Strong stabilization of non-dissipative operators in Hilbert spaces with input saturation

Author(s):  
M. Laabissi ◽  
A. M. Taboye
Author(s):  
Sonal Singh ◽  
Shubhi Purwar

Background and Introduction: The proposed control law is designed to provide fast reference tracking with minimal overshoot and to minimize the effect of unknown nonlinearities and external disturbances. Methods: In this work, an enhanced composite nonlinear feedback technique using adaptive control is developed for a nonlinear delayed system subjected to input saturation and exogenous disturbances. It ensures that the plant response is not affected by adverse effect of actuator saturation, unknown time delay and unknown nonlinearities/ disturbances. The analysis of stability is done by Lyapunov-Krasovskii functional that guarantees asymptotical stability. Results: The proposed control law is validated by its implementation on exothermic chemical reactor. MATLAB figures are provided to compare the results. Conclusion: The simulation results of the proposed controller are compared with the conventional composite nonlinear feedback control which illustrates the efficiency of the proposed controller.


Author(s):  
Renqiang Wang ◽  
Qinrong Li ◽  
Shengze Miao ◽  
Keyin Miao ◽  
Hua Deng

Abstract: The purpose of this paper was to design an intelligent controller of ship motion based on sliding mode control with a Radial Basis Function (RBF) neural network optimized by the genetic algorithm and expansion observer. First, the improved genetic algorithm based on the distributed genetic algorithm with adaptive fitness and adaptive mutation was used to automatically optimize the RBF neural network. Then, with the compensation designed by the RBF neural network, anti-saturation control was realized. Additionally, the intelligent control algorithm was introduced by Sliding Mode Control (SMC) with the stability theory. A comparative study of sliding mode control integrated with the RBF neural network and proportional–integral–derivative control combined with the fuzzy optimization model showed that the stabilization time of the intelligent control system was 43.75% faster and the average overshoot was reduced by 52% compared with the previous two attempts. Background: It was known that the Proportional-Integral-Derivative (PID) control and self-adaptation control cannot really solve the problems of frequent disturbance from external wind and waves, as well as the problems with ship nonlinearity and input saturation. So, the previous ship motion controller should be transformed by advanced intelligent technology, on the basis of referring to the latest relevant patent design methods. Objective: An intelligent controller of ship motion was designed based on optimized Radial Basis Function Neural Network (RBFNN) in the presence of non-linearity, uncertainty, and limited input. Methods: The previous ship motion controller was remodeled based on Sliding Mode Control (SMC) with RBFNN optimized by improved genetic algorithm and expansion observer. The intelligent control algorithm integrated with genetic neural network solved the problem of system model uncertainty, limited control input, and external interference. Distributed genetic with adaptive fitness and adaptive mutation method guaranteed the adequacy of search and the global optimal convergence results, which enhanced the approximation ability of RBFNN. With the compensation designed by the optimized RBFNN, it was realized anti-saturation control. The chattering caused by external disturbance in SMC controller was reduced by the expansion observer. Results: A comparative study with RBFNN-SMC control and fuzzy-PID control, the stabilization time of the intelligent control system was 43.75% faster, the average overshoot was reduced by 52%, compared to the previous two attempts. Conclusion: The intelligent control algorithm succeed in dealing with the problems of nonlinearity, uncertainty, input saturation, and external interference. The intelligent control algorithm can be applied into research and development ship steering system, which would be created a new patent.


Author(s):  
D. E. Edmunds ◽  
W. D. Evans

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.


Sign in / Sign up

Export Citation Format

Share Document