this paper proposes a fast search method for optimal vector based on region reduction. The proposed method avoids the optimization process traversing all virtual space vectors, thus enabling a fast search for the optimal vector. The experimental results show that the proposed control strategy has good steady-state and dynamic performance.