Niyousha Rahimi

Niyousha Rahimi, Mehran Mesbahi

This paper addresses the problem of designing a data-driven feedback controller for complex nonlinear dynamical systems in the presence of time-varying disturbances with unknown dynamics. Such disturbances are modeled as the "unknown" part of the system dynamics. The goal is to achieve finite-time regulation of system states through direct policy updates while also generating informative data that can subsequently be used for data-driven stabilization or system identification. First, we expand upon the notion of "regularizability" and characterize this system characteristic for a linear time-varying representation of the nonlinear system with locally-bounded higher-order terms. "Rapid-regularizability" then gauges the extent by which a system can be regulated in finite time, in contrast to its asymptotic behavior. We then propose the Data-Guided Regulation for Adaptive Nonlinear Control ( DG-RAN) algorithm, an online iterative synthesis procedure that utilizes discrete time-series data from a single trajectory for regulating system states and identifying disturbance dynamics. The effectiveness of our approach is demonstrated on a 6-DOF power descent guidance problem in the presence of adverse environmental disturbances.

Shahriar Talebi, Siavash Alemzadeh, Niyousha Rahimi et al.

Learning, say through direct policy updates, often requires assumptions such as knowing a priori that the initial policy (gain) is stabilizing, or persistently exciting (PE) input-output data, is available. In this paper, we examine online regulation of (possibly unstable) partially unknown linear systems with no prior access to an initial stabilizing controller nor PE input-output data; we instead leverage the knowledge of the input matrix for online regulation. First, we introduce and characterize the notion of "regularizability" for linear systems that gauges the extent by which a system can be regulated in finite-time in contrast to its asymptotic behavior (commonly characterized by stabilizability/controllability). Next, having access only to the input matrix, we propose the Data-Guided Regulation (DGR) synthesis procedure that -- as its name suggests -- regulates the underlying state while also generating informative data that can subsequently be used for data-driven stabilization or system identification. We further improve the computational performance of DGR via a rank-one update and demonstrate its utility in online regulation of the X-29 aircraft.