Deep Model Reference Adaptive Control

We present a new neuroadaptive architecture: Deep Neural Network based Model Reference Adaptive Control (DMRAC). Our architecture utilizes the power of deep neural network representations for modeling significant nonlinearities while marrying it with the boundedness guarantees that characterize MRAC based controllers. We demonstrate through simulations and analysis that DMRAC can subsume previously studied learning based MRAC methods, such as concurrent learning and GP-MRAC. This makes DMRAC a highly powerful architecture for high-performance control of nonlinear systems with long-term learning properties.Comment: Accepted in IEEE CDC-201

RKHS Embedding for Estimating Nonlinear Piezoelectric Systems

Nonlinearities in piezoelectric systems can arise from internal factors such as nonlinear constitutive laws or external factors like realizations of boundary conditions. It can be difficult or even impossible to derive detailed models from the first principles of all the sources of nonlinearity in a system. As a specific example, in traditional modeling techniques that use electric enthalpy density with higher-order terms, it can be problematic to choose which polynomial nonlinearities are essential. This paper introduces adaptive estimator techniques to estimate the nonlinearities that can arise in certain piezoelectric systems. Here an underlying assumption is that the nonlinearities can be modeled as functions in a reproducing kernel Hilbert space (RKHS). Unlike traditional modeling approaches, the approach discussed in this paper allows the development of models without knowledge of the precise form or structure of the nonlinearity. This approach can be viewed as a data-driven method to approximate the unknown nonlinear system. This paper introduces the theory behind the adaptive estimator and studies the effectiveness of this approach numerically for a class of nonlinear piezoelectric composite beams.Comment: 20 pages, 15 figures, 2 tables, 1 algorith