Inequality Constraints Research Articles

Application of the L2-orthogonal decomposition of the second fundamental form of the hypersurfaces and the ahlfors laplacian to the study of the general relativistic vacuum constraint equations

Application of the <i>L</i>²-orthogonal decomposition of the second fundamental form of the hypersurfaces and the ahlfors laplacian to the study of the general relativistic vacuum constraint equations

Row Column Reduction Method for Solving Trapezoidal Fuzzy Transportation Problem

The primary goal of the transportation issue is to reduce the cost of moving goods from several warehouses to various showrooms. Fuzzy approaches are frequently employed to eliminate uncertainty. When the cost of transportation is uncertain, we sometimes use a fuzzy approach to resolve the issue. In this paper the values used in constraint equation are trapezoidal number and applied our proposed method, row column reduction method to get an optimal transportation cost.

The Use of Slack Variables in the Adjoint Method Handling Inequality Constraints in Optimal Control and the Application to Tumor Drug Dosage

Abstract In this article a modified gradient approach, based on the adjoint method, is introduced, to deal with optimal control problems involving inequality constraints. So far, the only way to incorporate inequality constraints in the adjoint approach, is to introduce additional penalty terms in the cost functional. However, this may distort the optimal control due to weighting factors required for these terms and raise serious concerns about the magnitude of the weighting factors. The method in this article avoids penalty functions and can be used for the iterative computation of optimal controls. In order to demonstrate the key idea, first, a static optimization problem in the Euclidean space is considered. Second, the presented approach is applied to the tumor anti-angiogenesis optimal control problem in medicine, which addresses an innovative cancer treatment approach that aims to inhibit the formation of the tumor blood supply. The tumor anti-angiogenesis optimal control problem with free final time involves inequality and final constraints for control and state variables and is solved by a modified adjoint gradient method introducing slack variables. It has to be emphasized that the novel formulation and the special use of slack variables in this article delivers high accurate solutions without distorting the optimal control.

Sequential Quadratic Optimization for Stochastic Optimization with Deterministic Nonlinear Inequality and Equality Constraints

Sequential Quadratic Optimization for Stochastic Optimization with Deterministic Nonlinear Inequality and Equality Constraints

An improved coupled beam method for predicting longitudinal bending behaviour in luxury cruise ships

ABSTRACT This paper describes an improved coupled beam method, designated as MBS-CB, that estimates elastic response in the longitudinal bending of a cruise ship. Initially, the ship structure is discretised into beams, and the coupling relationships between adjacent beams are analysed. Secondly, connector elements with equal stiffness constraints are refined to simulate the coupling behaviour between adjacent beam elements. Meshed beam sections are introduced to simplify the beams involved in total longitudinal bending. A spatial beam system model of the ship structure is established to predict the interaction between adjacent beams and to characterise the longitudinal bending behaviour of the ship. Ultimately, the accuracy of the method is validated through instance analysis. Furthermore, the method is employed to investigate the longitudinal bending characteristics of a large passenger ship, and the participation of different superstructures in the ship's longitudinal bending is obtained through moment distribution coefficients and length proportions.

Constraint‐Driven Multilane Merging Control for Underactuated Connected and Automated Vehicle System With Mismatched Uncertainty

ABSTRACTThis article investigates the merging control for underactuated connected and automated vehicle (CAV) systems with mismatched uncertainty. The objective is to guarantee the safe and prescribed dynamic performance of the system during multilane merging. For CAV multidimensional motions, a strongly coupled vehicle dynamics with time‐varying uncertainties is constructed. For the nominal system, the control objectives are designed as system constraints, with equality constraints guaranteeing merging and time‐varying inequality constraints guaranteeing dynamic performance bounds. Based on the diffeomorphism method and bounded constraint, the system constraints are reconstructed to a unified representation. Combining system constraints and underactuated structure, the nominal controller is derived based on constraint‐following. For the uncertain system, the uncertainty is decomposed into matched and mismatched portions by orthogonal decomposition. The adaptive robust controller is designed based only on matched uncertainty. Through Lyapunov minimax analysis, the control renders the errors uniformly bounded and uniformly ultimately bounded. Simulation results show that merging and platooning are effectively achieved with the proposed control. The system has excellent transient and steady state performance even in the presence of time‐varying uncertainties.

Prescribed‐time distributed optimization for multi‐agent system subject to inequality constraints

Prescribed‐time distributed optimization for multi‐agent system subject to inequality constraints

Correction to: Cooperative game-theoretic optimization of adaptive robust constraint-following control for fuzzy mechanical systems under inequality constraints

Correction to: Cooperative game-theoretic optimization of adaptive robust constraint-following control for fuzzy mechanical systems under inequality constraints

Finite Tube Method for buckling analysis of tubular members using Fourier-approximation for the displacements

In this paper an efficient numerical method for the static analysis of cylindrical tubes is introduced. The method is designed for the linear buckling analysis of wind turbine support towers which are, most typically, built up from conical and/or cylindrical cans. Accordingly, the developed method uses cylindrical tube segments as elementary building blocks, along with specialized shape functions, and is named the Finite Tube Method. Within a tube segment the displacements are approximated by two-dimensional Fourier series. The curved nature of the surface is directly considered in the kinematic equations. The segments are joined and/or supported to the ground by constraint equations or by elastic links. In the current implementation internal stresses are determined in a simplified way: the circumferential stress distributions are calculated from the internal forces/moment by classic strength of material formulae, while the longitudinal distribution within each segment is quadratic. The considered internal forces/moments are: normal force, shear force, bending moment, and torsional moment. The internal forces can be arbitrarily combined. In the paper the underlying derivations are briefly summarized, then the method is demonstrated and validated by numerical examples, comparing the results to analytical and alternative numerical solutions. The authors are actively developing the method and will provide future work on utilization of the method for buckling mode identification and decomposition, as well as practical advancements to make the method a useful tool in the engineering design and analysis of wind turbine support towers.

Surrogate modeling of multi-dimensional premixed and non-premixed combustion using pseudo-time stepping physics-informed neural networks

Physics-informed neural networks (PINNs) have emerged as a promising alternative to conventional computational fluid dynamics (CFD) approaches for solving and modeling multi-dimensional flow fields. They offer instant inference speed and cost-effectiveness without the need for training datasets. However, compared to common data-driven methods, purely learning the physical constraints of partial differential equations and boundary conditions is much more challenging and prone to convergence issues leading to incorrect local optima. This training robustness issue significantly increases the difficulty of fine-tuning PINNs and limits their widespread adoption. In this work, we present improvements to the prior field-resolving surrogate modeling framework for combustion systems based on PINNs. First, inspired by the time-stepping schemes used in CFD numerical methods, we introduce a pseudo-time stepping loss aggregation algorithm to enhance the convergence robustness of the PINNs training process. This new pseudo-time stepping PINNs (PTS-PINNs) method is then tested in non-reactive convection–diffusion problem, and the results demonstrated its good convergence capability for multi-species transport problems. Second, the effectiveness of the PTS-PINNs method was verified in the case of methane–air premixed combustion, and the results show that the L2 norm relative error of all variables can be reduced within 5%. Finally, we also extend the capability of the PTS-PINNs method to address a more complex methane–air non-premixed combustion problem. The results indicate that the PTS-PINNs method can still achieve commendable accuracy by reducing the relative error to within 10%. Overall, the PTS-PINNs method demonstrates the ability to rapidly and accurately identify the convergence direction of the model, surpassing traditional PINNs methods in this regard.

Optimizing reserve-constrained economic dispatch: Cheetah optimizer with constraint handling method in Static/Dynamic/Single/ Multi-Area Systems

Managing the power-generating units on the horizon of one-day scheduling considering all practical equality, inequality, and realistic constraints has always been a significant challenge in power systems. The constraints, such as valve-point effects, prohibited operation zones, transmission losses, and ramp rate limits corresponding to dynamic economic dispatch, change the optimization problem to a complex, nonlinear, non-smooth, high-dimensional, and non-convex one. Therefore, an efficient algorithm and a suitable constraint handling method are needed to solve practical constrained dynamic economic dispatch (DED). This paper proposes a newly developed Cheetah optimizer (CO) that coincides with a backward-forward constraint handling method to tackle the optimum operational cost. The CO algorithm’s performance is verified using eight DED and ED test cases from five different systems. The suggested technique is compared with several state-of-the-art optimization algorithms regarding the effectiveness of achieved results. Numerical results evaluate the performances of the CO advantages on the benchmarks and the DED cases where the results of 5-,10- and 30-unit systems are enhanced in different cases. To achieve a higher level of realism in modeling the ED and DED problem, adopting a multi-area DED (MADED) approach has emerged as a promising strategy. In this paper, three distinct cases of MAED and MADED problems are investigated to demonstrate the effectiveness of the proposed method. Specifically, in cases involving DED-10 and 30 units, two-area 40 units ED, and four-area 40 units DED, significantly improved solutions were obtained compared to previous studies.

Weak form quadrature shell elements based on absolute nodal coordinate formulation

Weak form quadrature elements for moderately thick shells with arbitrary initial configurations are developed under the framework of continuum mechanics and the absolute nodal coordinate formulation (ANCF). Locking problems of shell analysis are discussed. Nonlinear analysis of various shell structures is conducted. The joint constraint equations for shells with discontinuous slopes are established. Five examples encompassing static and dynamic shell analysis, post-buckling analysis of shells, as well as analysis of shells with discontinuous mid-surface slopes are examined to assess the performance of the proposed elements. Satisfactory results are obtained, validating the efficacy of the proposed elements.

Exact Solution to The Wheeler-DeWitt Equation: Early and Current Universe

In this paper, we present exact solutions to the Wheeler-DeWitt equation in two different scenarios: the early Universe, where the ordering parameter of kinetic energy is important, and the current Universe, where the ordering parameter effect is negligible. To make the exact solutions as general as possible, we incorporate as many different types of energy density as possible into the Hamiltonian, including baryonic and non-baryonic matter (dark matter), radiation, vacuum, and quintessence (dark energy). In the early Universe scenario, we obtain exact solutions in terms of the Biconfluent Heun functions, whereas in the current Universe, the exact solutions are given in terms of the Triconfluent Heun functions. Furthermore, by applying the polynomial conditions to each case, we obtain a constraint equation that supports the notion that the Wheeler-DeWitt equation can be viewed as an eigenvalue problem for the cosmological constant.

Enhancing high-resolution reconstruction of flow fields using physics-informed diffusion model with probability flow sampling

The application of artificial intelligence (AI) technology in fluid dynamics is becoming increasingly prevalent, particularly in accelerating the solution of partial differential equations and predicting complex flow fields. Researchers have extensively explored deep learning algorithms for flow field super-resolution reconstruction. However, purely data-driven deep learning models in this domain face numerous challenges. These include susceptibility to variations in data distribution during model training and a lack of physical and mathematical interpretability in the predictions. These issues significantly impact the effectiveness of the models in practical applications, especially when input data exhibit irregular distributions and noise. In recent years, the rapid development of generative artificial intelligence and physics-informed deep learning algorithms has created significant opportunities for complex physical simulations. This paper proposes a novel approach that combines diffusion models with physical constraint information. By integrating physical equation constraints into the training process of diffusion models, this method achieves high-fidelity flow field reconstruction from low-resolution inputs. Thus, it not only leverages the advantages of diffusion models but also enhances the interpretability of the models. Experimental results demonstrate that, compared to traditional methods, our approach excels in generating high-resolution flow fields with enhanced detail and physical consistency. This advancement provides new insights into developing more accurate and generalized flow field reconstruction models.

Adaptive robust constraint-following control method for improving carbody hunting stability of high-speed trains

The low-frequency carbody hunting motion of high-speed trains (HSTs) frequently occurs due to the complex operating environment and deterioration of wheel–rail contact conditions. It not only affects ride comfort but also poses a risk of derailment safety accidents for HSTs. In such scenarios, traditional passive suspension systems struggle to ensure satisfactory dynamic performance of HSTs. However, active suspension systems can offer an effective solution. To enhance the low-frequency carbody hunting stability and environmental adaptability of HSTs, this study proposes a novel adaptive robust displacement inequality constraint following control (AICFC) method for active suspension utilising the beneficial nonlinearity inspired by bio-inspired structures (BIS). The effectiveness of the proposed AICFC-BIS method is validated through numerical simulations comparing it with other control strategies. Simulation results show that the AICFC-BIS method can effectively suppress low-frequency carbody hunting motion and improve the dynamic performance of HSTs. Compared with conventional passive suspensions and other active suspensions, HSTs equipped with AICFC-BIS active suspension exhibit significantly reduced operational safety risk and improved ride comfort indices while being energy efficient.

New method for stability of probabilistic Boolean networks with inequality constraints

This paper studies the stability of probabilistic Boolean networks (PBNs) with state inequality constraints by establishing a new algebraic representation. On one hand, combining with the semi-tensor product (STP) of matrices and the law of total expectation, the algebraic representation of PBNs is established. On the other hand, based on the STP of matrices, an algorithm is proposed to determine the solution set of the state inequality constraints. Then, based on the algebraic representation and the inequality constrained solution set, a new form of transition probability matrix is constructed for PBNs. Finally, by the proposed transition probability matrix, new criteria are proposed for the finite-time stability with positive probability of PBNs. Several simulation examples are used to illustrate the effectiveness of the obtained results.

Modified preview repetitive control with equivalent-input-disturbance based on two-dimensional model

This paper deals with the problem of two-dimensional (2D) system-based modified preview repetitive control (MPRC) with equivalent-input-disturbance (EID) for continuous-time systems. First, an EID-based MPRC law is used to improve the tracking performance and disturbance attenuation. Next, by using a new equality constraint, a continuous-discrete 2D system is established and the design problem of the EID-based MPRC law is transformed into the stability problem of the 2D system. Then, we employ the 2D system theory together with the linear matrix inequality (LMI) approach, a sufficient condition is derived to ensure the stability of the closed-loop system. By solving an LMI, the gains of the controller and state observer can be obtained. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of the developed controller design technique.

Deterministic scenarios guided [formula omitted]-Adaptability in multistage robust optimization for energy management and cleaning scheduling of heat transfer process

The heat transfer process is of paramount importance for energy management and heat recovery, but the inevitable uncertain fouling poses significant challenges to sustainable energy-saving efforts. This study aims to solve the energy management and cleaning scheduling problems under fouling uncertainty. To achieve this, a novel multistage Robust Optimization (RO) method based on the Deterministic Scenarios Guided K-Adaptability (DSGKA) strategy is proposed. The process scheduling problem is initially tackled through long-period Mixed Integer Optimal Control Problems (MIOCPs) with deterministic scenarios. Subsequently, considering the slow transition characteristics of energy efficiency degradation caused by fouling, the candidate paths generation algorithm guided by deterministic MIOCPs is developed. Additionally, the K-Adaptability method is employed to segment decision-dependent uncertainty sets into finite partitions, facilitating the resolution of the multistage RO problem through worst-case analysis. In theory, the rationality of the proposed guidance algorithm is established. Simulation results on a heat exchanger network are also provided to demonstrate the effectiveness of the DSGKA scheme. By transforming the original multistage RO problem into a finite-dimensional optimization problem solvable with intelligent heuristic algorithms, the proposed method adeptly manages nonlinearity in constraint equations, thereby improving its applicability for equipment maintenance scheduling across various slow transition industrial processes.

Dynamic Analysis of a Vehicle–Bridge System Under Excitation of Random Road Irregularities

This paper presents a comprehensive study of the dynamic response analysis of vehicle–bridge coupled systems, with detailed simulation methods for the vehicles, bridges, and wheel–road coupling relationships. The simulation of the entire vehicle–bridge coupling system is carried out using the open-source finite element analysis platform OpenSees. A novel three-dimensional wheel–road coupling element is introduced to model the interactions between the wheel and road nodes. This element facilitates precise computation of the dynamic responses within the vehicle–bridge coupled system, including both vehicle and bridge behaviors, along with the interaction forces between the wheels and the bridge surface. The coupling element consists of a wheel node and all potential road nodes on the bridge surface that the wheel may traverse. This configuration preserves the finite element model of the entire vehicle–bridge coupled system throughout the vehicle’s movement, thereby improving the efficiency of numerical simulations of vehicle–road interactions. The study accounts for the impact of random road irregularities on the dynamic responses of both the vehicle and the bridge. These irregularities are treated as input parameters for the wheel–road coupling element rather than being accounted for through the wheel–road interaction constraint equations, thereby improving the convenience of simulating random road irregularities.

Point-based Models: A Unified Approach for Geometric Constraint Analysis of Planar N-Bar Mechanisms with Rotary, Sliding, and Rolling Joints

Abstract Kinematic simulation of planar n-bar mechanisms has been an intense topic of study for several decades now. However, a large majority of efforts have focused on position analysis of such mechanisms with limited links and joint types. This paper presents a novel, unified approach to analysis of geometric constraints of planar n-bar mechanisms with revolute joint (R-joint), prismatic joint (P-joint), and rolling joint. This work is motivated by a need to create and program a system of constraint equations, which deal with different types of joints in a unified way. A key feature of this work is that the rolling joint constraints are represented by four-point models, which enables us to use the well-established undirected graph rigidity analysis algorithms. As a result, mechanisms with an arbitrary combination of revolute-, prismatic-joints, and wheel/gear/wheel-belt chains without any limitations on their actuation, can be analyzed and simulated efficiently for potential implementation in an interactive computer software and large-scale data generation.