Robust Control Algorithm Design For Strict Feedback System With Multiple Unknown Control Directions

In practical engineering applications,nonlinear systems are affected by many uncertain factors,such as unknown control gain and disturbance.In view of these uncertainties,the stability of strictly feedback nonlinear systems with multiple unknown and different control directions is studied in this paper.However,the current method of solving single unknown control direction is not suitable for the system with multiple unknown control directions,so the control design of nonlinear system with multiple unknown control directions is still a great challenge.In this paper,two new control schemes are proposed for two kinds of systems: decentralized stabilization for interconnected systems with mixed models and unknown control directions and predistributed error control for strictly feedback nonlinear systems with mismatched disturbances and unknown control directions.The results of theoretical analysis and simulation verify the effectiveness of the two control schemes.The main contents of this paper are as follows:1.A new Nussbaum function is proposed to solve the problem of multiple unknown control directions in the system.The function can solve not only the constant control gain but also the time-varying control gain.The properties and lemma related to the new Nussbaum function are also presented.The lemma plays a crucial role in analyzing the stability of systems with multiple unknown control directions.2.A decentralized stabilization method is proposed for interconnected systems with mixed models and unknown control directions.In interconnected systems,we consider two sets of typical but different models whose control coefficients are unknown constants and unknown time variations,respectively,which broadens the diversity of interconnected systems.Using the new Nussbaum function and its lemma,the decentralized control of the two systems is designed based on the backward step method.Theoretical analysis and simulation results show that the proposed method is effective for the asymptotic stability of interconnected systems with mixed models and multiple unknown control directions.3.In the case of mismatched disturbance,the control problem of strict feedback nonlinear system with unknown control direction is solved,and the predistributable steady-state error is achieved.The new Nussbaum function is used to solve the problem of unknown control direction.To counteract the external interference,a new auxiliary error transformation function is introduced,which has global Lipschitz continuity,differentiability of any order everywhere,and zero flatness over a small predistributable 0 neighbor.With the help of the new Nussbaum function and auxiliary transformation,it is proved by theoretical analysis and experimental simulation that the stability error can be stabilized to the predistributable neighborhood of zero.