Sampled-Data Observer-Based Deterministic Learning And Its Applications

Recently,machine learning for dynamical systems(dynamic learning)has gradually become a hot topic in the field of artificial intelligence.One of the main subjects is to learn physically interpretable models of dynamical systems from time series generated from dynamical processes,which will support recognition,classification,prediction,and control tasks in engineering,medicine,national defense,and other fields.In addition,due to the system itself,or economic and physical constraints,it is often impossible to obtain all state variables of dynamical systems in many practical applications,which makes the study of dynamical systems more challenging.In this thesis,for the sampling data of system output(i.e.,univariate time series),the problem of identification,observation,recognition,and control of nonlinear dynamical systems is investigated by combining sampled-data observer and deterministic learning.The main contents are as follows:1.In the state observation task of sampled-data systems with unknown nonlinear dynamics,several issues require special attention,including how to achieve accurate identification of unknown dynamics when the system states are unavailable,and how to use the identified dynamics to improve observation performance.To this end,a unified approach is proposed to design sampled-data observers based on deterministic learning.First,a discrete-time implementation of the high-gain observer is utilized to obtain state trajectory from sampled output measurements.By taking the recurrent estimated trajectory as inputs to a radial basis function network(RBFN),a partial persistent exciting(PE)condition is satisfied,and a locally accurate approximation of nonlinear dynamics can be realized along the estimated trajectory.By using the identified dynamics,a new RBFN-based observer is then designed to achieve non-high-gain state estimation,which would effectively attenuate the detrimental effects resulting from high-gain designs.2.In the recognition task of univariate time series,several issues require special attention,including how to represent the inherent dynamical patterns of univariate time series,how to achieve rapid recognition of univariate time series,and how to guarantee the accuracy of the recognition result.To this end,two dynamical pattern recognition approaches are proposed for univariate time series based on the sampled-data observer,i.e.,high-gain and non-high-gain recognition approaches.First,locally-accurate modeling of the inherent dynamics of training time series is achieved by a sampled-data high-gain observer and RBFN identifiers.The modeling results(i.e.,constant RBFN models of dynamical patterns)are stored in a pattern library.Then,several high-gain and non-highgain observer-based estimators are designed by using the pattern library,respectively.The recognition problem of the test time series is transformed into the stability analysis of the estimator residual systems.The corresponding recognition conditions are derived through the performance analysis,which is beneficial to verify the accuracy of the recognition results.These approaches do not require complicated modeling of the test time series,which ensures rapid recognition of the test pattern.Finally,comparative studies of two approaches are carried out for recognition tasks on a large data set.3.In the learning and control task of sampled-data systems with only output measurements,several issues require special attention,including how to achieve accurate learning/identification of the closed-loop dynamics from output feedback control,how to employ the learned knowledge to improve tracking performance,and how to design parameters to obtain better learning and control performance.To this end,a unified learning and control approach is proposed by integrating the deterministic learning and sampleddata observer.First,an adaptive RBFN controller with a sampled-data high-gain observer is designed to track a recurrent reference model.Along the trajectory estimated by the observer,it is demonstrated that the RBFN weights can exponentially converge to their ideal values with the satisfaction of a partial PE condition,and the closed-loop dynamics can be accurately learned during the output-feedback process.Then,using the learning results,a knowledge-based output-feedback controller is developed to improve the tracking performance.Further research shows that choosing appropriate parameters for the observer and RBFN can guarantee learning and control performance.In particular,we cannot always obtain better state estimation by increasing the gain of the sampled-data observer,and better RBFN approximation for the closed-loop dynamics by increasing the density of neural nodes.4.In the warning task of flow instability in axial flow compressors,several issues require special attention,including how to identify the dynamical models of the flow instability from sampling data of a single measurement point(i.e.,univariate time series),and how to use the pattern library under different working conditions to give effective warning of flow instability.To this end,a sampled-data observer-based warning approach of flow instability is proposed for axial compressors under different conditions.First,a sampled-data observer and RBFN identifiers are used to identify the dynamical models of flow instability from univariate time series,and a dynamical pattern library of flow instability for different conditions is constructed.Then,several dynamical estimators are designed using the pattern library,and corresponding decision indicators are generated.Based on this,a practical two-level decision-making procedure is developed to realize the early warning of flow instability under different conditions.In comparison with several common warning approaches,the proposed approach can quickly and accurately generate warning results for flow instability.