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A Class Of Modified Hopfield Networks For Control Of Linear And Nonlinear Systems, Jie Shen, S. N. Balakrishnan
A Class Of Modified Hopfield Networks For Control Of Linear And Nonlinear Systems, Jie Shen, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
This paper presents a class of modified Hopfield neural networks (MHNN) and their use in solving linear and nonlinear control problems. This class of networks consists of parallel recurrent networks which have variable dimensions that can be changed to fit the problems under consideration. It has a structure to implement an inverse transformation that is essential for embedding optimal control gain sequences. Equilibrium solutions are discussed. Numerical results for a motivating aircraft control problem (linear) are presented. Furthermore, we formulate the state-dependent Riccati equation method (SDRE) for a class of nonlinear dynamical system and show how MHNN provides the solution. …
Robustness Analysis Of Hopfield And Modified Hopfield Neural Networks In Time Domain, Jie Shen, S. N. Balakrishnan
Robustness Analysis Of Hopfield And Modified Hopfield Neural Networks In Time Domain, Jie Shen, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A variant of the Hopfield network, called the modified Hopfield network is formulated. This network which consists of two mutually recurrent networks has more free parameters than the well-known Hopfield network. Stability analysis of this network is presented. The analysis is carried out in the time domain with an application of the Lyapunov method and robust control Lyapunov function. The current flow in the network is treated as a "control". This "controller" is shown to guarantee "a practically stabilizing control". Analysis of the Hopfield network is also included for completion.