Multi-objective Optimal Control Research Articles

Mixed H2/H∞ Optimal Voltage Control Design for Smart Transformer Low-Voltage Inverter

The smart transformer has been widely applied for the integration of renewables and loads. For the smart transformer application, the voltage control of low-voltage inverter is important for feeding the load. In this paper, a multi-objective optimization control design approach which comprehensively considers all aspects of indexes, such as linear quadratic (LQ) index, H∞ norm, and closed-loop poles placement, is proposed based on the linear matrix inequality (LMI) solution. The proposed approach is able to alleviate the weight of the designer from the tedious design process of the multiple resonant controllers and the selection of the weighting matrix for the LQ control. Besides that, some excellent performances such as fast recovering time, low total harmonic distortion (THD) and high robustness are achieved by the proposed approach. The THD are 0.5% and 1.7% for linear and non-linear loads, respectively. The voltage drop for linear load step is reduced to 10 V. The proposed approach is applied to a 5 kVA three-phase inverter to yield an optimal control law. Results from the simulation and experiment presented herein will illustrate and validate the proposed approach.

Optimization Analysis of Full Life Cycle Energy Efficiency Multi-Objective Parallel Pump Sets

Aiming at the problem that the current single-objective control model of parallel pumping groups only focuses on the optimization of energy efficiency of operating conditions and operating costs, and cannot adjust the real-time working conditions of the pump group according to the comprehensive energy efficiency state of the pump group in the whole life cycle and adjust the pump group operation strategy accordingly, A multi-objective optimal control model for energy efficiency of a pump set is proposed, which can adjust the weight coefficients of three objective functions autonomously according to the current energy efficiency state of the pump set in the whole life cycle. In this way, the high energy efficiency of the parallel pump group in the low wear stage, that is, the low target deviation and specific energy consumption, and the high reliability in the high wear stage, that is, the lower impeller load improves the efficiency of the pump group in the whole life cycle and extend the service life of the pump group. Determine the multi-objective energy efficiency optimization control model of the pump group, use the main function linear and geometric weighting method, the ideal point value, and the distance deviation method to determine the objective function, and solve the multi-objective ideal point model with the help of LINGO, and obtain the optimal solution of the highest system total efficiency, the lowest pump group specific energy consumption and the highest system reliability. Pareto Frontier Comparison is used to study the transversality of the ideal point model solution set. Experimental results show that through the distribution of the model solution in the indicator space, the model can adjust the control strategy according to the real-time state of the pump group by adjusting the target weight combination.

Model Predictive Control for Automotive Climate Control Systems via Value Function Approximation

Among the auxiliary loads in light-duty vehicles, the air conditioning system is the single largest energy consumer. For electrified vehicles, the impact of heating and cooling loads becomes even more significant, as they compete with the powertrain for battery energy use and can significantly reduce the range or performance. While considerable work has been made in the field of optimal energy management for electrified vehicles and optimization of vehicle velocity for eco-driving, few contributions have addressed the application of energy-optimal control for heating and cooling loads. This letter proposes an energy management strategy for the thermal management system of an electrified powertrain, based on Model Predictive Control. Starting from a nonlinear model of the vapor compression refrigeration system that captures the dynamics of the refrigerant in the heat exchangers and the power consumption of the system, a constrained multi-objective optimal control problem is formulated to reduce energy consumption while tracking a desired thermal set point. An efficient implementation of MPC is proposed for real-time applications by introducing a terminal cost obtained from the approximation of the global optimal solution.

Deep Reinforcement Learning Control for Pulsed Power Load Online Deployment in DC Shipboard Integrated Power System

Online deployment of pulsed power load (PPL) is one of the most challenging issues in DC shipboard integrated power systems (SIPSs), which leads to a multi-objective optimal control problem subject to various constraints in this paper. Since traditional model-based methods face difficulties in designing the optimal control policy and are prone to model inaccuracy and parameter uncertainty, there is an urgent need for a model-free and also high-performance control approach. Thus, a deep reinforcement learning (DRL) optimal control, which employs the twin-delayed deep deterministic policy gradient (TD3) algorithm, is presented in this paper. The DRL optimal control adopts a stack-based state observation technique to enhance learning and control performance, and it uses a multi-objective reward function design to signify the overall dynamic performance. Besides achieving the safe and fast online deployment of PPL, it also fulfills the regulation of DC bus voltage and the proportional current sharing among distributed generations (DGs). Moreover, the DRL control has an advantage in handling the ramp rate constraints of SIPS. The optimal control satisfying ramp rate constraints can be obtained through a deep learning process. The performance of the proposed DRL control is validated by case studies considering different load conditions.

Infinite-dimensional multiobjective optimal control in continuous time

Infinite-dimensional multiobjective optimal control in continuous time

Predictive control research for cement burning system using two-cycle coupling optimization

A stable, high quality cement burning system producing clinker with low energy consumption is important for cement company. However, in the actual operation of the combustion system, there are contradictory indicators such as electricity consumption, coal consumption and clinker quality that are difficult to be jointly optimized, as well as dynamic and complex working conditions that are difficult to be artificially adjusted to the optimal state. In order to solve the above problems, a multi-objective optimal predictive control model is proposed in this paper. The prediction part of the model consists of a prediction model of cement burning system based on convolutional neural network. The optimization part, on the other hand, combines electricity and coal consumption into one energy target and uses cement clinker quality as a constraint to find the optimal production state. This modeling approach simplifies the problem and avoids the need to solve for the Pareto optimal solution. The control part is then based on the above-mentioned model with a double-cycle coupled cycle optimization to obtain set values of controlled variables that satisfy the changing operating conditions and finally control target to track the dynamic operating conditions. Experimental results show that the method described in this paper reduces the content of free calcium oxide after cement combustion, thus improving the quality of cement clinker, while reducing the fluctuations of the control variables in each production process and improving the stability of the combustion system. There is also a significant reduction in production energy consumption.

A multi-objective power flow optimization control strategy for a power split plug-in hybrid electric vehicle using game theory

A multi-objective power flow optimization control strategy for a power split plug-in hybrid electric vehicle using game theory

Multi-Objective Unified Optimal Control Strategy for DAB Converters with Triple-Phase-Shift Control

To solve the problems of large current stress, difficult soft-switching of all switches, and slow dynamic response of dual active bridge converters, a multi-objective unified optimal control strategy based on triple-phase-shift control was proposed. The forward power flow global modes of triple-phase-shift control were analyzed, and three high-efficiency modes were selected to establish the analytical models of current stress and soft-switching. Combined with these models, the optimal solutions in different modes were derived by using the cost function-optimization equation to overcome the limitation of the Lagrange multiplier method, such that the DAB converter achieved the minimum current stress, and all switches operated in the soft-switching state over the entire power range. At the same time, the virtual power component was introduced in the phase-shift ratio combination, which improved the dynamic response of output voltage under the input voltage or load steps changed by power control. The theoretical analysis and experimental results show that the proposed control strategy can optimize the performance of the DAB converter from three aspects, such as current stress, soft-switching, and dynamic response, which achieves multi-objective optimization of the steady-state and dynamic performance of DAB converters.

Multi-objective infinite horizon optimal control problems: characterization of the Pareto fronts and Pareto solutions

Multi-objective infinite horizon optimal control problems: characterization of the Pareto fronts and Pareto solutions

Multi-objective optimal control for proton exchange membrane fuel cell via large-scale deep reinforcement learning

To achieve a high operation efficiency and control performance of proton exchange membrane fuel cell (PEMFC), a multi-objective optimal fractional-order proportion integration differentiation (FOPID) controller is proposed to maintain the oxygen excess ratio (OER) and output voltage at the reference value simultaneously. In addition, a novel large-scale deep reinforcement learning called demonstration curriculum strategy large-scale multi-delay deep deterministic policy gradient (DCSL-MD3PG) algorithm is designed to operate as the tuner of this controller. This algorithm applies the teacher–student large-scale deep reinforcement learning strategy as well as the demonstration curriculum learning strategy and a number of techniques in the offline training to improve robustness and optimize control ability of the controller. Simulation results show that, taking the benefits of the excellent adaptability and model-free features of deep reinforcement learning, the adaptive optimal FOPID algorithm can ensures the optimal and comprehensive control performance of OER and output voltage while satisfying the security constraints of PEMFC.

Retraceable and online multi-objective active optimal control using belief rule base

A new approach that employs the belief rule base (BRB) is proposed in this study with the goal of Retraceable and Online Multi-objective Active (ROMA) optimal control for complex systems, namely ROMA-BRB. Active optimal control means that multiple objectives are controlled by actively identifying and optimizing key factors in the input. The retraceability requirement means that the procedural and final outputs can be traced back to the inputs to provide maximum accountability. The online requirement is met if the procedures are derivable and only adopting deterministic optimization approaches. To meet those requirements, BRB is adopted owing to its derivable procedures as a white box. There are four major steps in the new ROMA-BRB approach. First, multiple BRBs are constructed for multiple outputs. Then, the contribution of each factor in the input made to each output is calculated. Third, key factors are identified by comparing their contributions to multiple outputs. Finally, the identified key factors are optimized for actively controlling multi-objectives by pushing the Pareto frontier in an online manner. A practical tunnel-induced safety control case is studied whose goal is to reduce both the settlement and the building tilt rate (BTR). Case study results validate that both the settlement and BTR are effectively reduced by optimizing only the key operational factors. The validity of the proposed ROMA-BRB approach is also confirmed by comparing the results of pursuing only one objective, as well as using different numbers of key factors and other weight settings.

Model Predictive Control of Internal Combustion Engines: A Review and Future Directions

An internal combustion engine (ICE) is a highly nonlinear dynamic and complex engineering system whose operation is constrained by operational limits, including emissions, noise, peak in-cylinder pressure, combustion stability, and actuator constraints. To optimize today’s ICEs, seven to ten control actuators and 10–20 feedback sensors are often used, depending on the engine applications and target emission regulations. This requires extensive engine experimentation to calibrate the engine control module (ECM), which is both cumbersome and costly. Despite these efforts, optimal operation, particularly during engine transients and to meet real driving emission (RDE) targets for broad engine speed and load conditions, has still not been obtained. Methods of model predictive control (MPC) have shown promising results for real-time multi-objective optimal control of constrained multi-variable nonlinear systems, including ICEs. This paper reviews the application of MPC for ICEs and analyzes the recent developments in MPC that can be utilized in ECMs. ICE control and calibration can be enhanced by taking advantage of the recent developments in the field of Artificial Intelligence (AI) in applying Machine Learning (ML) to large-scale engine data. Recent developments in the field of ML-MPC are investigated, and promising methods for ICE control applications are identified in this paper.

Infinite horizon multiobjective optimal control of stochastic cooperative linear-quadratic dynamic difference games

This article is concerned with the infinite horizon stochastic cooperative linear-quadratic (LQ) dynamic difference game in both the regular and the indefinite cases. Firstly, due to the constraints imposed on the weighting matrices and the linearity of the dynamic system, the costs are shown to be convex spontaneously for the regular stochastic cooperative LQ difference game, which yields the equivalence between the minimization of the weighted sum of costs and the Pareto optimal control. Secondly, the Pareto optimal control is derived for the regular game on the ground of the solution to the weighted algebraic Riccati equation (WARE) under exact observability, and then Pareto solutions are identified via the optimal feedback gain matrices and the solution to the weighted algebraic Lyapunov equation (WALE). Moreover, a new criterion which is also necessary and sufficient is developed to guarantee the costs to be convex for the indefinite case, and the Pareto optimality is investigated based on the solutions to the weighted generalized algebraic Riccati equation (WGARE) and the weighted generalized algebraic Lyapunov equation (WGALE) combining with the semidefinite programming (SDP). Finally, the fishery management game in the economy is presented to illustrate the obtained results.

Aging Affects Multi-Objective Optimal Control Strategies during Obstacle Crossing

Obstacle crossing challenges balance and increases the risk of falls in older people. Knowledge of the control strategies adopted by older people will be helpful for the study of the mechanisms of falls during obstacle crossing and the development of fall-prevention approaches. A mechanical model of the body combined with measured gait data was used to study the control strategies adopted by 17 healthy older and 17 young adults when crossing obstacles of different heights, in terms of the best-compromise weighting sets for the objectives of minimizing energy expenditure and maximizing the toe-obstacle and heel-obstacle clearances. The older group showed increased leading toe-obstacle clearance and trailing toe-obstacle distance, but decreased leading heel-obstacle distance. Compared with the young, the crossing strategy of older people emphasized the foot-obstacle clearance to reduce the risk of tripping, at the expense of energy expenditure. It appears that the multi-objective optimal control strategy relies on the muscular strength of the lower extremities and precise end-point control. Therefore, maintaining or improving the muscle strength and the ability of limb position control is critical for safe and successful obstacle-crossing in the older population.

Second-Order Lagrange Multiplier Rules in Multiobjective Optimal Control of Infinite Dimensional Systems Under State Constraints and Mixed Pointwise Constraints

Second-Order Lagrange Multiplier Rules in Multiobjective Optimal Control of Infinite Dimensional Systems Under State Constraints and Mixed Pointwise Constraints

Automatic Guided Vehicle Global Path Planning Considering Multi-objective Optimization and Speed Control

Automatic Guided Vehicle Global Path Planning Considering Multi-objective Optimization and Speed Control

Single and Multiobjective optimal control of epidemic models involving vaccination and treatment

Introduction: A rigorous multiobjective optimal control strategy (that does not require the use of weighting functions) of the epidemic models that consider vaccination and treatment strategies is presented. Modifications of the standard susceptible-infectious-removed, susceptible-exposed-infectious-removed, and the modified susceptible-infectious-removed models are dynamically optimized to minimize the number of infected individuals while, controlling the rate at which the individuals are vaccinated and treated. Method:The optimization program, Pyomo , where the differential equations are automatically converted to a Nonlinear Program using the orthogonal collocation method is used for performing the dynamic optimization calculations. The Lagrange-Radau quadrature with three collocation points and 10 finite elements are chosen. The resulting nonlinear optimization problem was solved using the solver BARON 19.3, accessed through the Pyomo-GAMS27.2 interface. Results: The computational results how that the multiobjective optimal control profiles generated by this strategy are very similar to those produced when weighting functions are used. Conclusion: The main conclusion of this work is to demonstrate that one can perform a rigorous dynamic optimization of epidemic models without the use of weighting functions that have the potential to produce some uncertainty and doubt in the results, in addition to dealing with unnecessary additional variables.

Optimization-Driven Powertrain-Oriented Adaptive Cruise Control to Improve Energy Saving and Passenger Comfort

Assessing the potential of advanced driver assistance systems requires developing dedicated control algorithms for controlling the longitudinal speed of automated vehicles over time. In this paper, a multiobjective off-line optimal control approach for planning the speed of the following vehicle in adaptive cruise control (ACC) driving is proposed. The implemented method relies on the principle of global optimality fostered by dynamic programming (DP) and aims to minimize propelling energy consumption and enhance passenger comfort. The powertrain model and onboard control system are integrated within the proposed car-following optimization framework. The retained ACC approach ensures that the distance between the following vehicle and the preceding vehicle is always maintained within allowed limits. The flexibility of the proposed method is demonstrated here through ease of implementation on a wide range of powertrain categories, including a conventional vehicle propelled by an internal combustion engine solely, a pure electric vehicle, a parallel P2 hybrid electric vehicle (HEV) and a power-split HEV. Moreover, different driving conditions are considered to prove the effectiveness of the proposed optimization-driven ACC approach. Obtained simulation results suggest that up to 22% energy-saving and 48% passenger comfort improvement might be achieved for the ACC-enabled vehicle compared with the preceding vehicle by implementing the proposed optimization-driven ACC approach. Engineers may adopt the proposed workflow to evaluate corresponding real-time ACC approaches and assess optimal powertrain design solutions for ACC driving.

Modeling illegal logging in Brazil

Deforestation is a major threat to global environmental wellness, with illegal logging as one of the major causes. Recently, there has been increased effort to model environmental crime, with the goal of assisting law enforcement agencies in deterring these activities. We present a continuous model for illegal logging applicable to arbitrary domains. We model the practice of criminals under influence of law enforcement agencies using tools from multiobjective optimal control theory and consider non-instantaneous logging events and load-dependent travel velocity. We calibrate our model using real deforestation data from the Brazilian rainforest and demonstrate the importance of geographically targeted patrol strategies.

Generalized Clarke epiderivatives of the extremum multifunction to a multi-objective parametric discrete optimal control problem

<p style='text-indent:20px;'>This paper deals with the generalized Clarke epiderivative of the extremum multifunction of a multi-objective parametric convex discrete optimal control problem with linear state equations and control constraints. By establishing an abstract result on the generalized epiderivative of the extremum multifunction of a multi-objective parametric convex mathematical programming problem, we derive a formula for computing the generalized Clarke epiderivative of the extremum multifunction to a multi-objective parametric convex discrete optimal control problem. Examples are given to illustrate the obtained results.</p>