Robust pole assignment for synthesizing feedback control systems using recurrent neural networks

Sparse signal reconstruction via collaborative neurodynamic optimization

In this paper, we formulate a mixed-integer problem for sparse signal reconstruction and reformulate it as a global optimization problem with a surrogate objective function subject to underdetermined linear equations. We propose a sparse signal reconstruction method based on collaborative neurodynamic optimization with multiple recurrent neural networks for scattered searches and a particle swarm optimization rule for repeated repositioning. We elaborate on experimental results to demonstrate the outperformance of the proposed approach against ten state-of-the-art algorithms for sparse signal reconstruction.

Research on the control problem of actuator anti-saturation of supercavitating vehicle

In the theoretical controller design of the high-speed supercavitating vehicle (HSSV), there will always be the problem that the physical saturation limit has to be exceeded by the motion range of the actuator to satisfy the requirements of stable motion of the supercavitating vehicle. This paper proposes a solution which could satisfy the requirements of stable motion of the vehicle without saturation of the actuator. First of all, the rotation range of the actuator and the motion performance of the vehicle with robust controller are analyzed under the condition where saturation is neglected. Then, according to the analysis conclusion, the controller is improved by using linear active disturbance rejection control (LADRC) method, which provides the additional control component to reduce the rotation angle and rotation speed of the actuator. Finally, the simulation proves that the solution could realize the stable motion of vehicle without saturation of actuator.

Two-Timescale Multilayer Recurrent Neural Networks for Nonlinear Programming

This article presents a neurodynamic approach to nonlinear programming. Motivated by the idea of sequential quadratic programming, a class of two-timescale multilayer recurrent neural networks is presented with neuronal dynamics in their output layer operating at a bigger timescale than in their hidden layers. In the two-timescale multilayer recurrent neural networks, the transient states in the hidden layer(s) undergo faster dynamics than those in the output layer. Sufficient conditions are derived on the convergence of the two-timescale multilayer recurrent neural networks to local optima of nonlinear programming problems. Simulation results of collaborative neurodynamic optimization based on the two-timescale neurodynamic approach on global optimization problems with nonconvex objective functions or constraints are discussed to substantiate the efficacy of the two-timescale neurodynamic approach.

Two-timescale neurodynamic approaches to supervised feature selection based on alternative problem formulations

Feature selection is a crucial step in data processing and machine learning. While many greedy and sequential feature selection approaches are available, a holistic neurodynamics approach to supervised feature selection is recently developed via fractional programming by minimizing feature redundancy and maximizing relevance simultaneously. In view that the gradient of the fractional objective function is also fractional, alternative problem formulations are desirable to obviate the fractional complexity. In this paper, the fractional programming problem formulation is equivalently reformulated as bilevel and bilinear programming problems without using any fractional function. Two two-timescale projection neural networks are adapted for solving the reformulated problems. Experimental results on six benchmark datasets are elaborated to demonstrate the global convergence and high classification performance of the proposed neurodynamic approaches in comparison with six mainstream feature selection approaches.

A Two-Timescale Duplex Neurodynamic Approach to Mixed-Integer Optimization

This article presents a two-timescale duplex neurodynamic approach to mixed-integer optimization, based on a biconvex optimization problem reformulation with additional bilinear equality or inequality constraints. The proposed approach employs two recurrent neural networks operating concurrently at two timescales. In addition, particle swarm optimization is used to update the initial neuronal states iteratively to escape from local minima toward better initial states. In spite of its minimal system complexity, the approach is proven to be almost surely convergent to optimal solutions. Its superior performance is substantiated via solving five benchmark problems.

A Two-Timescale Duplex Neurodynamic Approach to Biconvex Optimization

This paper presents a two-timescale duplex neurodynamic system for constrained biconvex optimization. The two-timescale duplex neurodynamic system consists of two recurrent neural networks (RNNs) operating collaboratively at two timescales. By operating on two timescales, RNNs are able to avoid instability. In addition, based on the convergent states of the two RNNs, particle swarm optimization is used to optimize initial states of the RNNs to avoid local minima. It is proven that the proposed system is globally convergent to the global optimum with probability one. The performance of the two-timescale duplex neurodynamic system is substantiated based on the benchmark problems. Furthermore, the proposed system is applied for L₁ -constrained nonnegative matrix factorization.

Neural-Dynamic Optimization-Based Model Predictive Control for Tracking and Formation of Nonholonomic Multirobot Systems

In this paper, a neural-dynamic optimization-based nonlinear model predictive control (NMPC) is developed for the multiple nonholonomic mobile robots formation. First, a model-based monocular vision method is developed to obtain the location information of the leader. Then, a separation-bearing-orientation scheme (SBOS) control strategy is proposed. During the formation motion, the leader robot is controlled to track the desired trajectory and the desired leader-follower relationship can be maintained through the SBOS method. Finally, the model predictive control (MPC) is utilized to maintain the desired leader-follower relationship. To solve the MPC generated constrained quadratic programming problem, the neural-dynamic optimization approach is used to search for the global optimal solution. Compared to other existing formation control approaches, the proposed solution is that the NMPC scheme exploit prime-dual neural network for online optimization. Finally, by using several actual mobile robots, the effectiveness of the proposed approach has been verified through the experimental studies.

A Neurodynamic Approach to Distributed Optimization With Globally Coupled Constraints

In this paper, a distributed neurodynamic approach is proposed for constrained convex optimization. The objective function is a sum of local convex subproblems, whereas the constraints of these subproblems are coupled. Each local objective function is minimized individually with the proposed neurodynamic optimization approach. Through information exchange between connected neighbors only, all nodes can reach consensus on the Lagrange multipliers of all global equality and inequality constraints, and the decision variables converge to the global optimum in a distributed manner. Simulation results of two power system cases are discussed to substantiate the effectiveness and characteristics of the proposed approach.

Multiobjective Evolution of Biped Robot Gaits Using Advanced Continuous Ant-Colony Optimized Recurrent Neural Networks

This paper proposes the optimization of a fully connected recurrent neural network (FCRNN) using advanced multiobjective continuous ant colony optimization (AMO-CACO) for the multiobjective gait generation of a biped robot (the NAO). The FCRNN functions as a central pattern generator and is optimized to generate angles of the hip roll and pitch, the knee pitch, and the ankle pitch and roll. The performance of the FCRNN-generated gait is evaluated according to the walking speed, trajectory straightness, oscillations of the body in the pitch and yaw directions, and walking posture, subject to the basic constraints that the robot cannot fall down and must walk forward. This paper formulates this gait generation task as a constrained multiobjective optimization problem and solves this problem through an AMO-CACO-based evolutionary learning approach. The AMO-CACO finds Pareto optimal solutions through ant-path selection and sampling operations by introducing an accumulated rank for the solutions in each single-objective function into solution sorting to improve learning performance. Simulations are conducted to verify the AMO-CACO-based FCRNN gait generation performance through comparisons with different multiobjective optimization algorithms. Selected software-designed Pareto optimal FCRNNs are then applied to control the gait of a real NAO robot.

A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems

This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.

Laplacian Echo State Network for Multivariate Time Series Prediction

Echo state network is a novel kind of recurrent neural networks, with a trainable linear readout layer and a large fixed recurrent connected hidden layer, which can be used to map the rich dynamics of complex real-world data sets. It has been extensively studied in time series prediction. However, there may be an ill-posed problem caused by the number of real-world training samples less than the size of the hidden layer. In this brief, a Laplacian echo state network (LAESN), is proposed to overcome the ill-posed problem and obtain low-dimensional output weights. First, an echo state network is used to map the multivariate time series into a large reservoir. Then, assuming that an unknown underlying manifold is inside the reservoir, we employ the Laplacian eigenmaps to estimate the manifold by constructing an adjacency graph associated with the reservoir states. Finally, the output weights are calculated by the low-dimensional manifold. In addition, some criteria of transient stability, local controllability, and local observability are given. Experimental results based on two real-world data sets substantiate the effectiveness and characteristics of the proposed LAESN model.

A Two-Time-Scale Neurodynamic Approach to Constrained Minimax Optimization

This paper presents a two-time-scale neurodynamic approach to constrained minimax optimization using two coupled neural networks. One of the recurrent neural networks is used for minimizing the objective function and another is used for maximization. It is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization. The effectiveness and characteristics of the proposed approach are illustrated using several examples. Furthermore, the proposed approach is applied for H_∞ model predictive control.

Echo State Networks With Orthogonal Pigeon-Inspired Optimization for Image Restoration

In this paper, a neurodynamic approach for image restoration is proposed. Image restoration is a process of estimating original images from blurred and/or noisy images. It can be considered as a mapping problem that can be solved by neural networks. Echo state network (ESN) is a recurrent neural network with a simplified training process, which is adopted to estimate the original images in this paper. The parameter selection is important to the performance of the ESN. Thus, the pigeon-inspired optimization (PIO) approach is employed in the training process of the ESN to obtain desired parameters. Moreover, the orthogonal design strategy is utilized in the initialization of PIO to improve the diversity of individuals. The proposed method is tested on several deteriorated images with different sorts and levels of blur and/or noise. Results obtained by the improved ESN are compared with those obtained by several state-of-the-art methods. It is verified experimentally that better image restorations can be obtained for different blurred and/or noisy instances with the proposed neurodynamic method. In addition, the performance of the orthogonal PIO algorithm is compared with that of several existing bioinspired optimization algorithms to confirm its superiority.

Recurrent-Neural-Network-Based Multivariable Adaptive Control for a Class of Nonlinear Dynamic Systems With Time-Varying Delay

At the beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent a class of multivariable nonlinear dynamic systems with time-varying delay. It is known that the disadvantages of robust control for the NARMA model are as follows: 1) suitable control parameters for larger time delay are more sensitive to achieving desirable performance; 2) it only deals with bounded uncertainty; and 3) the nominal NARMA model must be learned in advance. Due to the dynamic feature of the NARMA model, a recurrent neural network (RNN) is online applied to learn it. However, the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions. In this situation, a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of RNN. An e -modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation. Under suitable conditions, the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed RNN-based multivariable adaptive control. Finally, simulations are presented to verify the effectiveness and robustness of the proposed control.

Synchronization of Neural Networks With Control Packet Loss and Time-Varying Delay via Stochastic Sampled-Data Controller

This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-data controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov-Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results.

Neurodynamics-Based Robust Pole Assignment for High-Order Descriptor Systems

In this paper, a neurodynamic optimization approach is proposed for synthesizing high-order descriptor linear systems with state feedback control via robust pole assignment. With a new robustness measure serving as the objective function, the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem. A neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high-order singular systems with guaranteed optimality and exact pole assignment. Two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach.