Research On The Hierarchical Control Of Nonlinear Systems

The hierarchical control problem for linear and nonlinear systems has been studied over the last decade.This problem is,briefly,concerned with designing a control law for a complex system such that its output trajectory satisfies some asymptotical properties and certain output specifications such as reachability,invariance and obstacle avoid-ance.Due to the complex system dynamics and these sophisticated control objectives,it is usually difficult to control the system directly.Instead,a hierarchical approach to control synthesis is highly desirable to solve this problem in a different way.While the low layer consists of the original system to be controlled finally,the high layer consists of a simple system,called the abstract system or simply,abstraction,which is used to fa-cilitate control synthesis in turn reduce the complexities.Both of the systems are linked by a so-called interface.This interface drives the output of low-level system to track approximately the high-level abstraction.Then the goal achievement of the abstraction guarantees that of the original system.In addition,a so-called simulation function could be used to synthesize the interface.This theory has be applied to several areas,such as robotics,electromechanics,quadrotor,planar cantilever crane,multi-agent and so on.This dissertation mainly focuses the design of interface between the nonlinear concrete systems and the linear abstract systems.The main contents are summarized as follows:First of all,the notion of interface is endowed with new features.The interface in the previous work,short for the interface function,assumes that all the state vari-ables of the concrete system are available.The hierarchical controller having the output feedback form or containing a dynamic equation is never,to the best knowledge of the author,considered.In order to incorporate this case,we introduce the notion of interface dynamic.Interface also refers to interface dynamic,not just interface function.Within this setting,not only a state feedback control law but also an output feedback controller can be designed.And then the problem of hierarchical control is formulated in a new way.In the original formulation,only transient property of the output error is consid-ered.We add the asymptotical or steady behavior in this problem,which incorporates the asymptotic tracking problem in a sense.Second,two interfaces of linear systems,i.e.,interface function and interface dy-namic are designed.For linear system,we construct an abstraction such that it is pos-sible to achieve the synthesis of a new interface function from the feedback gain of the abstraction and characterize a new simulation function by a low-order positive definite matrix associated to the abstraction.In other words,what we need only is the infor-mation of the abstraction rather than that of the concrete system which is assumed to be given a priori.Obviously,the former is obtained more easily than the latter.As for the output feedback hierarchical control problem,an interface dynamic is achieved by using a state observer.Then,for a very general kind of nonlinear systems,we design an interface func-tion by means of feedback linearization technique.Owing to the unavailability of the internal part of system state in practical situations,another interface function is derived which only makes use of the derivatives of the output.Meanwhile,for a special kind of nonlinear systems,an interface dynamic with only the output information is realized by high gain observer which is used to generate estimations of the derivatives of output.A single-link robot arm system example is given to illustrate the proposed interface.When some uncertainties appear in the plant model,the problem of hierarchical control for this case remains unexplored.Hence we consider the problem of robust output feedback hierarchical control for a class of uncertain nonlinear systems.The robust output interface dynamic is designed by an iterative procedure by resorting to the notion of internal model which is from output regulation and is used to reproduce some feedforward information.Then,an adaptive interface dynamic is also introduced for the same uncertain nonlinear systems.Finally,the hierarchical problem of the large-scale control system network is in-vestigated.As a natural extension of traditional simulation function,the new notion of vector simulation function is introduced for investigating the hierarchies of inter-connected systems.By constructing a comparison system,we present a generalized result on this problem which,in the case of a scalar simulation function,specializes to the classical result.When a class of interconnected nonlinear systems are considered,an easily checkable sufficient condition is obtained to facilitate the compositional con-struction of abstractions.Based on the condition,we propose a particular construction of abstractions for interconnected linear systems.