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This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…
We present a monotonic numerical algorithm including time optimization for generating quantum gates for open systems. Such systems are assumed to be governed by Lindblad master equations for the density operators on a large Hilbert-space…
Mathematical problems of optimal control in quantum systems attract high interest in connection with fundamental questions and existing and prospective applications. An important problem is the development of methods for constructing…
We propose a two-phase systematical framework for approximation algorithm design and analysis via Lyapunov function. The first phase consists of using Lyapunov function as an input and outputs a continuous-time approximation algorithm with…
We introduce a quantum algorithm integrating counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to tackle combinatorial optimization problems. This approach offers versatility, allowing implementation as either a…
We derive a feedback control law for the control of the downstream flow in a 1-D open channel by manipulating the water flow at an upstream location. We use backstepping for controller design and Lyapunov techniques for stability analysis.…
This paper delves into the challenges posed by the increasing complexity of modern control systems, specifically focusing on bilinear systems, a prevalent subclass of non-linear systems characterized by state dynamics influenced by the…
In this paper, we consider the tracking control problem for robot manipulators which are affected by constant bounded disturbances. Three control schemes are applied for the problem, which composed of integral action and tracking…
By computing Lyapunov functions of a certain, convenient structure, Lyapunov-based methods guarantee stability properties of the system or, when performing synthesis, of the relevant closed-loop or error dynamics. In doing so, they provide…
For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system…
Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this…
Robust performance of control schemes for open quantum systems is investigated under classical uncertainties in the generators of the dynamics and nonclassical uncertainties due to decoherence and initial state preparation errors. A…
This article presents a robust control strategy using Time-Optimal Model Predictive Control (TOMPC) for a two-level quantum system subject to bounded uncertainties. In this method, the control field is optimized over a finite horizon using…
In this work, we introduce a novel data-driven model-reference control design approach for unknown linear systems with fully measurable state. The proposed control action is composed by a static feedback term and a reference tracking block,…
We propose nearly-optimal control strategies for changing states of a quantum system. We argue that quantum control optimization can be studied analytically within some protocol families that depend on a small set of parameters for…
Deep learning methods have demonstrated significant potential for addressing complex nonlinear control problems. For real-world safety-critical tasks, however, it is crucial to provide formal stability guarantees for the designed…
The Feedback-based Algorithm for Quantum Optimization (FALQON) is a Lyapunov inspired quantum algorithm proposed to tackle combinatorial optimization problems. In this paper, we examine the robustness of FALQON against coherent control…
In traditional adaptive control, the certainty equivalence principle suggests a two-step design scheme. A controller is first designed for the ideal situation assuming the uncertain parameter was known and it renders a Lyapunov function.…
A mathematical model of oscillatory systems control with liquid dampers is considered which differs from the classical ones by replacing the first derivative of such a fractional derivative that is between numbers 0 and 2 other than unity.…
We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to…