Minimization Of Cost Function Research Articles

Use of neural networks for safe collision avoidance for groups of autonomous vessels

This article analyzes and compares the effectiveness of two algorithms for collision avoidance in groups of autonomous vessels: one based on geometric analysis of vessel approach and cost function minimization for calculating a safe maneuver (traditional algorithm), and an algorithm utilizing a neural network. Both algorithms assume external control of a group of vessels within a specific area using a vessel traffic management system and coordinated maneuvering of dangerously approaching vessels. Descriptions of these algorithms are provided along with their simplified block diagrams; to solve the task of safely maneuvering a group of vessels, a sequential analysis of all possible vessel pairs in the group and changes in their courses is proposed. The process of creating three test datasets is described, two of which were generated using a program and included 100 scenarios each, while the third was manually composed and included 30 scenarios for different vessel group approach variations. During the testing of the neural network algorithm, two neural networks trained to predict safe courses for vessel pairs were utilized. The neural network used in the algorithm, trained on 743671 samples, allowed the processing of test vessel approach scenarios with an accuracy comparable to the traditional algorithm. Depending on the number of dangerously approaching vessels in the area, the neural network algorithm processed test scenarios 2–14 times faster than the traditional algorithm. The paper highlights the limitations of the described algorithms and outlines planned improvements for subsequent research, including the optimization of the safe maneuver selection methodology and further training of the neural network on larger data volumes.

Dynamic overmodulation strategy based on torque and flux optimal tracking for DTC‐SVM of surface‐mounted PMSM drives

AbstractDirect torque control with space vector modulation has been increasingly attracting emphasis for permanent‐magnet synchronous machine control, benefiting from a high dynamic response and low torque ripple. However, the rapid tracking performance of torque and stator flux linkage is gradually deteriorating as the machine enters the overmodulation region because of the output‐voltage limitation of the inverter. Therefore, to enhance the system tracking performance in the overmodulation region, an innovative overmodulation method based on torque and flux optimal tracking is proposed. In contrast to the conventional overmodulation method where only one of the torque and stator flux linkage tracking is considered, the proposed strategy first constructs the weightless cost function to achieve a trade‐off control between the torque and stator flux linkage. Then, by using an equivalent geometric path to intuitively express the weightless cost function, the minimum cost function can be easily solved and the optimal output voltage vector can be determined correspondingly, to achieve the fast‐tracking of both the torque and stator flux linkage. Additionally, the voltage utilization of different overmodulation schemes is also analysed. Finally, the experimental results demonstrate the efficiency and practicality of the proposed strategy.

ENHANCED MODEL-FREE PREDICTIVE CONTROL FOR VOLTAGE SOURCE INVERTERS USING AN ADAPTIVE OBSERVER

In this paper, a free model predictive control based on the active vector execution time (AVET-MFPC) using an adaptive observer is proposed for two-level voltage source inverters. The traditional model-free predictive control (MFPC) uses the sampling period to select one voltage vector for all candidate vectors according to the minimizing cost function principle. With the proposed control, two vectors are selected at one sampling period. The first vector is an active vector that uses the execution time of the active vector to select it, while the second one is a zero vector as it is applied after the active vector. The execution time is calculated using the ultra-local model (ULM) equation. In the traditional MFPC, the factor in the ULM is chosen with approximate values ranging between ±50 % of the nominal value. This paper proposes an adaptive sliding mode observer (ASMO) with an improved design to observe the variation of this factor, especially in case of mismatch parameters and during a step change in the reference signal. Combining the proposed ASMO observer and the AVET-MFPC controller gives faster system response, good tracking results, and less computational burden. Finally, the effectiveness of the proposed control model is approved and confirmed under various conditions, as well as the simulations carried out and the results obtained.

Self-learning Markov prediction algorithm based aging-oriented gradient drop power control strategy for the transient modes of fuel cell hybrid electric vehicles

The power transients caused by switching from drive mode to brake mode in fuel cell hybrid electric vehicles (FCHEV) can result in significant degradation cost losses to the fuel cell. To address this issue, this study proposes a self-learning Markov prediction algorithm based aging-oriented gradient drop power control strategy. First, a real-time self-learning Markov predictor (SLMP) based on the traditional offline training Markov improvement is designed to predict the demand power and combined with the sequential quadratic programming (SQP) optimization algorithm to solve for the inner optimal demand power based on its global cost function minimization characteristic. On this basis, the fuel cell gradient drop power (FGDP) strategy is proposed to optimize the operating state of the vehicle powertrain under vehicle mode switching. This involves establishing a power gradient drop step based on considering the fuel cell hydrogen consumption cost and its lifetime degradation cost to further obtain the outer fuel cell demand power at the optimal step. And three execution modes are designed to trigger the FGDP strategy. Finally, by combining the above efforts, the SLMP-FGDP optimization control strategy is constructed. The numerical verification and hardware in loop experiments results show that the proposed improved SLMP can predict the vehicle demand power more accurately. Compared with the non-FGDP system, the SLMP-FGDP strategy can effectively near-eliminate the fuel cell power transient due to any braking scenario, thus effectively controlling the fuel cell lifetime degradation cost in a lower range and realizing a reduction of up to 52.21% of the fuel cell usage costs without significantly sacrificing the hydrogen fuel economy.

State Feedback Via Judicious Pole Placement and Linear Quadratic Regulator – Application to Rotary Inverted Pendulum

In the control system regulatory concept, placing closed loop poles too far from the origin in the stability region produces fast regulation time but requires huge forcing energy as a trade-off. As such, stabilizing an unstable system with minimum energy is needed, though this presents a challenge to the designer. At the design phase, the designer may ponder the optimized energy while compromising the possibility of catastrophic stabilization phenomena due to minimal forcing thrust towards the poles. In this manuscript, a simple Linear Quadratic Regulator (LQR) is proposed as an alternative to full state feedback (FSF) with judicious pole placement. The efficacy of both approaches was observed by exploiting a Rotary Inverted Pendulum (RIP) as a testbed. Beforehand, the RIP system dynamics were developed in the time domain. RIP is an under-actuated mechanical system that is inherently nonlinear and unstable. The main control objectives of RIP are swing-up control, stabilization control, switching control, and trajectory control. The methodology involved the appearance of weighted matrices that were necessary for the minimum cost function. The Riccati and Lyapunov criteria are also exploited to facilitate design. The result shows the comparative transient performances of the two approaches, where the LQR outperforms the FSF in many aspects.

Experimental investigation of predictive control for PMSM-based wind turbine generation system

The theoretical analysis of permanent magnet synchronous machine (PMSM)-based wind turbine generation system was presented by many researchers; nevertheless, although the practical setup is still quite difficult, it is more valid. Moreover, the main challenge facing wind power systems is figuring out how to extract the most energy from varying wind speeds. Since wind turbine maintenance is hard and expensive, using wind speed sensors is a challenging operation. Therefore, this research suggests an effective and practical control system based on the Model Predictive Control Scheme (MPCS) for both the grid-side converter (GSC) and the machine-side converter (MSC) to optimize power extraction from wind energy. Detailed exploration of the MPCS for the PMSM and predictive power control (PPC) for the GSC involves stages such as flux estimation, torque prediction, and cost function minimization. The results obtained validate the higher performance of MPCS in comparison to the direct torque control (DTC) method. Furthermore, excellent tracking with high accuracy is achieved in relation to simulation and experimental data. Additionally, an evaluation indices based on root mean square error (RMSE) and gross system efficiency are used for wind turbine performance. These indices are used to show that, the feasibility of the MPCS approach compared with DTC under the same WT conditions. This approach offers a promising avenue for cost-effective wind energy conversion. The control systems were designed and implemented utilizing a DSPACE 1104 card. Experimental results confirm the effectiveness of the proposed mechanism in achieving maximum power point tracking (MPPT).

The neuroanatomical organization of the hypothalamus is driven by spatial and topological efficiency.

The hypothalamus in the mammalian brain is responsible for regulating functions associated with survival and reproduction representing a complex set of highly interconnected, yet anatomically and functionally distinct, sub-regions. It remains unclear what factors drive the spatial organization of sub-regions within the hypothalamus. One potential factor may be structural connectivity of the network that promotes efficient function with well-connected sub-regions placed closer together geometrically, i.e., the strongest axonal signal transferred through the shortest geometrical distance. To empirically test for such efficiency, we use hypothalamic data derived from the Allen Mouse Brain Connectivity Atlas, which provides a structural connectivity map of mouse brain regions derived from a series of viral tracing experiments. Using both cost function minimization and comparison with a weighted, sphere-packing ensemble, we demonstrate that the sum of the distances between hypothalamic sub-regions are not close to the minimum possible distance, consistent with prior whole brain studies. However, if such distances are weighted by the inverse of the magnitude of the connectivity, their sum is among the lowest possible values. Specifically, the hypothalamus appears within the top 94th percentile of neural efficiencies of randomly packed configurations and within one standard deviation of the median efficiency when packings are optimized for maximal neural efficiency. Our results, therefore, indicate that a combination of geometrical and topological constraints help govern the structure of the hypothalamus.

Optimal energy storage configuration to support 100 % renewable energy for Indonesia

This study presents a renewable energy (RE) optimization study to model the pathway to achieve 100 % carbon abatement, focussing on options for storage, using Indonesia's national electricity grid as a case study. Utilizing the PLEXOS energy simulation tool, the study covers the period 2021–2045. It employs an optimization of cost minimization function approach, encompassing investment, operation, maintenance, and unserved energy. The study integrates various components, including electricity supply and demand, transmission, renewable sources, and energy storage, while considering operational, build, and renewable energy target constraints. A range of scenarios are explored, varying in RE targets, battery capacities, and whether to include open-cycle gas turbines. The key novelty of this study is considering multiple versions of battery storage, with different options for the number of hours of storage. The findings indicate that higher RE targets lead to increased total installed nameplate capacity, with a significant portion from battery storage. In the early phases, batteries with 2-hour of capacity prioritized for short-term needs. As the focus shifts to more extended targets, batteries with a 4-hour capacity are recognized as more cost-effective and become the predominant choice. Over time, the least-cost strategy evolves to incorporate 10-hour capacity batteries to meet long-term energy storage requirements. To achieve a 100 % RE target by 2045, it is estimated that alongside every 100 MW of wind and solar capacity, there should be a corresponding 42 MW of energy storage. However, interpretations of these findings must consider the limited temporal resolution, uncertainties in demand and cost, and challenges related to grid inertia from energy storage, which may affect the stability and feasibility of the proposed solutions. This research offers crucial insights for energy policy and infrastructure development in renewable energy and storage system implementation.

Robust fixed-time distributed optimization with predefined convergence-time bound

This paper introduces a distributed optimization scheme for achieving formation control in multi-agent systems operating under switching networks and external disturbances. The proposed approach utilizes the zero-gradient sum property and consists of two steps. First, it guides each agent towards the minimizer of its respective local cost function. Subsequently, it achieves a formation around the minimizer of the global cost function. The distributed optimization scheme guarantees convergence before a predefined time, even under simultaneous switching networks and external disturbances, distinguishing it from existing finite and fixed-time schemes. Moreover, the algorithm eliminates the need for agents to exchange local gradients or Hessians of the cost functions or even prior knowledge of the number of agents in the network. Additionally, the proposed scheme copes with external disturbances using integral sliding modes. The scheme’s effectiveness is validated through an application to distributed source localization, for which several numerical results are provided.

Reduced complexity model predictive direct power control for unbalanced grid

The model predictive control (MPC) group is frequently used as a controller in PWM rectifiers because of its accuracy. Yet, the requirement of a processor with high computational efficiency for its real-time implementation has been a significant drawback. Although a few low-complexity MPCs have been reported in the past, none of such methods are validated in an unbalanced grid. Hence, this work aims to propose a reduced-complexity MPC algorithm that can also handle an unbalanced grid. The conventional MPC evaluates the cost function for all the switching vectors and then chooses the switching vector that produces the minimum cost. In contrast, by equating its first-order derivative of the cost function to 0, the proposed analytical approach directly evaluates switching vectors, resulting in a minimum value of the cost function. Thus, the controller estimates only the closest possible solutions of the cost function minimization process and abandons the rest. Furthermore, the proposed method also endorses the use of additional non-linear constraints in the cost function, which eradicates one of the major drawbacks of the previous low-complexity techniques. To ascertain the practicability of the proposed method, it is examined in the MATLAB/Simulink environment and the real-time system. The obtained results look promising as the proposed controller is able to imitate the performance of conventional MPC with less computational burden.

A novel weighting factor determined method of model predictive torque control for permanent magnet synchronous motor

AbstractIn the cost function of model predictive torque control (MPTC) of permanent magnet synchronous motor (PMSM), torque and flux linkage have different dimensions, and the weighting factor needs to be properly adjusted to optimise the control performance. Therefore, based on the discrete mathematical model of PMSM, the torque predictive error and flux predictive error expressions are mapped to the two‐phase static coordinate system, which is equivalent to the distance expressions from the endpoint of the voltage vector to the straight line and to the circle respectively. Because they have the same dimension, they can be directly superimposed to form the cost function proposed, which eliminates the selection process of the weighting factor. Then, the candidate voltage vector is substituted into the cost function in turn, and the optimal voltage vector with the minimum cost function is selected as the voltage input of the next control cycle. Finally, the simulation model and an experimental platform are established to compare the steady‐state and dynamic performance of the geometric solution‐based weighting factor determined method proposed with other MPTC methods.

ADAPTIVE CONTROL OF A SUBMARINE FOR VARIOUS DIVING DEPTHS USING AN EXPONENTIAL

Due to the progress of deep submergence capabilities, a submarine is extensively employed on many sides of marine science. For that reason, it has become necessary to design an effective submarine position controller while achieving a fast and stable mission. An adaptive analytical scheme for the underwater submarine was developed. The main purpose of the adaptive analytical scheme is to provide a powerful analytical controller that can successfully steer the submarine from the current state under the water to the surface of water in a short time. To achieve that, a seventh-term exponential function was proposed to reshape the reference diving depth while maintaining the control variable limitation and satisfying initial and final boundary conditions. The direct search method with two cascade loops was employed to achieve a minimum cost function by determining an appropriate constant of the function and minimum final time. However, using the direct search method can be time-consuming since a number of algebraic operations are executed inside these two loops. Therefore, the curve fitting method was used to fit the set of direct search method data using power functions. Then, at a certain diving depth, the function coefficients were computed based on the final settling time and function constant using the Gaussian elimination method. A nominal numerical simulation of the submarine’s model was implemented using both adaptive analytical and linear controllers.

Modified Memoryless Spectral-Scaling Broyden Family on Riemannian Manifolds

This paper presents modified memoryless quasi-Newton methods based on the spectral-scaling Broyden family on Riemannian manifolds. The method involves adding one parameter to the search direction of the memoryless self-scaling Broyden family on the manifold. Moreover, it uses a general map instead of vector transport. This idea has already been proposed within a general framework of Riemannian conjugate gradient methods where one can use vector transport, scaled vector transport, or an inverse retraction. We show that the search direction satisfies the sufficient descent condition under some assumptions on the parameters. In addition, we show global convergence of the proposed method under the Wolfe conditions. We numerically compare it with existing methods, including Riemannian conjugate gradient methods and the memoryless spectral-scaling Broyden family. The numerical results indicate that the proposed method with the BFGS formula is suitable for solving an off-diagonal cost function minimization problem on an oblique manifold.

Securing Internet-of-Medical-Things networks using cancellable ECG recognition

Reinforcement of the Internet of Medical Things (IoMT) network security has become extremely significant as these networks enable both patients and healthcare providers to communicate with each other by exchanging medical signals, data, and vital reports in a safe way. To ensure the safe transmission of sensitive information, robust and secure access mechanisms are paramount. Vulnerabilities in these networks, particularly at the access points, could expose patients to significant risks. Among the possible security measures, biometric authentication is becoming a more feasible choice, with a focus on leveraging regularly-monitored biomedical signals like Electrocardiogram (ECG) signals due to their unique characteristics. A notable challenge within all biometric authentication systems is the risk of losing original biometric traits, if hackers successfully compromise the biometric template storage space. Current research endorses replacement of the original biometrics used in access control with cancellable templates. These are produced using encryption or non-invertible transformation, which improves security by enabling the biometric templates to be changed in case an unwanted access is detected. This study presents a comprehensive framework for ECG-based recognition with cancellable templates. This framework may be used for accessing IoMT networks. An innovative methodology is introduced through non-invertible modification of ECG signals using blind signal separation and lightweight encryption. The basic idea here depends on the assumption that if the ECG signal and an auxiliary audio signal for the same person are subjected to a separation algorithm, the algorithm will yield two uncorrelated components through the minimization of a correlation cost function. Hence, the obtained outputs from the separation algorithm will be distorted versions of the ECG as well as the audio signals. The distorted versions of the ECG signals can be treated with a lightweight encryption stage and used as cancellable templates. Security enhancement is achieved through the utilization of the lightweight encryption stage based on a user-specific pattern and XOR operation, thereby reducing the processing burden associated with conventional encryption methods. The proposed framework efficacy is demonstrated through its application on the ECG-ID and MIT-BIH datasets, yielding promising results. The experimental evaluation reveals an Equal Error Rate (EER) of 0.134 on the ECG-ID dataset and 0.4 on the MIT-BIH dataset, alongside an exceptionally large Area under the Receiver Operating Characteristic curve (AROC) of 99.96% for both datasets. These results underscore the framework potential in securing IoMT networks through cancellable biometrics, offering a hybrid security model that combines the strengths of non-invertible transformations and lightweight encryption.

Robust predictive control strategy of SCIG-based drive system

This article presents a robust finite control set predictive scheme for a stand-alone squirrel cage induction generator (SCIG) drive. This technique is considered an alternative to the drive system due to the inclusion of system nonlinearities and fast dynamic response. The control objective in the distributed generation environment is to fix the output voltage to follow the stand-alone requirement. The strategy establishes optimized switching instants for cost function minimization for both source and load converter control and diminished cross-coupling amid active and reactive power during transient scenarios. The scheme is designed to achieve the minimal effect caused by the parameter uncertainties. During source and load changes, this work will also address the maintenance of dc-link voltage, machine, and load variables at the set value, supported by machine and load-end converter control to achieve stand-alone load objectives. In addition, the presented scheme is also tested with random variation of speed to check the efficacy of the control configuration. The drive performance is evaluated by simulation using MATLAB/Simulink environment. Comprehensive real-time findings obtained from a scaled laboratory test bench using dSPACE-1104 are provided to verify the feasibility of the predictive solution.

High-resolution US methane emissions inferred from an inversion of 2019 TROPOMI satellite data: contributions from individual states, urban areas, and landfills

Abstract. We quantify 2019 annual mean methane emissions in the contiguous US (CONUS) at 0.25° × 0.3125° resolution by inverse analysis of atmospheric methane columns measured by the Tropospheric Monitoring Instrument (TROPOMI). A gridded version of the US Environmental Protection Agency (EPA) Greenhouse Gas Emissions Inventory (GHGI) serves as the basis for the prior estimate for the inversion. We optimize emissions and quantify observing system information content for an eight-member inversion ensemble through analytical minimization of a Bayesian cost function. We achieve high resolution with a reduced-rank characterization of the observing system that optimally preserves information content. Our optimal (posterior) estimate of anthropogenic emissions in CONUS is 30.9 (30.0–31.8) Tg a−1, where the values in parentheses give the spread of the ensemble. This is a 13 % increase from the 2023 GHGI estimate for CONUS in 2019. We find emissions for livestock of 10.4 (10.0–10.7) Tg a−1, for oil and gas of 10.4 (10.1–10.7) Tg a−1, for coal of 1.5 (1.2–1.9) Tg a−1, for landfills of 6.9 (6.4–7.5) Tg a−1, for wastewater of 0.6 (0.5–0.7), and for other anthropogenic sources of 1.1 (1.0–1.2) Tg a−1. The largest increase relative to the GHGI occurs for landfills (51 %), with smaller increases for oil and gas (12 %) and livestock (11 %). These three sectors are responsible for 89 % of posterior anthropogenic emissions in CONUS. The largest decrease (28 %) is for coal. We exploit the high resolution of our inversion to quantify emissions from 70 individual landfills, where we find emissions are on median 77 % larger than the values reported to the EPA's Greenhouse Gas Reporting Program (GHGRP), a key data source for the GHGI. We attribute this underestimate to overestimated recovery efficiencies at landfill gas facilities and to under-accounting of site-specific operational changes and leaks. We also quantify emissions for the 48 individual states in CONUS, which we compare to the GHGI's new state-level inventories and to independent state-produced inventories. Our posterior emissions are on average 27 % larger than the GHGI in the largest 10 methane-producing states, with the biggest upward adjustments in states with large oil and gas emissions, including Texas, New Mexico, Louisiana, and Oklahoma. We also calculate emissions for 95 geographically diverse urban areas in CONUS. Emissions for these urban areas total 6.0 (5.4–6.7) Tg a−1 and are on average 39 (27–52) % larger than a gridded version of the 2023 GHGI, which we attribute to underestimated landfill and gas distribution emissions.

Acoustic 2-D Full-Waveform Inversion with Non-Balanced Finite differences and Adaptive Weight Decay Methods

Full waveform inversion (FWI) is a powerful seismic imaging technique that aims to achieve high-resolution subsurface models by iteratively comparing recorded seismic waveforms with modeled waveforms. The success of FWI relies on the precision of forward modeling algorithms and the effectiveness of optimization strategies. In this study, we propose a FWI methodology that leverages non-balanced staggered-grid finite differences schemes (NBFD) in the forward modeling process. By employing operators with spatial differencing of varying lengths, these schemes enhance the efficiency of forward modeling.For the optimization process, we employ adaptive gradient-based optimization with weight decay, a widely-used approach in machine learning and deep learning algorithms for model training. These methods demonstrate efficient optimization processing for large data volumes with high precision. The objective of adaptive gradient-based optimization is to dynamically adjust the update rate model parameters during the iterative process. This facilitates improved convergence speed, enhances stability, and overcomes challenges associated with traditional fixed-rate adjustment methods.To ensure accurate inversion results and avoid local minima in the cost function minimization, we implement a Multiscaling inversion strategy within the workflow. The obtained results are compared with those achieved through conventional FWI using standard staggered finite differences and various optimization methods. Our findings demonstrate that employing non-balanced staggered-grid finite differences scheme leads to significant improvements compared to the previously reported results in the literature.

Output feedback distributed optimization algorithms of higher‐order uncertain nonlinear multi‐agent systems

AbstractOutput feedback distributed optimization problem is studied for higher‐order multi‐agent systems with uncertain nonlinearities, which are assumed to satisfy linear growth conditions. The agents dynamics are permitted to be heterogenous with different nonlinearities. The problem is solved by embedded control approach based output feedback distributed optimization algorithms. First, a first‐order optimal signal generator is designed, of which outputs reach the minimizer of the global cost function. Second, embedding the generator into the feedback loop and taking the outputs of the generator as the reference outputs of the agents, output feedback tracking controllers are designed for the higher‐order multi‐agent systems on the basis of nonseparation principle and feedback domination technique. Under the proposed control algorithms, all the agents outputs asymptotically approach a bounded neighbor region of the global minimizer. Simulations demonstrate the effectiveness of the proposed output feedback distributed optimization algorithms.

Predictive controllers for synchronous reluctance motor drive systems

This paper proposes the design and implementation of predictive controllers for synchronous reluctance motor drive systems to enhance their dynamic responses. The predictive speed and current controllers in this paper are designed in systematic procedures. The predictive speed controller is implemented by using Laguerre function procedure. The Laguerre function is used to simplify the algorithm and to minimize the execution time of the digital signal processor. For predictive current controller, a finite control set method improves the current tracking ability. The measured currents are used to predict the future phase-current based on the motor model. The optimal control inputs of both predictive controllers are determined by using a cost function minimization method. Experimental results show the proposed drive system provides a wide adjustable speed range, from 2 r/min to 1800 r/min. It has better performance than a proportional-integral (PI) controller including fast rise time, which is 0.9 second, small steady state error, which is 0.32 r/min, and small current ripples. A 32-bit floating-point digital signal processor, TMS-320-F-28335 DSP, is employed to implement the control algorithms.

A minimum objective function trim procedure for VTOLs noise reduction

The present paper proposes a novel approach for multi-rotor acoustic nuisance mitigation based on the identification of optimal control settings. This strategy is possible thanks to the peculiarity of multi-rotor systems (like, for instance, those involved in urban air mobility applications) to have redundant controls. The idea is to take full advantage of the control redundancy by defining the control settings that guarantee the desired steady-state flight conditions while, at the same time, optimizing selected target functions such as performance or noise emissions. To this aim, the trim problem is recast into a constrained cost function minimization problem. Since the objective is to reduce as much as possible the noise disturbance of trimmed VTOL, an aeroacoustic tool based on the chordwise-compact form of the Farassat 1A formulation for the evaluation of noise radiation is suitably coupled with a trim solver. The numerical investigations consider quadcopter and hexacopter configurations in level flight at several advancing speeds. Comparisons of the proposed minimum-noise trim strategy with two other trim strategies based on the minimization of rotor torque and control effort prove its capability to provide an overall reduction of noise throughout the entire velocity range examined.