Non-parametric Modeling And Control Of Dynamical Systems Based On Limited Data

Data-driven control approach is a method of system modeling of unknown dynamical systems based on limited data and controller design based on the modeled systems.Compared with the model-based control approaches,the data-driven control approach starts directly from the available data of the system and gets rid of the dependence on the model of the controlled object,thus improving the robustness of the control system,and can effectively deal with the control problems that are difficult to model for the controlled object.In view of the fact that the existing data-driven control methods have not systematically extended to nonlinear systems,this paper carries out research on non-parametric modeling and controller design of systems using the data-driven approach.The main contents of this paper are as follows:(1)A non-parametric modeling and sampling control method based on limited data is proposed for a class of linear systems with unknown system parameters.Firstly,the system is identified by using the data-driven approach,and then the sampled-data control design of the identified system is performed by using the input-delay approach.The asymptotic stability of the closed-loop system is proved by using Lyapunov stability theory.Then,the design approach of the feedback gain matrix of the sampling controller is given and solved by linear matrix inequalities.Finally,a numerical simulation example verifies the identification reliability of the proposed data-driven approach and the effectiveness of the proposed control strategy.(2)For a class of bilinear systems with unknown system parameters,a saturation controller based on collected data is designed to stabilize the system.Firstly,when the system parameter matrices are unknown,the random input and output data of the system are collected offline.Then,the state-feedback control gain of the controller with saturation input is directly determined by using the polynomial sum of squares decomposition technology through the collected data.Finally,the effectiveness of the control strategy is verified by numerical simulation.(3)For a class of Lorenz-type chaotic systems with unknown system parameters,a non-parametric modeling and state-feedback control approach based on limited data is proposed.Firstly,the Lorenz system is modeled as a state-dependent linear form.Then,the input and output data of the system are sampled offline,and the expression of the state-feedback controller is directly designed using the collected data.At the same time,the global asymptotic stability of the closed-loop system is proved.Finally,the effectiveness of direct data driven control is verified by solving the controller parameters using the SOSTOOLS.(4)For a class of polynomial systems with unknown system parameters,the direct data-driven saturation control approach is studied.Firstly,some asymptotic stability results for a class of polynomial systems with saturation input are given.Secondly,in the case of unknown parameters,the input and output data of the system are collected offline under the random input,and the gain of the state-feedback saturation controller is determined by the collected offline data and the sum of squares approach.Finally,the effectiveness of the proposed control strategy is verified through numerical simulation and circuit experiment in the Van der Pol oscillator system.