We show in the paper that the, so–called, “new architecture” of L1–adaptive control is, indeed, different from classical model reference adaptive control. Alas, it is not new, since it exactly coincides with a full–state feedback, linear time–invariant proportional plus integral (PI) controller with a decaying additive disturbance. Moreover, it is shown that if the PI controller does not stabil...

This paper presents the design and experimental implementation of the L1 adaptive controller on a tethered underwater vehicle. This controller, well known for its fast adaptation and its robusntess, is for the first time applied in the field of underwater vehicle control. This paper summarizes the implementation and experimental results obtained on a modified version of the AC-ROV underwater ve...

We consider the l1-regularized Markowitz model, where a l1-penalty term is added to the objective function of the classical mean-variance one to stabilize the solution process, promoting sparsity in the solution and avoiding short positions. In this paper, we consider the Bregman iteration method to solve the related constrained optimization problem. We propose an iterative algorithm based on a...

The paper presents a generalized framework for an L1 adaptive state-feedback controller with proportional adaptation gain. Using the decoupling property for estimation and control loops of the L1 adaptive controller, we show that this generalized architecture has the potential of unifying several nonlinear control methods in a single framework. In all cases, the proposed controller, similar to ...

In Part I of this paper, [1], we have developed a novel L1 adaptive control architecture that enables fast adaptation and leads to uniformly bounded transient and asymptotic tracking for system’s both signals, input and output, simultaneously. In this paper, we derive the stability margins of L1 adaptive control architecture, including time-delay and gain margins in the presence of time-varying...

This paper considers downhole directional drilling systems in the presence of unexpected variations in steering force, input delays, measurement noise and measurement delays, and explores the application of L1 adaptive controller for the trajectory control problem. The Explicit Force, Finitely Sharp, Zero Mass (EFFSZM) model is used for the steering system, in which spatial delays, modeling ina...