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To develop a simplified robust control scheme for a class of nonlinear time‐varying uncertain chaotic systems.

By means of input‐to‐state stability theory, a new robust adaptive control scheme is designed, which is simpler than the one proposed by Li et al. and applicable to a larger class of nonlinear systems. Only one parameter is adjusted in the controller and the scheme assures that all the signals remain bounded. The behavior of the proposed control scheme is also analyzed through simulations on the Rössler system.

By adjusting only one parameter in the controller and imposing only one mild assumption on the time‐varying parameters, the proposed control algorithm assures that all the signal remain bounded and that the state of the original system will follow a desired trajectory defined either by the trajectory and its first time derivative, or given by a reference model.

The results are limited to a particular class of nonlinear systems where the dimension of the input vector is equal to the order of the system (dimension of the state vector).

The main advantage of the proposed method is that the modification introduced leads to a substantially simpler adaptive robust controller whose practical implementation will be easier.

The contribution of the proposed method is in the simplification of the control algorithm applied to a class of nonlinear time‐varying uncertain chaotic systems. This will be useful for control engineers to control complex industrial plants.

To develop a new predictive control scheme based on neural networks for linear and non‐linear dynamical systems.

The approach relies on three different multilayer neural networks using input‐output information with delays. One NN is used to identify the process under control, the other is used to predict the future values of the control error and finally the third one is used to compute the magnitude of the control input to be applied to the plant.

This scheme has been tested by controlling discrete‐time SISO and MIMO processes already known in the control literature and the results have been compared with other control approaches with no predictive effects. Transient behavior of the new algorithm, as well as the steady state one, are observed and analyzed in each case studied. Also, online and offline neural network training are compared for the proposed scheme.

The theoretical proof of stability of the proposed scheme still remains to be studied. Conditions under which non‐linear plants together with the proposed controller present a stable behavior have to be derived.

The main advantage of the proposed method is that the predictive effect allows to suitable control complex non‐linear process, eliminating oscillations during the transient response. This will be useful for control engineers to control complex industrial plants.

This general approach is based on predicting the future control errors through a predictive neural network, taking advantage of the NN characteristics to approximate any kind of relationship. The advantage of this predictive scheme is that the knowledge of the future reference values is not needed, since the information used to train the predictive NN is based on present and past values of the control error. Since the plant parameters are unknown, the identification NN is used to back‐propagate the control error from the output of the plant to the output of the controller. The weights of the controller NN are adjusted so that the present and future values of the control error are minimized.

To apply and simulate under different conditions, the combined model reference adaptive control (CMRAC) technique to control the pitch angle in a subsonic plane. Comparisons with the classical PID controller and the adaptive direct MRAC are also performed.

The methodology used in this work is the CMRAC. This is a relatively new adaptive control technique which combines the information coming from the identification procedure as well as that from the direct control scheme, and use it in the adaptive laws. The identification parameters and the controller parameters are simultaneously adjusted using the identification error, the control error and the so‐called close‐loop identification error. This combination has shown to improve the transient behavior of the adaptive systems.

This control scheme has been tested by simulation on a model of a CESSNA 182 plane, to control the pitch angle (longitudinal movement). The results have been compared with other control approaches such as the classical PID and the adaptive direct MRAC. Although the PID control satisfies all the control specifications as much as the CMRAC, it is not able to adapt when changes in the operating conditions occur, as in the case of the CMRAC. The direct MRAC does no perform well in this study.

The implementation at practical level remains to be studied and analyzed, to verify the theoretical and simulation results presented here.

The main advantage of the proposed method is that it behaves well even under different operating conditions, which is one of the most important characteristics for an implementation at practical level.

It is the first time in the control literature that the CMRAC is applied to control the pitch angle of a plane in a longitudinal movement. The results are quite promising remaining the practical implementation to verify the performance of the proposed scheme under real conditions.

This paper presents a method for designing a fixed controller, which is able to control in a stable fashion a family of linear time‐invariant n‐th order plants with arbitrary relative degree. This plant family is defined in terms of a nominal transfer function of rational type and bounded variations of the coefficients of numerator and denominator polynomials. The design method is based on the algebraic relationship existing in the model reference adaptive control technique between the true plant parameters, the ideal controller parameters and the model reference parameters. While applying the proposed method, the resulting plant families are broader if compared with other techniques used to design robust controllers.