Adaptive Multi-Dimensional Taylor Network Control Of Switched Nonlinear Systems With Input-Output Constraints

With the intelligentization of industrial production processes,the physical limitations of the practical controlled systems are increasing,and the security requirements are getting higher and higher.Therefore,the constrained control problem of input-output has attracted a massive amount of attention from the engineering control field.There is an acknowledged fact that the control ideas of many practical systems can be provided by a profound study of switched nonlinear systems,which is a mathematical model that can describe interrelated controlled objects.Consequently,the control of switched nonlinear systems with input-output constraints has been a research hotspot in the control community.However,how to design the switching rules to achieve effective control of the system is a difficult point.Under the premise of overcoming the nonlinearity,unknowns,and uncertainty existing in the controlled systems,how to construct the real-time controller with a simple structure is a research focus of scholars.In the framework of arbitrary switching,aiming at the input-output constraints problem,the Lyapunov stability criterion is established,and some constrained control tools are developed.Combining adaptive control,backstepping design and multidimensional Taylor network approximation technique,the tracking control problems of several classes of switched nonlinear systems are studied.The main research results can be summarized in the following three points:(1)The adaptive control issue of large-scale switched nonlinear systems subject to asymmetric input saturation and output hysteresis is investigated with the following two research techniques: One is to use the smooth function to estimate the saturation input,which can be transformed into the sum of a smooth function and a bounded function.The other is to express the unknown output hysteresis as a combination of a linear term and a similar disturbance term according to the modified Bouc-Wen hysteresis model.In the case of arbitrary switching,an adaptive decentralized backstepping control strategy is constructed by multi-dimensional Taylor network technique and mean value theorem.(2)The finite-time control problem of switched nonlinear systems is studied when multiple high-power combinations of the system output are constrained.In order to satisfy multiple objective constraints,a time-varying and asymmetric barrier function is constructed,which transforms multiple objective constrained systems into unconstrained systems.Based on this,the dynamic surface technique is introduced into the backstepping control process,and the filter error is reduced by constructing the error compensation system.The finite-time-based adaptive multi-dimensional Taylor network control strategy is proposed to avoid the "singularity" problem and ensure that objective functions never violate constraints.(3)The adaptive global tracking control problem of switched nonlinear systems is studied based on prescribed performance control that does not depend on the initial state.The constraint problem of tracking error is transformed into a bounded problem of barrier function by introducing a predetermined function and a normalized function.For the purpose of resulting in optimal control performance,on the basis of considering the traditional adaptive control law of dominant approximation,an extra robust adaptive law is introduced,which is used to cope with situations outside the approximate domain,and a multi-switching controller is constructed.Based on multi-dimensional Taylor network approximation technique,an adaptive backstepping control strategy is given,which achieves globally asymptotically stable.According to Lyapunov stability theory,numerical simulations and practical system simulations,the feasibility of the above adaptive control strategies in theory and application is verified.These research results open up a new way for the control of switched nonlinear systems.