UC Merced

Data-driven techniques are growing at an unprecedented pace due to the recent super-fast computational tools and resources and the availability of big data by sensors. In the field of dynamics and control, many researchers are investigating algorithms to learn from data to model systems, estimate physical parameters, and design controllers, especially for complex dynamical systems. However, many of these researches are still limited to simulations due to the unavoidable noise in practical cases and the limitations in data acquisition. Some techniques lack any physical meaning and it makes it hard to analyze the effect of parameters in the system's performance. Low performance to predict the system response for unseen data is another issue that researchers are dealing with. Therefore, it is of great potential to develop intelligent and robust data-driven algorithms to model and estimate parameters of the system, where the reliable model can be used for the model-based control design.

We propose a nonparametric system identification technique to discover the governing equation of nonlinear dynamic systems with a focus on practical aspects. The algorithm builds on Brunton’s work in 2016 and combines sparse regression with algebraic calculus to estimate the required derivatives of the measurements. This reduces the required derivative data for system identification. Furthermore, we make use of the concepts of K-fold cross-validation from machine learning and information criteria for model selection. This allows the system identification with fewer measurements than the typically required data for the sparse regression. The result is an optimal model for the underlining system of the data with a minimum number of terms. The proposed system identification method is applicable for multiple-input–multiple-output systems. Two examples are presented to demonstrate the proposed method. The first one makes use of the simulated data of a nonlinear oscillator to show the effectiveness and accuracy of the proposed method. The second example is a nonlinear rotary flexible beam. Experimental responses of the beam are used to identify the underlining model. The Coulomb friction in the servo motor together with other nonlinear terms of the system variables are found to be important components of the model. These are, otherwise, not available in the theoretical linear model of the system.

We also extend the sparse optimization algorithm to nonlinear systems with time delay. We further integrate the bootstrapping resampling technique with the sparse regression to obtain the statistical properties of estimation. We use Taylor expansion to parameterize time delay. The proposed algorithm in this paper is computationally efficient and robust to noise. A nonlinear Duffing oscillator is simulated to demonstrate the efficiency and accuracy of the proposed technique. An experimental example of a nonlinear rotary flexible joint is presented to further validate the proposed method.

Finally, we examine the efficiency of our identified model to design model\_based controllers. First, we propose a robust flat output-based sliding mode control for trajectory tracking and to deal with the under-actuated degree of freedom. Moreover, we investigate the optimal control design. Optimal control design needs the solution of the Hamilton-Jacobi-Bellman equation, where the nonlinearities in the model make the solution challenging or even infeasible. We propose an efficient algorithm to estimate a neural network solution to gain the feedback control law. We examine the efficiency of our algorithm through several popular examples in the optimal control community and more importantly our identified nonlinear model of rotary flexible manipulator link.