Abstract This paper discusses multi-agent path navigation in unknown environments. It is a challenging task to design an effective communication-based algorithm with minimal error, which would ensure secure navigation of multi-agent paths under complex circumstances, reduce the length of the travelled path, and minimize the runtime. A leader agent path navigation (LAPN) algorithm is proposed in this paper for multi-agent communication. The obstacle avoidance mechanism is used in the first part of the algorithm. The execution time of the algorithm is influenced by the process of leader-to-follower path update, since the updating process determines how quickly the followers receive corrected trajectories. One leader and two follower agents were considered in simulation environments to establish the feasibility of the algorithm. The LAPN algorithm achieves an average percentage deviation, calculated as the relative difference from the ideal straight-line path of 2.82% in travel time and 31% in path length, showing satisfactory navigation efficiency under obstacle-constrained conditions.
Abstract The paper addresses the Two-Constraint Binary Knapsack Problem. It is assumed that some of the problem coefficients are the realizations of mutually independent random variables. Asymptotic probabilistic properties of selected problem characteristics are investigated for special cases of Lagrange multipliers with small, moderate and mixed values.
This study introduces an observer-based dual strategy for optimizing block mode placement in matrix polynomial control systems, focusing on improving stability and performance in multivariable feedback applications. It introduces two approaches: a static state feedback compensator for a challenging Bidirectional Inductive Power Transfer (IPT) System, and a dynamic observer-based output feedback compensator for a defensive air-to-surface missile control problem. Both designs exploit the Grey Wolf Optimizer to solve the nonlinear convex optimization, associated with block mode selection. The dynamic plan employs Luenberger observer principles for unmeasured state estimation, ensuring system reliability through strict observability conditions. Simulation results reveal that the proposed optimal placement methods enhance tracking, boost stability margins, and substantially minimize control effort. Overall, this methodology offers an effective frame-work for robust controller design and state estimation across disparate, complex dynamic systems, while reducing computational burden and improving control efficiency.
We use first- and second-order approximations to establish necessary and suffcient optimality conditions for nonsmooth generalized bilevel optimization problems with variational inequality constraints. To transform the hierarchical problem into a single-level optimization problem, we employ two approaches: the gap function reformulation and the KKT reformulation. We compare these approaches and provide examples to illustrate the applicability of the results.
The article is concerned with the nonlinear optimal control problem of two cable-driven 3-DOF robotic cranes. Such cranes can be used in ship maintenance and repair. These are underactuated robotic systems comprising a 2-cable driven cart with a payload suspended from it. Such robotic mechanisms have three degrees of freedom and can move in the entire 2D vertical plane. Using Euler-Lagrange analysis the state-space model of the two cable-driven 3-DOF robotic crane is obtained. It is also proven that this dynamic model is differentially flat. Next, to solve the associated nonlinear optimal control problem, the dynamic model of the two cable-driven 3-DOF 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 crane an optimal (H-infinity) feedback controller is designed. This controller stands for the 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. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Besides, the method avoids change of state variables and state-space model transformations and the control inputs it computes are applied directly on the initial nonlinear state-space model of the crane.
The combined defuzzification of multiple fuzzy sets under a shared constraint is an extension of traditional defuzzification. The problem concerns defuzzifying multiple fuzzy sets at once, adhering to a constraint that involves their defuzzified values. This specific problem emerged in an application of fuzzy rulebase systems with the goal of regridding spatial data; the constraint stems from the need to keep the total modelled value over a region consistent. Through the introduction of goal functions, the combined defuzzification problem was translated to an optimization problem; the goal functions allow to use objective criteria to evaluate and rank different solutions. Different goal functions for the combined defuzzifier have been presented in the relevant literature, in this contribution, the aim is to evaluate solvers in order to develop a usable implementation of the novel defuzzifier and to verify their stability and performance for the presented problem.
In this article, we propose a method for analysing 3D point clouds. To this aim, we take advantage of the octree data structure to compress and analyse the 3D point data. The motivation for the study undertaken comes from the field of Cultural Heritage. As 3D acquisition methods become more and more ubiquitous in this field, there is an increasing need for methods, which help to efficiently store, display, and share large data sets. There is also a need to segment and classify the recorded data. We show that the octree data structure provides an efficient tool for handling complex 3D data, coming from different applications. Although we tested our method on a data set, coming from the field of archaeology, based on photogrammetric method, we believe that the approach proposed has much wider use. The method proposed can be applied to any 3D data, represented in a given coordinate system.
In this paper, we address a non-convex vector optimization problem, in which the objective function and constraints are defined as differences of convex vector-valued maps. By employing a separation argument, we derive necessary optimality conditions, expressed in terms of ε-regularized subdifferentials, for a point to be an ε-weak local quasi-efficient solution. To ensure the paper is self-contained, we also present sufficient optimality conditions and provide examples to illustrate the results.
The advent of deep learning enabled the extraction of complex feature representations from medical imaging data, which was considered impossible to be achieved with standard computer learning. The applications of deep learning in the field of medical image analysis a ord significant results. A key feature of deep learning techniques is their ability to automatically learn task-specific feature representations and extract relevant features without human intervention. Various deep learning models, including CNN, AlexNet, ResNet, DenseNet and U-Net were developed for medical image analysis. Among these models, U-Net is a popular model, used for medical image segmentation. The present article provides a comprehensive review of the deep learning segmentation models, which use U-Net and its variants, applied in the domain of medical image segmentation, specifically tailored to medical imaging modalities, such as ultrasound and MRI, along with respective pros and cons in the field of image segmentation. The analysis reveals that the performance of di erent U-Net variants varies significantly based on imaging modality and segmentation complexity.
In this paper, the explicit necessary and sufficient conditions are established for the existence of proportional-integral observer for the state estimation of linear time-invariant continuous-time systems. In particular, it is proven that for a given linear time-invariant continuous-time system of order n , having m inputs and p linearly independent outputs, a proportional-integral observer of order n can be constructed if and only if the given system is detectable. Furthermore a simple procedure is given for the construction of proportional-integral observer. Our approach is based on properties of real and polynomial matrices.
Aeropendulum systems are nonlinear systems, in which a motor-propeller assembly drives a rod. They are used for educational purposes and testing control laws in real systems. Feedback linearization is a nonlinear control technique that algebraically linearizes a plant’s dynamics via a feedback law and has been applied to various systems. This paper designs a feedback linearization control law incorporating an integrator into the control loop. The integrator enhances robustness in respect to constant disturbances, but alters the closed-loop dynamics, preventing it from following exactly the dynamics, associated with the desired characteristic roots under constant input. To address this, the integrator’s initial condition is treated as an additional variable, selected to ensure the expected closed-loop response. Finally, simulations and bench experiments on an Aeropendulum system validate the approach, demonstrating the integrator’s e ectiveness in handling constant disturbances and the impact of selecting an appropriate initial condition.
The paper studies the dual problems of second order, associated with a new class of ( η, ξ ;)-bonvex interval-valued variational control problems. More precisely, by considering the corresponding necessary optimality conditions, we prove the associated duality (weak, strong, strictly converse) results under the new ( η , ξ )-bonvexity assumptions of the involved functionals. In addition, illustrative examples are provided in order to highlight the theoretical elements established in the paper.
Abstract We investigate the identification problem for the one-phase Stefan problem. As the inverse Stefan problem is not well posed, an optimal control problem is considered instead. In the paper we develop a dual dynamic programming approach to derive sufficient approximate optimality conditions for that optimal control problem. As a next step we formulate and prove a verification theorem for approximate solution. The verification Theorem 4.1 is the basis for the development of a numerical algorithm. Having the verification theorem we do not need the convergence of our algorithm.
Abstract The aim of this paper is to recourse to topology optimization method to synthesize mechanical matematerials, based on the topologial derivative. Material symmetries play a major role in the very definition and expression of the homogenized properties; the search of optimal microstructures is done in given symmetry classes characterized by invariants of the homogenized moduli. We synthesize thanks to this methodology periodic microstructures prone to auxetic and anti-auxetic behaviors, or with a very large or small bulk to shear modulus ratio.
Abstract A discontinuous Galerkin finite element method is developed for structural topology optimization with the level set method. The discontinuous Galerkin finite element method is employed to discretize and solve both the elasticity system, possible adjoint, and the transport equation of the level set function. Structural compliance and compliant mechanisms are considered for linear and nonlinear elastic structures. Numerical examples are provided to verify the effectiveness of the algorithm presented.
We introduce and analyze a lower envelope method (LEM) for the tracking of interfaces motion in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides with exactly one of the functions. We show that a variety of complex lower-dimensional interfaces naturally appear in the process. The phases evolution is then achieved by solving a set of transport equations. In the first part of the paper, we show several theoretical properties, give conditions to obtain a well-posed behaviour, and show that the level set method is a particular case of the LEM. In the second part, we propose a LEM-based numerical algorithm for multiphase shape optimization problems. We apply this algorithm to an inverse conductivity problem with three phases and present several numerical results.
Abstract In this paper, we study the question of stabilization of nonlinear Korteweg-de Vries equation with boundary time-delay feedback in presence of saturated source term. Thanks to Banach fixed-point theorem the well-posedness is proved. The exponential stability result is demonstrated, using an appropriate Lyapunov functional.
The aim of this study is to establish the sufficient higher-order KKT (Karush Kuhn Tucker) criteria of optimality for a set-valued fractional-type optimization problem (SFP) (FP). Under the presumptions of higher-order contingent epi-derivative and higher-order κ-arcwisely connectedness, these requirements are derived. We also look into the effects of these constraints on the higher-order duality of Mond-Weir (MWD), Wolfe (WD), and mixed (MD) kinds.
Abstract In this paper, we obtain approximate necessary and sufficient optimality conditions, characterizing an approximately efficient solution of a semi-infinite multiobjective fractional problem under the closedness qualification condition. As a consequence, we derive approximate necessary and sufficient optimality conditions characterizing an approximately efficient solution for a constrained multiobjective fractional programming problem. Furthermore, we present examples illustrating our main results.
Abstract This paper is devoted to passivity analysis for a class of chaotic memristive neural networks with distinct memductance approach, subject to actuator failures. Based on the existence of memristor, actuators and activation function, it was possible for the proposed model to stay in a stable state and reach the critical point by designing a strong reliable state-feedback controller. The qualitative analysis of this model can be developed using differential inclusion theory in the sense of Fillipov’s solution with suitable Lyapunov functional to acquire the results in terms of linear matrix inequalities (LMIs). Considering the known and unknown actuators cases, some sufficient conditions are derived for both state-dependent switched system and state-dependent continuous system based on passivity theory along with its chaotic phenomena. The reliable state-feedback controller is designed to guarantee that the considered closed loop system is internally stable by adopting the stabilizing control law. Finally, numerical examples are presented to demonstrate theoretical results via graphical illustrations.
