Adaptive control using multiple parallel dynamic neural networks

An observer-based adaptive inverse optimal control (AIOC) scheme is developed for unknown nonlinear systems. First, a dynamic neural network (DNN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed based on control Lyapunov function (CLF) via inverse optimal method to obtain the optimal feedback control. In this framework, a two-layer DNN is used to construct the observer which can be implemented to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics. The optimal control scheme is implemented to online control the unknown nonlinear systems and the DNN observer simultaneously. An asymptotic stability of the closed-loop system is guaranteed using Lyapunov-based analysis. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

In this paper, we are dealing with the problem of regulating unknown nonlinear dynamical systems. First a dynamical neural network identifier is employed to perform ‘black box’ identification and then a regular static feedback is developed to regulate the unknown system to zero. Not all the plant states are assumed to be available for measurement.

A direct nonlinear adaptive state regulator, for unknown dynamical systems that are modeled by dynamic neural networks is discussed. In the ideal case of complete model matching, convergence of the state to zero plus boundedness of all signals in the closed loop is ensured. Moreover, the behavior of the closed loop system is analyzed for cases in which the true plant differs from the dynamic neural network model in the sence that it is of higher order, or due to the presence of a modeling error term. In both cases, modifications of the original control and update laws are provided, so that at least uniform ultimate boundedness is guaranteed, even though in some cases the stability results obtained for the ideal case are retained.

Since all of adaptive models converge to the same point in parameter space, classical second level multiple model adaptive control method cannot deal with linear time-varying system. In order to deal with this drawback, this paper proposes a modified second level adaptive control method based on combining the advantages of adaptive model and fixed model for a class linear discrete time-varying plant where only a little prior information which is known. Firstly, multiple adaptive models are selected in the space of parameters, and the parameters are identifying and the controller is designed based on second level adaptive method. Secondly, when one of sub-model of the adaptive models are closed to the real parameters of the system, all of these adaptive models are fixed, and then the controller is designed based on multiple fixed models. Lastly, simulations have demonstrated that this method is effectively to a class of linear time-varying system.

This paper presents an online modeling and control strategy for a class of linearizable nonlinear systems with unknown parameters and nonlinearities. A dynamic neural network (DNN) is utilized for modeling of nonlinear systems in their equivalent feedback linearized form. Lyapunov techniques are used to derive the adaptation rules for training the DNN's weight matrices. An adaptive state feedback stabilizing control is developed based on the equivalent DNN model of the systems. An observer is also designed to estimate the states of the DNN model of the system. Subsequently, an adaptive output feedback stabilizing control law is derived for unknown nonlinear systems, using their equivalent DNN model, with guaranteed closed-loop stability. Simulation results show the effectiveness of the proposed technique.

It is well-known that the controls of neural network require that all the inputs of their input layer are available. Under this circumstance, the architecture of the neural network is constrained. Hence, this kind of neurocontrol cannot apply to a wide class of nonlinear and unknown dynamical systems, or the control system that requires more sensors. Although the unknown system state and the unknown system dynamics can be achieved from an adaptive observer and a learning neural network, respectively, the simultaneous existence of the estimated state error and the modeling error makes the control system more likely to be unstable. In this paper, a novel neurocontroller based on the concept of sliding mode with estimated state is constructed to tackle a wide class of unknown and nonlinear dynamical systems. The focal stability of the overall system can be verified by the Lyapunov stability criteria. Finally, simulations are presented to verify the usefulness of the proposed method.

A new hybrid scheme which contains multiple fixed and adaptive Takagi-Sugeno (T-S) identification models is proposed in this paper in order to control efficiently a class of unknown nonlinear dynamical fuzzy systems. One state feedback fuzzy controller corresponds to each T-S model, producing its signal according to the certainty equivalence approach. A performance index and an appropriate switching rule are used to determine the T-S model which best approximates the plant and consequently to pick the best available controller at every time instant. There are two kind of adaptive models: one free running adaptive model and one reinitialized adaptive model which uses the parameters of the best fixed model at every time instant. Lyapunov stability theory is used in order to obtain the adaptive law for every adaptive model's parameters ensuring the asymptotic stability of the system. Singularity problems in the control signal are avoided by modifying the adaptive law and the Next Best Controller Logic (NBCL) ensures the controller's feasibility. A computer simulation example is given to verify the theoretical results.

This article investigates adaptive control problems for unknown second-order nonlinear multiagent systems (MASs) via an event-triggered approach. An adaptive event-triggered consensus controller is given to second-order MAS with unknown nonlinear dynamics. We prove that the proposed consensus controller is free from Zeno behavior. Next, an adaptive event-triggered tracking controller is developed for leader-follower MAS with the leader having bounded nonzero control input. Both consensus and tracking controllers are fully distributed, which means that event-triggered controllers only use local cooperative information. Finally, an unknown second-order nonlinear MAS is used to verify the given event-triggered controllers.

Direct and indirect techniques to control unknown nonlinear dynamical systems using dynamical neural networks

This paper proposes an indirect adaptive fuzzy neural network (FNN) controller with state observer and supervisory controller for a class of uncertain nonlinear dynamic time delay systems. First, the approximate function of unknown time delay system is inferred by the adaptive time delay FNN system. Next, a state observer is designed to estimate the unknown system states and the indirect adaptive fuzzy controller is constructed. Finally, the closed loop controller is obtained by incorporating the supervisory controller with the indirect adaptive fuzzy controller. Therefore, if the system tends to unstable, i.e., error dynamics is larger than a prescribed constraint which is determined by designer, the supervisory controller will activate to force the state to be stable. The free parameters of the indirect adaptive FNN controller can be tuned online by observer-based output feedback control law and adaptive laws by means of Lyapunov stability criterion. The resulting simulation example shows that the performance of nonlinear time delay chaotic system is fully tracking the reference trajectory. Meanwhile, simulation results show that the adaptive control effort of the proposed control scheme is much less due to the assist of the supervisory controller.

Robust adaptive control of chaotic system with uncertainty was investigated in the presence of modeling error. The scheme of adaptation was based on identification estimates via dynamical neural networks. By using proposed nonlinear adaptive controller, the chaotic signal of the unknown system dynamics tends to be driven into a well controlled steady state. Moreover, the mathematical proof of stability properties of the system was guaranteed. Finally, simulation results have demonstrated the effectiveness of the proposed method through application on the Chen's chaotic system.

We propose a new type of neural adaptive control via dynamic neural networks. For a class of unknown nonlinear systems, a neural identifier-based feedback linearization controller is first used. Dead-zone and projection techniques are applied to assure the stability of neural identification. Then four types of compensator are addressed. The stability of closed-loop system is also proven.

The paper proposes a combined control scheme for completely unknown nonlinear system with an adaptive neural network (ANN) inverse controller based on online least squares support vector machines (LS-SVM) identifier. The neural network controller parameters are adjusted by gradient information of online LS-SVM for the unknown nonlinear system. As well as, considering of the parameter regulating process of ANN, a proportional-integral-derivative (PID) controller is combined to improve the control performance in initial stage. The simulation experiments are made to illustrate the efficiency of the proposed method. The results show that the proposed control method is effective and can achieve better control performance for completely unknown nonlinear system.

A COMPARISON OF IDENTIFICATION ALGORITHMS FOR RAPIDLY TIME-VARYING PARAMETERS ON A REAL PROCESS

Chapter Seven - Bio-inspired Algorithms to Improve Neural Controllers for Discrete-time Unknown Nonlinear System