T. Parisini

A multiple model based nonlinear control scheme for nonlinear discrete-time systems is considered. A set of optimal receding-horizon feedback control functions is defined, based on a description of the nonlinear plant by means of interpolation of a set of local models, using a family of nonlinear validity functions. To obtain the control law to be applied to the plant, interpolation of the local control actions is done, using the same validity function family. This choice allows to carry out the stability analysis of the equilibrium of the multiple model control scheme.

An approach to the solution of the optimal filtering problem by means of neural networks is proposed. It is a nonlinear filtering method using feedforward neural networks. In comparison with classical methods, like the extended Kalman filter, the approach involves no linearization, and requires no strong prior assumptions about the statistical properties of the random noises acting on both the dynamic system and the observation channel.

No general analytical tools are available to estimate the state of a nonlinear stochastic system observed through a nonlinear noisy channel. This problem is addressed in the paper under the assumption that the statistics of the random variables are unknown, hence a statistical approach is followed instead of a probabilistic one. The following approximations are enforced: (i) the state estimator is finite-memory, (ii) the estimation functions are given fixed structures in which a certain number of parameters have to be optimized (multilayer feedforward neural networks are chosen from among various possible nonlinear approximators), (iii) the algorithms for optimizing the parameters (i.e., the network weights) rely on stochastic approximation. Simulation results are reported to compare the behavior of the proposed estimator with the extended Kalman filter Author(s) Alessandri, A. Dept. of Commun., Comput. & Syst. Sci., Genoa Univ., Italy Parisini, T. ; Zoppoli, R.

The state estimation problem for a section of a real power plant is addressed by means of a recently proposed sliding‐window neural state estimator. The complexity and the nonlinearity of the considered application prevent us from successfully using standard techniques as Kalman filtering. The statistics of the distribution of the initial state and of noises are assumed to be unknown and the estimator is designed by minimizing a given generalized least‐squares cost function. The following approximations are enforced: (i) the state estimator is a finite‐memory one, (ii) the estimation functions are given fixed structures in which a certain number of parameters have to be optimized (multilayer feedforward neural networks are chosen from among various possible nonlinear approximators), (iii) the algorithms for optimizing the parameters (i.e., the network weights) rely on a stochastic approximation. Extensive simulation results on a complex model of a part of a real power plant are reported to compare the behaviour of the proposed estimator with the extended Kalman filter. Copyright © 2001 John Wiley & Sons, Ltd.