J. Humberto Pérez-Cruz

Evolving intelligent system for the modelling of nonlinear systems with dead-zone input

In this paper, the modelling problem of nonlinear systems with dead-zone input is considered. To solve this problem, an evolving intelligent system is proposed. The uniform stability of the modelling error for the aforementioned system is guaranteed by means of a Lyapunov-like analysis. The effectiveness of the proposed technique is verified by simulations.

Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone

This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term.

Robust Adaptive Neurocontrol of SISO Nonlinear Systems Preceded by Unknown Deadzone

In this study, the problem of controlling an unknown SISO nonlinear system in Brunovsky canonical form with unknown deadzone input in such a way that the system output follows a specified bounded reference trajectory is considered. Based on universal approximation property of the neural networks, two schemes are proposed to handle this problem. The first scheme utilizes a smooth adaptive inverse of the deadzone. By means of Lyapunov analyses, the exponential convergence of the tracking error to a bounded zone is proven. The second scheme considers the deadzone as a combination of a linear term and a disturbance-like term. Thus, the estimation of the deadzone inverse is not required. By using a Lyapunov-like analyses, the asymptotic converge of the tracking error to a bounded zone is demonstrated. Since this control strategy requires the knowledge of a bound for an uncertainty/disturbance term, a procedure to find such bound is provided. In both schemes, the boundedness of all closed-loop signals is guaranteed. A numerical experiment shows that a satisfactory performance can be obtained by using any of the two proposed controllers.

System Identification Using Multilayer Differential Neural Networks: A New Result

In previous works, a learning law with a dead zone function was developed for multilayer differential neural networks. This scheme requires strictly a priori knowledge of an upper bound for the unmodeled dynamics. In this paper, the learning law is modified in such a way that this condition is relaxed. By this modification, the tuning process is simpler and the dead-zone function is not required anymore. On the basis of this modification and by using a Lyapunov-like analysis, a stronger result is here demonstrated: the exponential convergence of the identification error to a bounded zone. Besides, a value for upper bound of such zone is provided. The workability of this approach is tested by a simulation example.

Trajectory tracking based on differential neural networks for a class of nonlinear systems

A very successful scheme to accomplish trajectory tracking of unknown nonlinear systems consists of identifying the unknown dynamics using differential neural networks and on the basis of the so obtained mathematical model to develop an appropriate control law. The purpose of this paper is to present some new results in this sense. In particular, for the neural identifier, a new online learning law which permits to guarantee the boundedness for both the weights and the identification error without using a dead zone function is showed. Likewise, based on this neural identifier, a new control law to guarantee the boundedness of the tracking error is developed. These results are proved using a Lyapunov like analysis. With respect to the approach based on the local optimal control theory, the new approach has a similar performance but its main advantage consists of simplifying considerably the design process. The workability of the suggested approach is illustrated by simulation.

Singularity-Free Neural Control for the Exponential Trajectory Tracking in Multiple-Input Uncertain Systems with Unknown Deadzone Nonlinearities

The trajectory tracking for a class of uncertain nonlinear systems in which the number of possible states is equal to the number of inputs and each input is preceded by an unknown symmetric deadzone is considered. The unknown dynamics is identified by means of a continuous time recurrent neural network in which the control singularity is conveniently avoided by guaranteeing the invertibility of the coupling matrix. Given this neural network-based mathematical model of the uncertain system, a singularity-free feedback linearization control law is developed in order to compel the system state to follow a reference trajectory. By means of Lyapunov-like analysis, the exponential convergence of the tracking error to a bounded zone can be proven. Likewise, the boundedness of all closed-loop signals can be guaranteed.

DESIGN OF A SLIDING MODE NEUROCONTROLLER FOR A NUCLEAR RESEARCH REACTOR

Abstract This paper presents the application of a special technique which combines neural networks and sliding modes for solving the robust tracking problem in a nuclear reactor when only the input and the output are available. Due to the appropriate sensor absence, the design is based on a differential neural network observer. The highly nonlinear structure provided by this neural network is linearized using sliding mode. Finally, this linear model is employed for determining a sliding mode control for tracking a reference model. The efficiency of this technique with a guaranteed bound for the averaged tracking error is illustrated by simulation.

Automatic startup of nuclear reactors using differential neural networks

Abstract In this paper, the automatic startup of a nuclear reactor subjected to period scram constraint is considered. To achieve this operation in a minimum time avoiding the difficulties associated with the application on-line of maximum principle or dynamic programming, first the optimal trajectory is calculated off-line. Next, the nuclear plant considered as a black box is identified by a differential neural network. The structure provided by this neural identifier is fed back to follow the optimal trajectory. The modeling error is compensated by the usage of the power derivative. Thus, the asymptotic stability of the tracking error can be guaranteed.