Solving nonlinear equality constrained multiobjective optimization problems using neural networks

A Projection Neural Network to Nonsmooth Constrained Pseudoconvex Optimization

In this article, a single-layer projection neural network based on penalty function and differential inclusion is proposed to solve nonsmooth pseudoconvex optimization problems with linear equality and convex inequality constraints, and the bound constraints, such as box and sphere types, in inequality constraints are processed by projection operator. By introducing the Tikhonov-like regularization method, the proposed neural network no longer needs to calculate the exact penalty parameters. Under mild assumptions, by nonsmooth analysis, it is proved that the state solution of the proposed neural network is always bounded and globally exists, and enters the constrained feasible region in a finite time, and never escapes from this region again. Finally, the state solution converges to an optimal solution for the considered optimization problem. Compared with some other existing neural networks based on subgradients, this algorithm eliminates the dependence on the selection of the initial point, which is a neural network model with a simple structure and low calculation load. Three numerical experiments and two application examples are used to illustrate the global convergence and effectiveness of the proposed neural network.

Improved Stability Criteria for Delayed Neural Networks via a Relaxed Delay-Product-Type Lapunov–Krasovskii Functional

In this paper, the asymptotic stability problem of neural networks with time-varying delays is investigated. First, a new sufficient and necessary condition on a general polynomial inequality was developed. Then, a novel augmented Lyapunov–Krasovskii functional (LKF) was constructed, which efficiently introduces some new terms related to the previous information of neuron activation function. Furthermore, based on the suitable LKF and the stated negative condition of the general polynomial, two criteria with less conservatism were derived in the form of linear matrix inequalities. Finally, two numerical examples were carried out to confirm the superiority of the proposed criteria, and a larger allowable upper bound of delays was achieved.

Effective and Safe Trajectory Planning for an Autonomous UAV Using a Decomposition-Coordination Method

In this paper, we present a Decomposition Coordination (DC) method applied to solve the problem of safe trajectory planning for autonomous Unmanned Aerial Vehicle (UAV) in a dynamic environment. The purpose of this study is to make the UAV more reactive in the environment and ensure the safety and optimality of the computed trajectory. In this implementation, we begin by selecting a dynamic model of a fixed-arms quadrotor UAV. Then, we define our multi-objective optimization problem, which we convert afterward into a scalar optimization problem (SOP). The SOP is subdivided after that into smaller sub-problems, which will be treated in parallel and in a reasonable time. The DC principle employed in our method allows us to treat non-linearity at the local level. The coordination between the two levels is achieved after that through the Lagrange multipliers. Making use of the DC method, we can compute the optimal trajectory from the UAV’s current position to a final target practically in real-time. In this approach, we suppose that the environment is totally supervised by a Ground Control Unit (GCU). To ensure the safety of the trajectory, we consider a wireless communication network over which the UAV may communicate with the GCU and get the necessary information about environmental changes, allowing for successful collision avoidance during the flight until the intended goal is safely attained. The analysis of the DC algorithm’s stability and convergence, as well as the simulation results, are provided to demonstrate the advantages of our method and validate its potential.

Passivity Analysis of Delayed Neural Networks Based on Lyapunov-Krasovskii Functionals With Delay-Dependent Matrices

This paper is concerned with passivity of a class of delayed neural networks. In order to derive less conservative passivity criteria, two Lyapunov-Krasovskii functionals (LKFs) with delay-dependent matrices are introduced by taking into consideration a second-order Bessel-Legendre inequality. In one LKF, the system state vector is coupled with those vectors inherited from the second-order Bessel-Legendre inequality through delay-dependent matrices, while no such coupling of them exists in the other LKF. These two LKFs are referred to as the coupled LKF and the noncoupled LKF, respectively. A number of delay-dependent passivity criteria are derived by employing a convex approach and a nonconvex approach to deal with the square of the time-varying delay appearing in the derivative of the LKF. Through numerical simulation, it is found that: 1) the coupled LKF is more beneficial than the noncoupled LKF for reducing the conservatism of the obtained passivity criteria and 2) the passivity criteria using the convex approach can deliver larger delay upper bounds than those using the nonconvex approach.

A Collaborative Neurodynamic Approach to Multiple-Objective Distributed Optimization

This paper is concerned with multiple-objective distributed optimization. Based on objective weighting and decision space decomposition, a collaborative neurodynamic approach to multiobjective distributed optimization is presented. In the approach, a system of collaborative neural networks is developed to search for Pareto optimal solutions, where each neural network is associated with one objective function and given constraints. Sufficient conditions are derived for ascertaining the convergence to a Pareto optimal solution of the collaborative neurodynamic system. In addition, it is proved that each connected subsystem can generate a Pareto optimal solution when the communication topology is disconnected. Then, a switching-topology-based method is proposed to compute multiple Pareto optimal solutions for discretized approximation of Pareto front. Finally, simulation results are discussed to substantiate the performance of the collaborative neurodynamic approach. A portfolio selection application is also given.

Delay-distribution-dependent H∞ state estimation for delayed neural networks with (x,v)-dependent noises and fading channels

This paper deals with the H_∞ state estimation problem for a class of discrete-time neural networks with stochastic delays subject to state- and disturbance-dependent noises (also called (x,v)-dependent noises) and fading channels. The time-varying stochastic delay takes values on certain intervals with known probability distributions. The system measurement is transmitted through fading channels described by the Rice fading model. The aim of the addressed problem is to design a state estimator such that the estimation performance is guaranteed in the mean-square sense against admissible stochastic time-delays, stochastic noises as well as stochastic fading signals. By employing the stochastic analysis approach combined with the Kronecker product, several delay-distribution-dependent conditions are derived to ensure that the error dynamics of the neuron states is stochastically stable with prescribed H_∞ performance. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results.