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We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the…
Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural…
We introduce a novel algorithm for the task of coherently controlling a quantum mechanical system to implement any chosen unitary dynamics. It performs faster than existing state of the art methods by one to three orders of magnitude…
In recent years, the distributed-observer-based distributed control law has shown powerful ability to arbitrarily approximate the centralized control performance. However, the traditional distributed observer requires each local observer to…
This paper proposes a new adaptation methodology to find the control inputs for a class of nonlinear systems with time-varying bounded uncertainties. The proposed method does not require any prior knowledge of the uncertainties including…
In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
This paper is concerned with model reference adaptive controller design for a class of nonlinear fractional order systems. Recent works on this topic rarely include direct methods and they are mostly based on indirect methods where the…
The problem of encoded quantum gate generation is studied in this paper. The idea is to consider a quantum system of higher dimension $n$ than the dimension $\bar n$ of the quantum gate to be synthesized. Given two orthonormal subsets…
We extend the concepts of quantum complete synchronization and phase synchronization, which are proposed firstly in [Phys. Rev. Lett, 111 103605 (2013)], to more widespread quantum generalized synchronization. The generalized…
We have previously discussed the design of a neutral atom quantum computer with an on-demand interaction [E. Hosseini Lapasar, et al., J. Phys. Soc. Jpn. 80, 114003 (2011)]. In this contribution, we propose an experimental method to…
Koopman operator-based methods enable data-driven bilinear representations of unknown nonlinear control systems. Accurate representations often demand significantly higher dimensions than the original system, making control design…
In this work, we present a Lyapunov framework for establishing stability with respect to a compact set for a nested interconnection of nonlinear dynamical systems ordered from slow to fast according to their convergence rates, where each of…
The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one…
This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr\"odinger equation with coherent control. The open system's dynamics is governed by the…
This paper presents a method to stabilize state and input constrained nonlinear systems using an offline optimization on variable triangulations of the set of admissible states. For control-affine systems, by choosing a continuous piecewise…
Quantum optimal control can play a crucial role to realize a set of universal quantum logic gates with error rates below the threshold required for fault-tolerance. Open-loop quantum optimal control relies on accurate modeling of the…
As a hybrid of techniques from open-loop and feedback control, Lyapunov control has the advantage that it is free from the measurement-induced decoherence but it includes the system's instantaneous message in the control loop. Often, the…
The methods of mathematical control theory are widely used in the modern physics, but still they are less popular in quantum science. We will discuss the aspects of control theory, which are the most useful in applications to the real…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…