Nonlinear Optimization Approach Research Articles

Nonlinear optimal control for the 4-DOF underactuated robotic tower crane

Tower cranes find wide use in construction works, in ports and in several loading and unloading procedures met in industry. A nonlinear optimal control approach is proposed for the dynamic model of the 4-DOF underactuated tower crane. The dynamic model of the robotic crane undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed control approach is advantageous because: (i) unlike the popular computed torque method for robotic manipulators, the new control approach is characterized by optimality and is also applicable when the number of control inputs is not equal to the robot’s number of DOFs, (ii) it achieves fast and accurate tracking of reference setpoints under minimal energy consumption by the robot’s actuators, (iii) unlike the popular Nonlinear Model Predictive Control method, the article’s nonlinear optimal control scheme is of proven global stability and convergence to the optimum.

On the Design of a Heterogeneous Mechanical Test Using a Nonlinear Topology Optimization Approach

Numerical simulation is nowadays increasingly used to avoid the costs and time associated with the development and optimization of metal forming processes. However, the accuracy of the numerical results is still an issue. Material behavior and characteristics are required by simulation software, and these are usually obtained by performing a considerable number of classical mechanical tests. To improve this procedure, heterogeneous tests have been used instead. More and richer information can be obtained with a single test due to the heterogeneous displacement and strain fields that are induced. This work aims at designing a heterogeneous mechanical test using a topology-based optimization methodology. Highly heterogeneous displacement fields are induced on the sheet specimen by applying an extended version of the theory of compliant mechanisms. To account for large deformations, a geometrically nonlinear finite element analysis is proposed together with a consistent topology optimization approach. The material behavior is considered linear elastic. The performance of the obtained solutions is evaluated considering the heterogeneity of stress states using a mechanical indicator. Validation of the developed methodology is performed and an optimal mechanical test is obtained presenting a high diversity of stress states.

OpenAP.top: Open Flight Trajectory Optimization for Air Transport and Sustainability Research

Trajectory optimization has been an active area of research for air transport studies for several decades. But almost all flight optimizers proposed in the literature remain close-sourced, which presents a major disadvantage for the advancement of scientific research. This optimization depends on aircraft performance models, emission models, and operational constraints. In this paper, I present a fully open trajectory optimizer, OpenAP.top, which offers researchers easy access to the complex but efficient non-linear optimal control approach. Full flights can be generated without specifying flight phases, and specific flight segments can also be independently created. The optimizer adapts to meteorological conditions and includes conventional fuel and cost index objectives. Based on global warming and temperature potentials, its climate objectives form the basis for climate optimal air transport studies. The optimizer’s performance and uncertainties under different factors like varying mass, cost index, and wind conditions are analyzed. Overall, this new optimizer brings a high performance for optimal trajectory generations by providing four-dimensional and wind-enabled full-phase optimal trajectories in a few seconds.

An Energy Performance Contract Optimization Approach to Meet the Competing Stakeholder Expectations under Uncertainty: A Canadian Case Study

Energy performance contracts (EPC) can address economic sustainability challenges associated with residential energy retrofitting projects, including funding limitations, poor quality of project delivery, and landlord-tenant dilemma. Literature has overlooked the impact of weighted average cost of capital (WACC) and funding sources in EPC planning. However, the WACC, stakeholder priorities, and uncertainties can alter the project outcomes. This study proposes a Monte-Carlo simulation based non-linear multi-objective optimization approach to address the aforementioned challenges. A case study conducted in British Columbia indicated that the maximum overall project profitability can vary between $18,035 and $20,626 with decision priorities. The overall project profitability can vary over 9% due to uncertainties. The project profits can change over $3000 due to changes in the WACC. These observations confirmed the criticality of accounting for WACC, stakeholder priorities, and uncertainties in EPC planning. The risk of compensating for the performance compromises and profits increases simultaneously for the energy services company with the increasing contract periods, while it is inverse for the owners. Therefore, the contract period must be decided considering the profit expectations and risk tolerance of the stakeholders. Extended contract periods allow lower capital contributions from the building owners, potentially solving the principal-agent disputes in rental buildings.

Technical Note—Dual Approach for Two-Stage Robust Nonlinear Optimization

In “Dual Approach for Two-Stage Robust Nonlinear Optimization,” de Ruiter, Zhen, and den Hertog study adjustable robust minimization problems where the objective or constraints depend in a convex way on the adjustable variables. They reformulate the original adjustable robust nonlinear problem with a polyhedral uncertainty set into an equivalent adjustable robust linear problem, for which all existing approaches for adjustable robust linear problems can be used. The reformulation is obtained by first dualizing over the adjustable variables and then over the uncertain parameters. The polyhedral structure of the uncertainty set then appears in the linear constraints of the dualized problem, and the nonlinear functions of the adjustable variables in the original problem appear in the uncertainty set of the dualized problem. The authors show how to recover linear decision rules to the original primal problem and how to generate bounds on its optimal objective value.

A nonlinear optimal control approach for the truck and N-trailer robotic system

Truck and N-trailer mobile robots find use in freight transportation, urban transportation, mining as well as in agriculture. The article proposes a nonlinear optimal (H-infinity) control approach for the truck and N-trailer robotic system. The method has been successfully tested so far on the control problem of several types of robotic vehicles and here it is shown that it can also provide an optimal solution to the control problem of the underactuated truck and N-trailer mobile robot. To implement this control scheme, the state-space description of the kinematic model of the truck and N-trailer robotic system undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Next, an optimal (H-infinity) feedback controller is designed. To select the feedback gains of the optimal (H-infinity) controller an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. Finally, to implement state estimation-based feedback control, the H-infinity Kalman Filter is used as a robust state estimator.

Nonlinear Multi-Fidelity Bayesian Optimization: An Application in the Design of Blast Mitigating Structures

<div class="section abstract"><div class="htmlview paragraph">A common scenario in engineering design is the availability of several black-box functions that describe an event with different levels of accuracy and evaluation cost. Solely employing the highest fidelity, often the most expensive, black-box function leads to lengthy and costly design cycles. Multi-fidelity modeling improves the efficiency of the design cycle by combining information from a small set of observations of the high-fidelity function and large sets of observations of the low-fidelity, fast-to-evaluate functions. In the context of Bayesian optimization, the most popular multi-fidelity model is the auto-regressive (AR) model, also known as the co-kriging surrogate. The main building block of the AR model is a weighted sum of two Gaussian processes (GPs). Therefore, the AR model is well suited to exploit information generated by sources that present strong linear correlations. Recently, the non-linear auto-regressive Gaussian process (NARGP) model has appeared as an alternative to integrate information generated by non-linearly correlated black-box functions. The performance of the NARGP model in structural optimization has remained largely unexplored. This investigation presents a Bayesian optimization approach that implements the NARGP model as the multi-fidelity surrogate model. The optimization strategy is utilized in the design sandwich composite armors for blast mitigation. The armors are made of four layers: steel, carbon fiber reinforced polymer (CFRP), aluminum honeycomb (HC), and CFRP. The optimization problem has three design variables, which are the thickness of the CFRP and aluminum HC layers. Two objectives are minimized: the armor’s penetrations and the reaction force at the armor’s supports. The black-box functions are two finite element models with different levels of fidelity. The low-fidelity model assumes elastic behavior of the sandwich composite. The high-fidelity model considers the nonlinear behavior of each layer of the armor. The results show that the proposed non-linear multi-fidelity Bayesian optimization approach produces a more stable expansion of the Pareto front than an optimization strategy that employs the AR model. This outcome suggests that the NARGP model is an appealing alternative in design problems with a limited number of function evaluations of the high-fidelity source.</div></div>

Inspection of the Production Lot Using Two Successive Occasions Sampling Under Neutrosophy

The efficiency of the measuring tools and operators is a significant part of lot sentencing decisions. These tools have to pass some pre-specified quality levels to avoid problems during the quality assessment scenarios. These measurements have a serious risk to be encountered with any extent of ambiguity, doubt, or indeterminacy due to any of the factors like variation among the operating regimes, warming effects in the hot climatic conditions, the operators’ casual attitude, and so on. These factors as the most significant sources of extraneous variations can deeply affect the efficacy of lot sentencing decisions. Hence, the decision when based on the measurement through the operating tools and these tools have to pass which have fulfilled some adequate standards only then lot sentencing may avoid or save from the rejection of a good lot. The authors have put their focus on dealing with the factors that arise by measuring variability among the measured or determined values despite having the normal population distribution. In this study, the auxiliary information is used to estimate the variable of interest over the two successive occasions under the neutrosophic interval numbers and proved helpful to overcome this issue. The presented approach has discussed that in blurred, doubted, uncertain and undetermined datasets partially or completely, the efficacy of the decision for the whole lot cannot be decided on the single point crisped value. But the range of values around such a single crisp point in the form of neutrosophic theory is proved far better. In this context, the neutrosophic interval number successive sampling-based sampling plan is proposed which is the major contribution to the existing literature. It is explained in terms of operating characteristic function and the plan parameters are determined through the neutrosophic non-linear optimization approach. The comparative analysis is presented with the existing sampling plans and found efficient. Moreover, a real-life industrial dataset is used as an application of the concept.

Fast Cluster Detection in Networks by First Order Optimization

Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of s-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles those models in practice. In particular, we introduce an equivalent continuous formulation for the problem under analysis, and we analyze some tailored variants of the Frank-Wolfe algorithm that enable us to quickly find maximal s-defective cliques. The good practical behavior of those algorithmic tools, which is closely connected to their support identification properties, makes them very appealing in practical applications. The reported numerical results clearly show the effectiveness of the proposed approach.

A nonlinear optimal control method against the spreading of epidemics

To define a vaccination policy and antiviral treatment against the spreading of viral infections a nonlinear optimal (H-infinity) control approach is proposed. Actually, because of the scarcity of the resources for treating infectious diseases in terms of vaccines, antiviral drugs and other medical facilities, there is need to implement optimal control against the epidemics deployment. In this approach, the state-space model of the epidemics dynamics undergoes first approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization is based on Taylor series expansion and on the computation of the associated Jacobian matrices. Next, an optimal (H-infinity) feedback controller is developed for the approximately linearized model of the epidemics. To compute the controller’s feedback gains an algebraic Riccati equation is solved at each iteration of the control algorithm. Furthermore, the global asymptotic stability properties of the control scheme are proven through Lyapunov stability analysis. This paper’s results confirm that optimal control of the infectious disease dynamics allows for eliminating its spreading while also keeping moderate the consumption of the related medication, that is vaccines and antiviral drugs.

Nonlinear optimal control for a five-link parallel robotic manipulator

Control and stabilization of parallel robotic manipulators is a non-trivial problem because of nonlinearities and the multi-variable structure. In this article, a nonlinear optimal control approach is proposed for the dynamic model of such robotic systems, using as a case-study the model of a five-link parallel robot. The dynamic model of the parallel robotic manipulator undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system, a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands as a solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control without the need to measure the entire state vector of the parallel robotic manipulator, the H-infinity Kalman filter is used as a robust state estimator. Among the advantages of this control method, one can note that (i) unlike the popular computed-torque method for robotic manipulators, the new control approach is characterized by optimality and is also applicable when the number of control inputs is not equal to the robot’s number of DOFs and (ii) it achieves fast and accurate tracking of reference set points under minimal energy consumption by the robot’s actuators.

A nonlinear optimal control approach for permanent magnet AC motors with non-sinusoidal back EMF

A nonlinear optimal control approach for permanent magnet AC motors with non-sinusoidal back EMF

Bending characteristics of carbon nanotubes: Micropolar elasticity models and molecular dynamics simulations

The present paper aims at evaluating non-classical continuum parameters for each class of armchair and zigzag single-walled CNTs focusing on the scale effect in their flexural behavior observed in molecular dynamics (MD) simulations. Through a non-linear optimization approach, the bending rigidities obtained from atomistic simulations are compared to those derived from non-classical continua. For MD simulations, a novel method ensuring pure bending is introduced and for continuum modeling, micropolar, constrained micropolar, and modified couple stress theories are employed. The results reveal that adopted non-classical theories, notably micropolar theory, provide reasonable outcomes with an obvious failure of classical Cauchy theory.

Optimal Precursors Triggering Sudden Shifts in the Antarctic Circumpolar Current Transport Through Drake Passage

AbstractDue to the high nonlinearity, the accurate prediction of the Antarctic circumpolar current (ACC) transport is still challenging. Using the eddy‐permitting regional ocean modeling system and the conditional nonlinear optimal perturbation approach, the sudden shift in the ACC transport through Drake Passage (DP) is investigated by exploring its optimal precursor (OPR). Here, the sudden shift in the ACC transport is defined as a fluctuation exceeding double STD (∼16 Sv; 1 Sv = 106 m3 s−1) within 30 days. The results indicate that the OPRs for all three cases exhibit specific structures in the middle DP (58°–62°S, 72°–64°W) at the depth of 1,000–3,000 m, implying that the ACC transport is most sensitive to the initial perturbations there. The OPRs' evolutions show similar features: the OPR for each case triggers an eddy‐like dipole perturbation with a northern cyclone and a southern anticyclone, leading to a sudden reduction in the ACC transport of ∼40 Sv. It is verified that the density components in the OPRs determine such evolution processes. Furthermore, baroclinic instability is diagnosed to play a dominant role in the development of OPRs by analyzing the perturbed kinetic energy budget. This study suggests that the deep‐layer density perturbations in the Southern Ocean should be carefully monitored when considering the short‐range prediction of the ACC transport.

High-resolution pediatric age\u2013specific 18F-FDG PET template: a pilot study in epileptogenic focus localization

BackgroundPET imaging has been widely used in diagnosis of neurological disorders; however, its application to pediatric population is limited due to lacking pediatric age–specific PET template. This study aims to develop a pediatric age–specific PET template (PAPT) and conduct a pilot study of epileptogenic focus localization in pediatric epilepsy.MethodsWe recruited 130 pediatric patients with epilepsy and 102 age-matched controls who underwent 18F-FDG PET examination. High-resolution PAPT was developed by an iterative nonlinear registration-averaging optimization approach for two age ranges: 6–10 years (n = 17) and 11–18 years (n = 50), respectively. Spatial normalization to the PAPT was evaluated by registration similarities of 35 validation controls, followed by estimation of potential registration biases. In a pilot study, epileptogenic focus was localized by PAPT-based voxel-wise statistical analysis, compared with multi-disciplinary team (MDT) diagnosis, and validated by follow-up of patients who underwent epilepsy surgery. Furthermore, epileptogenic focus localization results were compared among three templates (PAPT, conventional adult template, and a previously reported pediatric linear template).ResultsSpatial normalization to the PAPT significantly improved registration similarities (P < 0.001), and nearly eliminated regions of potential biases (< 2% of whole brain volume). The PAPT-based epileptogenic focus localization achieved a substantial agreement with MDT diagnosis (Kappa = 0.757), significantly outperforming localization based on the adult template (Kappa = 0.496) and linear template (Kappa = 0.569) (P < 0.05). The PAPT-based localization achieved the highest detection rate (89.2%) and accuracy (80.0%). In postsurgical seizure-free patients (n = 40), the PAPT-based localization also achieved a substantial agreement with resection areas (Kappa = 0.743), and the highest detection rate (95%) and accuracy (80.0%).ConclusionThe PAPT can significantly improve spatial normalization and epileptogenic focus localization in pediatric epilepsy. Future pediatric neuroimaging studies can also benefit from the unbiased spatial normalization by PAPT.Trial registration.NCT04725162: https://clinicaltrials.gov/ct2/show/NCT04725162

A nonlinear optimal control approach for underactuated power-line inspection robots

AbstractThe article proposes a nonlinear optimal (H-infinity) control approach for a type of underactuated power-line inspection robots. To implement this control scheme, the state-space model of the power-line inspection robots undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the controller an algebraic Riccati equation is solved at each time step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. The significance of the article’s results is outlined in the following: (i) the proposed control method is suitable for treating underactuated robotic systems and in general nonlinear dynamical systems with control inputs gain matrices which are in a nonquadratic form, (ii) by achieving stabilization of the power-line inspection robots in underactuation conditions the proposed control method ensures the reliable functioning of these robotic systems in the case of actuators’ failures or enables the complete removal of certain actuators and the reduction of the weight of these robotic systems, (iii) the proposed control method offers a solution to the nonlinear optimal control problem which is of proven global stability while also remaining computationally tractable, (iv) the proposed nonlinear optimal control method retains the advantages of linear optimal control that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs, and (v) by minimizing the amount of energy that is dispersed by the actuators of the power-line inspection robots the proposed control method improves the autonomy and operational capacity of such robotic systems.

A Nonlinear Optimal Control Approach for Multi-DOF Brachiation Robots

This paper proposes a nonlinear optimal control approach for mulitple degrees of freedom (DOF) brachiation robots, which are often used in inspection and maintenance tasks of the electric power grid. Because of the nonlinear and multivariable structure of the related state-space model, as well as because of underactuation, the control problem of these robots is nontrivial. The dynamic model of the brachiation robots undergoes first approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the Jacobian matrices of the brachiation robots’ state-space model. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the brachiation robots, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control scheme are proven through Lyapunov analysis. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the brachiation robots, under moderate variations of the control inputs.

Improving the thermal structure predictions in the Yellow Sea by conducting targeted observations in the CNOP-identified sensitive areas

Targeted observation is an appealing procedure for improving model predictions. However, studies on oceanic targeted observations have been largely based on modeling efforts, and there is a need for field validating operations. Here, we report the results of a field targeted observation that is designed based on the sensitive areas identified by the Conditional Nonlinear Optimal Perturbation approach to improve the 7th day thermal structure prediction in the Yellow Sea. By introducing the technique of cycle data assimilation and the new concept of time-varying sensitive areas, an observing strategy is designed and validated by a set of Observing System Simulation Experiments. Then, the impact of targeted observations was investigated by a choreographed field campaign in the summer of 2019. The results of the in-field Observing System Experiments show that, compared to conventional local data assimilation, conducting targeted observations in the sensitive areas can yield more benefit at the verification time. Furthermore, dynamic analysis demonstrates that the refinement of vertical thermal structures is mainly caused by the changes in the upstream horizontal temperature advection driven by the Yellow Sea Cold Water Mass circulation. This study highlights the effectiveness of targeted observations on reducing the forecast uncertainty in the ocean.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Design Optimization of B-series Marine Propeller using NSGA-II, Iterative and Gekko Algorithm

The design of a propeller plays a significant role in naval architecture. Optimization of various design factors is the primary concern for effective and efficient propulsion. This study investigates the optimization of the B-series marine propellers using three different methods, i.e. (i) a non-linear constrained single-objective optimization approach using the Non-Dominated Sorting Genetic Algorithm (NSGA-II), (ii) a python package for dynamic optimization based optimization software ‘Gekko’, (iii) an iterative approach and results were compared with each other. Efficiency is considered as the single objective function whereas three constraints are imposed: cavitation, thrust and strength. Analogous characteristics have been found in the comparison of results from all three methods. Comparing the various factors, this study suggests that, Gekko can be used as the optimization algorithm.