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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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This paper is concerned with the problem of improvement of fuzzy H_infinity tracking controller for nonlinear systems modeled by T-S fuzzy scheme. The fuzzy tracking controller not only stabilizes the closed-loop system, but also results in the H_infinity tracking error norm to all the bounded external signals to be less than some given value. A new tracking control law is proposed for each linear local subsystem of T-S fuzzy model. A Linear Matrix Inequalities (LMIs) approach is proposed to find all the parameters of the control laws. The proposed approach results in a noticeable improved tracking performance with respect to the existing approaches. An investigation of the tracking performance of the proposed approach on the inverted pendulum system, in comparison with the other approaches, shows the improvement. 

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This paper is concerned with the problem of output feedback fuzzy mixed H2/H_inf tracking control design for nonlinear systems. A general and modified class of output-feedback controller structure is assumed. Using parallel distributed compensation, a fuzzy controller is proposed which not only satisfies an H_inf tracking control constraint, but also optimally minimizes a H2control performance measure. The proposed method leads to a trade-off between the tracking performance and the amount of control input effort. The problem formulation and the method of finding the optimal fuzzy tracking controller parameters involve a single step linear matrix inequalities form. On a benchmark example, the proposed method is applied on the inverted-pendulum system and is compared with traditional H_inf-only results from diffrent perspectives.
 

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Abstract: This paper designs an optimal controller for the simultaneous determination of physical model parameters and LQR controller parameters. In some systems, it is possible to determine some of the model parameters by the designer. In conventional methods of optimal controller design for this group of systems, first, the model parameters are determined by the designer, and then in a separate step, the controller is designed for the definite model. In this paper, a method for the simultaneous determination of these two sets of parameters is presented for continuous-time linear systems. Simultaneous parameter determination is a nonlinear and non-convex optimization problem that in this paper a new method is considered to solve this problem. The non-convex optimization problem is transformed into a convex optimization problem by performing simplifications and then solved by the CVX toolbox of MATLAB software. The result is a controller with less control cost in comparison to conventional methods for this group of systems. By providing a simulation example, the performance improvement of the proposed method is shown.