Yun-ng Chu

Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities

The class of nonlinear systems described by a discrete-time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered. Sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant Lyapunov functions or storage functions, satisfying appropriate linear matrix inequalities. Results are also presented for model reduction errors for such systems.

Stabilization and performance synthesis for systems with repeated scalar nonlinearities

The class of nonlinear systems described by a discrete-time state-equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered. Given a plant of this form, sufficient conditions are derived for: 1) the parametrization of all controllers of the same form such that the closed loop is stable in the sense of a diagonally dominant Lyapunov function; and (2) the synthesis of a controller of the same form so that the induced norm of the closed loop is under a prescribed level. Several of these conditions can be written into linear matrix inequalities.

A neural-network method for the nonlinear servomechanism problem

The solution of the nonlinear servomechanism problem relies on the solvability of a set of mixed nonlinear partial differential and algebraic equations known as the regulator equations. Due to the nonlinear nature, it is difficult to obtain the exact solution of the regulator equations. This paper proposes to solve the regulator equations based on a class of recurrent neural network, which has the features of a cellular neural network. This research not only represents a novel application of the neural networks to numerical mathematics, but also leads to an effective approach to approximately solving the nonlinear servomechanism problem. The resulting design method is illustrated by application to the well-known ball and beam system.

Robust control of combustion oscillations

The physics involved in combustion oscillations is complex, and the controller design has frequently been hampered by the lack of reliable models. We make use of a new theory, based on the constant flame speed model of Fleifil et al. (1996), for the nonlinear oscillations of a ducted flame burning in the wake of a bluff-body flame-holder to provide a vehicle on which a robust controller is developed. The feedback control we consider involves the unsteady addition of fuel in response to a signal monitoring the oscillation. A linear design is produced using H/sub /spl infin// loop-shaping techniques.

A neural network method for the nonlinear servomechanism problem

The solution of the nonlinear servomechanism problem relies on the solvability of a set of mixed nonlinear partial differential and algebraic equations known as the regulator equations. Due to the nonlinear nature, it is difficult to obtain the exact solution of the regulator equations. This paper proposes to solve the regulator equations based on a class of recurrent neural network, leading to an effective approach to approximately solving the nonlinear servomechanism problem.

Gain-scheduling for systems with repeated scalar nonlinearities

The class of nonlinear systems described by a discrete-time state-equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered. Given a plant of this form, sufficient conditions are derived for the synthesis of a controller of the same form so that the induced norm of the closed-loop is under a prescribed level, using positive definite diagonally dominant storage functions. Several of these conditions can be written into linear matrix inequalities.

Bounds of the induced norm and model reduction errors for a class of nonlinear systems

The class of nonlinear systems described by a discrete-time state equation containing a diagonal nonlinear term as in recurrent neural networks is considered. Sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant Lyapunov functions or storage functions, satisfying appropriate linear matrix inequalities. Preliminary results are also presented for model reduction errors for such systems.

A neural network which learns decision boundaries with nonlinear clustering

Presents a novel neural network which works as a classifier. It uses Euclidean distance similarity measurement to form clusters which are represented by output units. Uniquely, output units in the proposed network have nonlinear hard-limiter activation functions. Through this nonlinear activation function, complex decision boundaries from input patterns can be approximated. Furthermore, it does not forget previously remembered training patterns as it remembers newly shown patterns. This is shown with illustrative proofs. Simulation results are presented and compared with those from the backpropagation neural network. They demonstrate that the network described, with its simple architecture and learning, it is able to capture continuous distributions of complex decision boundaries from discrete patterns.<<ETX>>

Solving the nonlinear regulator equations by a single layer feedforward neural network

This paper proposes to solve the nonlinear regulator equations based on a single hidden layer feedforward neural network, leading to an effective approach to approximately solve the nonlinear servomechanism problem. The resulting design method is illustrated by application to the well-known ball and beam system.