In this paper, a class of unknown perturbed nonlinear systems is theoretically stabilized by using adaptive neural network control. The systems, with disturbances and nonaffine unknown functions, have low triangular structure, which generalizes both strict-feedback uncertain systems and pure-feedback ones. There do not exist any effective methods to stabilize this kind of systems. With some new conclusions for Nussbaum-Gain functions (NGF) and the idea of backstepping, semiglobal, uniformal, and ultimate boundedness of all the signals in the closed-loop is proved at equilibrium point. The two problems, control directions and control singularity, are well dealt with. The effectiveness of proposed scheme is shown by simulation on a proper nonlinear system.
A novel method is proposed for flexibility analysis of nonconvex heat exchanger networks. In this method, the direction matrix is introduced to describe the deviation direction of the uncertain parameter. Then by searching the critical directions that restrict the process flexibility with the simulated annealing algorithm, the flexibility index can be obtained. Since the directions are no longer limited to the vertices, this method can well deal with the nonconvex problems. Moreover, for largescale problems, a decoupling strategy is developed to enhance the efficiency. On the basis of this, the entire network is decomposed into several independent subnetworks, and the one with the lowest flexibility decides the global flexibility index. Two examples are studied, and the results well demonstrate the various aspects dealt with in this work.
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