Recurrent Neural Dynamics Models for Perturbed Nonstationary Quadratic Programs: A Control-Theoretical Perspective

Decomposition based neural dynamics for portfolio management with tradeoffs of risks and profits under transaction costs

Real-time online optimisation plays a crucial role in high-frequency trading (HFT) strategies. The Markowitz model, as a Nobel Prize-winning framework, is widely used for portfolio management optimisation by framing the problem as a constrained quadratic programming task. While conventional analytical methods are typically effective for solving quadratic programming problems with linear constraints, the introduction of both linear equality and inequality constraints in the Markowitz model necessitates the use of numerical methods. The complexity of these numerical solutions presents technical challenges for real-time online optimisation, especially in HFT environments where computational speed and efficiency are critical. To address this challenge, we propose a simplified model that decomposes the problem into analytically solvable and unsolvable components, alongside an innovative dynamic neural network designed to quickly solve the unsolvable components. Overall, this method helps reduce computational load and is well-suited for real-time online computations in HFT settings. Furthermore, we conducted a theoretical analysis and proof of the optimality and global convergence of the solutions obtained using this method. Finally, based on a large set of real stock data, we performed three numerical experiments to validate its effectiveness. Notably, in an experiment using Dow Jones Industrial Average (DJIA) stock data, our approach reduced total costs by 5.54% compared to the commonly used MATLAB quadprog() solver, demonstrating the potential of this method as an efficient tool for portfolio management in HFT scenarios.

MNTZNN for Solving Hybrid Double-Deck Dynamic Nonlinear Equation System Applied to Robot Manipulator Control

Compared with conventional dynamic nonlinear equation systems, a hybrid double-deck dynamic nonlinear equation system (H3DNES) not only has multiple layers describing more different tasks in practice, but also has a hybrid nonlinear structure of solution and its derivative describing their nonlinear constraints. Its characteristics lead to the ability to describe more complicated problems involving multiple constraints, and strong nonlinear and dynamic features, such as robot manipulator tracking control. Besides, noises are inevitable in practice and thus strong robustness of models solving H3DNES is also necessary. In this work, a multilayered noise-tolerant zeroing neural network (MNTZNN) model is proposed for solving H3DNES. MNTZNN model has strong robustness and it solves H3DNES successfully even when noises exist in both the two layers of H3DNES. In order to develop the MNTZNN model, a new zeroing neural network (ZNN) design formula is proposed. It not only enables equations with respect to solutions to become equations with respect to the second-order derivatives of solutions but also makes the corresponding model have strong robustness. The robustness of the MNTZNN model is proved when parameters in the model satisfy a loose constraint and the error bounds are programmable via setting appropriate parameter values. Finally, the MNTZNN model is applied to the tracking control of the six-link planar robot manipulator and PUMA560 robot manipulator with hybrid nonlinear constraints of joint angle and velocity.

A strictly predefined-time convergent and anti-noise fractional-order zeroing neural network for solving time-variant quadratic programming in kinematic robot control

This paper proposes a strictly predefined-time convergent and anti-noise fractional-order zeroing neural network (SPTC-AN-FOZNN) model, meticulously designed for addressing time-variant quadratic programming (TVQP) problems. This model marks the first variable-gain ZNN to collectively manifest strictly predefined-time convergence and noise resilience, specifically tailored for kinematic motion control of robots. The SPTC-AN-FOZNN advances traditional ZNNs by incorporating a conformable fractional derivative in accordance with the Leibniz rule, a compliance not commonly achieved by other fractional derivative definitions. It also features a novel activation function designed to ensure favorable convergence independent of the model's order. When compared to five recently published recurrent neural networks (RNNs), the SPTC-AN-FOZNN, configured with 0<α≤1, exhibits superior positional accuracy and robustness against additive noises for TVQP applications. Extensive empirical evaluations, including simulations with two types of robotic manipulators and experiments with a Flexiv Rizon robot, have validated the SPTC-AN-FOZNN's effectiveness in precise tracking and computational efficiency, establishing its utility for robust kinematic control.

Coevolutionary Neural Solution for Nonconvex Optimization With Noise Tolerance

The existing solutions for nonconvex optimization problems show satisfactory performance in noise-free scenarios. However, they are prone to yield inaccurate results in the presence of noise in real-world problems, which may lead to failures in optimizing nonconvex problems. To this end, in this article, we propose a coevolutionary neural solution (CNS) by combining a simplified neurodynamics (SND) model with the particle swarm optimization (PSO) algorithm. Specifically, the proposed SND model does not leverage the time-derivative information, exhibiting greater stability compared to existing models. Furthermore, due to the noise tolerance capacity and rapid convergence property exhibited by the SND model, the CNS can rapidly achieve the optimal solution even in the presence of various perturbations. Theoretical analyses ensure that the proposed CNS is globally convergent with robustness and probability. In addition, the effectiveness of the CNS is compared with those of the existing solutions by a class of illustrative examples. We further apply the proposed solution to design a finite impulse response (FIR) filter and a pressure vessel to demonstrate its performance.

Neural Networks for Portfolio Analysis With Cardinality Constraints

Portfolio analysis is a crucial subject within modern finance. However, the classical Markowitz model, which was awarded the Nobel Prize in Economics in 1991, faces new challenges in contemporary financial environments. Specifically, it fails to consider transaction costs and cardinality constraints, which have become increasingly critical factors, particularly in the era of high-frequency trading. To address these limitations, this research is motivated by the successful application of machine learning tools in various engineering disciplines. In this work, three novel dynamic neural networks are proposed to tackle nonconvex portfolio optimization under the presence of transaction costs and cardinality constraints. The neural dynamics are intentionally designed to exploit the structural characteristics of the problem, and the proposed models are rigorously proven to achieve global convergence. To validate their effectiveness, experimental analysis is conducted using real stock market data of companies listed in the Dow Jones Index (DJI), covering the period from November 8, 2021 to November 8, 2022, encompassing an entire year. The results demonstrate the efficacy of the proposed methods. Notably, the proposed model achieves a substantial reduction in costs (which combines investment risk and reward) by as much as 56.71% compared with portfolios that are averagely selected.

Lower limb movement intention recognition for rehabilitation robot aided with projected recurrent neural network

For the lower limb rehabilitation robot, how to better realize intention recognition is the key issue in the practical application. Recognition of the patient’s movement intention is a challenging research work, which needs to be studied from the shallow to the deep. Specifically, it is necessary to ensure that the movement intention of the normal person can be accurately recognized, and then improve the model to realize the recognition of the movement intention of the patients. Therefore, before studying the patient’s movement intention, it is essential to consider the normal person first, which is also for safety considerations. In recent years, a new Hill-based muscle model has been demonstrated to be capable of directly estimating the joint angle intention in an open-loop form. On this basis, by introducing a recurrent neural network (RNN), the whole prediction process can achieve more accuracy in a closed-loop form. However, for the traditional RNN algorithms, the activation function must be convex, which brings some limitations to the solution of practical problems. Especially, when the convergence speed of the traditional RNN model is limited in the practical applications, as the error continues to decrease, the convergence performance of the traditional RNN model will be greatly affected. To this end, a projected recurrent neural network (PRNN) model is proposed, which relaxes the condition of the convex function and can be used in the saturation constraint case. In addition, the corresponding theoretical proof is given, and the PRNN method with saturation constraint has been successfully applied in the experiment of intention recognition of lower limb movement compared with the traditional RNN model.