Design Methods And Application Of State Observers Using Hopfield Neural Networks

In the field of automatic control, the states feedback always is one of the most effective methods, however, the states are not available in the most practical systems, therefore the contradiction arises between the exclusiveness of the states feedback and it's impracticability. Observers design is a main problem not only in the analysis and design of control systems, but also in the fields such as the control and monitoring in electrical systems -. fault detection and diagnoses in manufacturing industrial process, synchronization and secrecy in communication systems and so on.To overcome the defaults of traditional algebra-based methods such as high gain, repetitive computation and disability of real-time solution, in this paper, we propose a novel method design of observers using Hopfield neural network. Hopfield neural network is a full-linked interconnected dynamical system with stronger computational ability than feedforward neural network, also it can be easy implemented by VLSI and it's solution can be obtained in millisecond, it provide a powerful tool for on-line observer design. For the time-invariant linear systems, we transform the problem of observer design to a special type of constrained nonlinear programming and present the method to solve this programming using Hopfield network, then, prove the convergence of the network. This method can guarantee the solution matrix of Sylvester equation to be inverse and the sum of the input gain norm and the observer gain norm is the minimum. For the linear systems with unknown parameters, we identify the parameters using Hopfield network, then design the observers using the identified parameters, the exponential convergence of adaptive observer is also proved. For the linear time-varying systems, a new network to solve the time-varying Sylvester equation is proposed, we analysis it's convergence and robustness, then, deign the linear time-varying observer using this network model, and we discuss the convergence of the observer and ruboustness to unknown match parameters. Finally, we present a new state feedback close-loop system structure based on separability principle and Hopfield observer, discuss the characteristic of this new close-loop system. For each of the new method in this paper, we give a corresponding numerical example to show the feasibility and effectiveness of the method.