No abstract

Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two-and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.

No abstract

This paper presents a parallel adaptive networks controller which is implemented by our Fuzzy Input Adaptive Network (FIAN). The FIAN is easy to be set initial parameters and structure by the human sense. All FIAN parameters can he adjusted by gradient descent based on Lyaplmov stability synthesis d&g the operation of networks. The gradient adaptive is applied via linear plant parameters approximation at the chain rule of gradient search. The performance of FIAN as controller can he shown by its application which is the controllers for nonlinear plants. Due to our experiments "water bath temperature conhol system'' and "single inverted pendulum'' are selected to test the system performance.Index Tenm ---Adaptive network, fuzzy input adaptive network, intelligent control. and parameter can he selected by user or designer easily. The THEN part of FIAN is based on linear equations which can be selected the initial parameters by human sense.Furthermore, FL4N's paramten can be adjusted by gradient descent method. This adaptive method is developd based on Lyapunov stability to find the suitable learning rate[3].The organization of the paper is as following. Section II represents the FIAN algorithm. The structure of FIAN as wntroller is introduced in section m. In section IV, the experiment results are given. Section V summarizes the wnclusion of this work. A Fuzzy Adaptive NetworkOur novel fuzzy inference system, FIAN is introduced in this section. This adaptive network can be presented by the graphic method and m y linear equations. The structure of FIAN is shown in Fie.1. lntroductionIn recent years, the integration between fuzzy logic and neural network called fuzzy neural network(FNN) has been represented [I, 2, 8 and 141. Many kinds of F N N s were applied in control engineering field 15.6, and 131. The functions of FNN include controller, modeling or approximation of unknown uncertainties of conholled system[7, 10.11 and 121. The structure of FNN is based on fuzzy system rules which include IF part and THEN pari The input parametes are separated by each membership function's range at IF part. Many nonlinear functions are used as membership such as radial basis fimction, uiangle, sigmoid, etc which can he designed and selected directly by users. J n contrast of THEN pari, many researchas have represented the other functions such as zero order equation, first order equation and so on.In the THEN pari, equations are not easy to implement or defme because these equations are not close for human sense. The calculation of FNN is based on fuzzy system which mcludes fuzzification, rule based condition and defuzzification. In the fuzzification, users can design range and shape of membership functions which cover the operating point of system or input parameters. The rules of fuzzy system can he implemented by the knowledge of user. However, many defuzzification methods do not close for user and need more calculation time. From the above problem of THEN part and defuvification which are not so easy to be defined and calcul...