Contents: Matrix Eigenvalue Methods.- Double Bracket Isospectral Flows.- Singular Value Decomposition.- Linear Programming.- Approximation and Control.- Balanced Matrix Factorizations.- Invariant Theory and System Balancing.- Balancing via Gradient Flows.- Sensitivity Optimization.- Linear Algebra.- Dynamical Systems.- Global Analysis.

Optimization and Dynamical Systems

Neural networks

The mathematics of coordinated control of prosthetic arms and manipulators.

Following the idea of using first-order time derivatives, this paper presents a general recurrent neural network (RNN) model for online inversion of time-varying matrices. Different kinds of activation functions are investigated to guarantee the global exponential convergence of the neural model to the exact inverse of a given time-varying matrix. The robustness of the proposed neural model is also studied with respect to different activation functions and various implementation errors. Simulation results, including the application to kinematic control of redundant manipulators, substantiate the theoretical analysis and demonstrate the efficacy of the neural model on time-varying matrix inversion, especially when using a power-sigmoid activation function.

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Design and analysis of a general recurrent neural network model for time-varying matrix inversion

Lecture notes in control and information sciences

Presents a recurrent neural network for solving the Sylvester equation with time-varying coefficient matrices. The recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time-varying solution of a given Sylvester equation. Theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network. Simulation results of time-varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network.

A recurrent neural network for solving Sylvester equation with time-varying coefficients

A recurrent neural network, called the Lagrangian network, is presented for the kinematic control of redundant robot manipulators. The optimal redundancy resolution is determined by the Lagrangian network through real-time solution to the inverse kinematics problem formulated as a quadratic optimization problem. While the signal for a desired velocity of the end-effector is fed into the inputs of the Lagrangian network, it generates the joint velocity vector of the manipulator in its outputs along with the associated Lagrange multipliers. The proposed Lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.

A Lagrangian network for kinematic control of redundant robot manipulators

In past decades, there has been a growing interest in the discussion and study of using underwater acoustic channel as the physical layer for communication systems, ranging from point-to-point communications to underwater multicarrier modulation networks. A series of review papers were already available to provide a history of the development of the field until the end of the last decade. In this paper, we attempt to provide an overview of the key developments, both theoretical and applied, in the particular topics regarding multicarrier communication for underwater acoustic communication such as the channel and Doppler shift estimation, video and image transmission throw multicarrier techniques, etc. This paper also includes acoustic propagation properties in seawater and underwater acoustic channel representation.

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Review Article: Multicarrier Communication for Underwater Acoustic Channel

A novel transmission scheme called fully generalised spatial modulation (FGSM) is proposed for underwater communication, where any subset of available transmitting antennas ( N t ) is activated at a time instant to transmit the data constellation symbol and the index of the active antenna is also harnessed to carry information. The FGSM offers better energy efficiency (EE) than previous spatial modulation (SM) and generalised SM systems. The proposed FGSM system is tested in an acoustic underwater multipath channel. Simulation results show that it can significantly improve the average bit error rate (ABER) as well as EE.

Fully generalised spatial modulation technique for underwater communication

A novel transmission scheme called zero-pseudorandom noise training sequence orthogonal frequency division multiplexing (ZPN-OFDM) is proposed, where the frame structure of dual-pseudorandom noise (PN) padding time domain synchronous OFDM is modified by replacing the first PN sequence by a zero sequence. The new ZPN-OFDM system offers better energy efficiency than previous OFDM systems. The ZPN-OFDM system is tested for significant tap delay multipath channels. Simulation results show that ZPN-OFDM can provide significant bit error rate improvement as well as energy efficiency improvement.

Danchi Jiang

Papers

A recurrent neural network for solving Sylvester equation with time-varying coefficients

A Lagrangian network for kinematic control of redundant robot manipulators

Review Article: Multicarrier Communication for Underwater Acoustic Channel

Fully generalised spatial modulation technique for underwater communication

Zero-pseudorandom noise training OFDM