Analysis And Synthesis Of Nonlinear Switching Systems With Complex Dynamics

In practical engineering,mode switching behaviors can be widely seen in the fields including mechatronic systems,chemical engineering processes,communication networks,etc.Such a switching may be a kind of stochastic switching that is not subject to artificial control,or a kind of time-/state-dependent constrained switching to be designed.Considering the simple case of linear subsystems,the linear switching systems have been extensively investigated in the past several decades.However,in the field of nonlinear switching systems,there are still quite many open and difficult problems,especially when the subsystems contain complex dynamics.This thesis is concerned with the problems of performance analysis and synthesis for several classes of nonlinear switching systems with complex system dynamics.The performance analysis focuses on stability and disturbance attenuation performance analysis,and the synthesis issues include stabilization,H∞ control and estimation.The complex dynamics concerned in this thesis include asynchronous mode identification,packet dropouts,external disturbance,and sensor limitation.The main works of this thesis are summarized below.Firstly,this thesis studies the state estimation problem of a class of stochastic switching nonlinear systems with asynchronous mode identification.The switching dynamics of the stochastic switching systems are governed by Markov processes,and the asynchronous mode identification is embodied in that the system state and the estimator state may not be in the same partitioned region of the state space.To analyze the stochastic stability and the H∞performance of the estimation error system,a mode-dependent piecewise Lyapunov function is constructed,which depends on the current mode and the region indices of both the system and estimator states,simultaneously.Then,the existence of a simultaneously mode-dependent and region-dependent fuzzy affine estimator is investigated by virtue of the S-procedure and ellipsoidal outer approximation method.A single-link manipulator system is taken as an illustrative example to verify the effectiveness of the proposed state estimation strategy,where the state estimation error is not greater than 0.005 for given bounded disturbances.Secondly,the thesis investigates the state estimator design problem for a class of stochastic switching nonlinear systems with time-varying probability of communication outage,since the outage of communication link can lead to random packet losses.The packet dropout rate of the network,which is considered to be variable,is described by the semi-Markov stochastic process that governs the switching dynamics of the fuzzy stochastic switching system.Then,the stability and H∞ performance of the estimation error system are analyzed.Then,sufficient conditions on the existence of a desired fuzzy mode-dependent state estimator are presented such that the estimation error system approaches to be mean-square stable and achieves a prescribed H∞ disturbance attenuation index.An illustrative example of a single-link robotic arm is provided in this part.Compared with the traditional estimator designed based on constant packet dropout rate,the state estimator based on variable packet dropout rate improves the state estimation performance.where the H∞ disturbance attenuation index is reduced by 45.9%.Hence,the effectiveness and the advantages of the proposed state estimator design method are demonstrated.Afterwards,the thesis explores the stabilizing control problem for a class of nonlinear stochastic switching systems with memory transition probabilities.A semi-Markov process,which is more general than a Markov process,is used to model the mode switching.The parameter variation is used to describe slow changes of parameters while the nondeterministic mode switching is for abrupt changes.The stochastic switching phenomenon is modeled by a semi-Markov stochastic process which is more generalized than a Markov process.With the construction of a Lyapunov function depending on both the parameter variation and system mode,numerical testable stability and stabilization criteria are established in the sense ofσ-error mean square stability with the aid of some mathematical techniques that can eliminate the terms containing matrix products.Numerical example shows the effectiveness of the proposed controller,where the system reaches the steady state at 8th sampling time with a steady-state error that is not greater than 5%of initial value.Moreover,the robust adaptive tracking control problem of a family of nonlinear switching systems under unknown disturbances is investigated,where the mode switching is considered to be a mode-dependent dwell time switching.Adaptive laws using tuning functions are proposed to address the parametric uncertainties and unknown disturbances,which can avoid the problem of over-parameterization.Based on the proposed time-constraint scheme,variation signals that are less conservative than those based on sojourn time are designed.Then.the globally uniformly ultimately boundness of the closed-loop multi-mode system is guaranteed.Also,the steady-state performance is presented,which is characterized by an ultimate bound of the tracking error.A numerical simulation demonstrates the effectiveness of the proposed method,where the tracking error of the system converges to the neighborhood of the origin in 2s for given initial error using the designed switching signal.Finally,as an application of the stochastic switching systems,the tracking control problem is addressed for a class of unmanned mobile platform based on stochastic switching nonlinear systems.In practice,due to the factors,such as limitation of field of view of sensors and blockage of target by obstacles,the omni-directional wheeled mobile robot is often difficult to obtain the target information continuously.To tackle this problem,a switching scheme contains two modes,i.e.,the mode when image is acquired,and the mode when image is lost,is developed via a continuous-time stochastic switching model,upon which the switching controllers are designed,then the system is proved to be mean square stable.The effectiveness of the proposed switching control approach is verified by simulations,where the tracking system can be stable in 4.5s in the cases that the initial tracking error is less than 6m.