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Obtaining the optimal control low for nonlinear systems is one of the most active subjects in the control theory. Solutions become more complicate in the presence of physical constraints, especially input constrains. In this paper, a new method has been developed to design a constrained nonlinear controller. In this method, the performance index is developed based on the predictive approach. Then, an optimization problem is solved to obtain the optimal control law in the presence of input constraints. Two constrained optimization methods have been used in this paper. The KKT-based method provides an analytical solution for obtaining the control law. The other method is based on the genetic algorithm (GA) which is considered a numerical optimization technique. These methods are implemented on an example and the results are compared

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In this study a model reference rough-radial basis function neural network controller with feedback error learning for control of a class of nonlinear systems subject to unknown bounded uncertainty is proposed. The proposed controller in hybrid form includes the classic controller and rough- radial basis function neural network controller. Because of using the classic controller with the neural network controller, it is expected that the transient response is bounded. The weights of the output layer of the neural network controller are interval variables. Using an appropriate Lyapunov function, stable adaptation laws for these weights according to the output of the classic controller and based on stability are derived. To show the efficacy of the proposed controller, results of simulation that is applied to Duffing Oscillator and Genesio- Tesi are shown and results are compared with the results when simple model reference radial basis function neural network is used as the controller. The results show that the proposed method is more robust against uncertainty when it is compared to model reference radial basis function neural network controller. Also, using the proposed controller, synchronization of chaotic systems is performed. The results verified the effectiveness of the proposed controller.

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This paper presents a robust model predictive control scheme for a class of discrete-time nonlinear systems subject to state and input constraints. Each subsystem is composed of a nominal LTI part and an additive uncertain non-linear time-varying function which satisfies a quadratic constraint. Using the dual-mode MPC stability theory, a sufficient condition is constructed for synthesizing the MPC’s stabilizing components; i.e. the local terminal cost function and the corresponding terminal set. The proposed control approach is applied to a CSTR. Simulation results show that the proposed robust MPC scheme is quite effective and it has a remarkable performance.

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In this paper, a robust model predictive control (MPC) algorithm is designed for nonlinear uncertain systems in presence of the control input constraint. To achieve this goal, first, the additive and polytopic uncertainties are formulated in the nonlinear uncertain system. Then, the control policy is chosen as a state feedback control law in order to minimize a given cost function at each known sample-time. Finally, the robust MPC problem is transformed into another optimization problem subject to some linear matrix inequality (LMI) constraints. The controller gains are determined via the online solution of the proposed minimization problem in real-time. The suggested method is simulated for a second order nonlinear uncertain system. The closed-loop performance is compared to other control techniques. The simulation results show the effectiveness of the proposed algorithm compared to some existing control methods.
 

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 In this paper an observer-based robust fault estimation scheme is proposed for a special class of Lipchitz nonlinear systems where the disturbances and faults are assumed to be coupled with the main system states. In the considered model of system, fault is assumed to enter both of the state and output equations as an unmeasured nonlinear function and coupled with the states. The disturbances and the uncertainties are considered as nonlinear functions coupled with the states. To the best of the authors’ knowledge these conditions have not been previously considered in related papers. In the proposed approach, a Luenberger observer is designed for the estimation of faults and states of system simultaneously. The effect of system disturbances is attenuated with the L2  norm. The necessary conditions for the existence of such observer is expressed in the form of Linear Matrix Inequality. The Lipchitz constant of the nonlinear function is obtained by solving the proposed Linear Matrix Inequality. Finally, the performance of the proposed method is simulated on a three-phase induction motor. The results indicate good performance of the proposed method.