UC Merced

Different challenges exist in the area of control, including but not limited to the high computational cost, model uncertainty, disturbances, nonlinearity, multi-objective optimization, constraints handling of partial differential equations, implementation, and real-time computation. In this dissertation, we focused on solving the issues of high computational cost, model uncertainty, nonlinearity, and disturbances in control design. The curse of dimensionality is a common issue for control design. Many mechanical systems with multi-degrees of freedom are underactuated by design. The dynamics of these systems live in a relatively high dimensional state space. However, many states are less controllable or observable for the high dimensional system.To keep the most controllable and observable states in the system, it is highly advantageous to develop a reduced order model. It turns out to be highly advantageous to develop a reduced order model to keep the most controllable and observable states in the system. Moreover, the curse of dimensionality also exists in the computation of neural networks solutions. The high computational cost is a severe issue in solving the neural network solutions in optimal control. In this dissertation, we adopted the balanced truncation and empirical balanced truncation to reduce the order of the dynamics systems. Moreover, the radial basis function neural networks (RBFNN) are adopted to solve the Hamilton-Jacobi-Bellman (HJB) equation in optimal control. The high-speed train bogie and the Quanser Qube2 system are adopted as practical applications to test the performance of the reduced order model-based control design. Especially for the Qube2 system, extensive numerical simulations and experimental validations show that the RBFNN with a reduced order model save the computational power and improve the optimal controller's robustness. Furthermore, transfer learning is adopted to improve the performance of the radial basis function based HJB solutions with limited experimental data. Except for reducing the dimension of the system, a new neural networks structure - separable Gaussian neural networks is proposed to reduce the computation cost by making use of the factorizable property of the Gaussian activation functions in RBFNN. Numerical simulation results show that the separable gaussian functions reduce the computation cost and the required parameters in neural networks to solve the partial differential equations.

Model uncertainty and disturbances also play an important role in control design. The Luenberger, extended state observers and neural networks are adopted to estimate the unmeasurable system states and approximate unmodelled system dynamics. The minimum number of sensors to estimate the unknown dynamics are investigated with the help of the special structure of the extended state observer. With the unknown dynamics estimated, the recursive least squares algorithm is adopted to identify the parameters in the unknown dynamics if the persistent excitation condition is satisfied. Numerical examples show that the extended state observer performs well in estimating the unknown dynamics with a limited number of sensors. Except for using the observers, neural networks are also adopted to approximate the unknown dynamics of the system. Here, we adopted the Delta robot as an engineering application to illustrate the performance of a neural networks model with sliding mode control. By leveraging the machine learning techniques, the model uncertainty issue can be well-solved during the control design.