Related papers: Perturbation theory of observable linear systems
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
In this paper, a fixed-time disturbance observerbased model predictive control algorithm is proposed for trajectory tracking of quadrotor in the presence of disturbances. First, a novel multivariable fixed-time disturbance observer is…
In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum principle when the admissible control set is compact, the…
Many robotic systems are underactuated, meaning not all degrees of freedom can be directly controlled due to lack of actuators, input constraints, or state-dependent actuation. This property, compounded by modeling uncertainties and…
In this paper, we study the use of state-of-the-art nonlinear system identification techniques for the optimal control of nonlinear systems. We show that the nonlinear systems identification problem is equivalent to estimating the…
In this paper it is showed that if a time-varying uncertain system is robustly completely detectable then there exists an estimator for this system, i.e. we can estimate asymptotically the state vector of the system. Moreover, if a…
This paper focuses on optimal mismatched disturbance rejection control for linear continuoustime uncontrollable systems. Different from previous studies, by introducing a new quadratic performance index to transform the mismatched…
This letter addresses optimal controller design for periodic linear time-varying systems under unknown-but-bounded disturbances. We introduce differential Lyapunov-type equations to describe time-varying inescapable ellipsoids and define an…
Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always…
The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The…
This paper addresses the stabilization of linear systems with multiple time-varying input delays. In scenarios where neither the exact delays information nor their bound is known, we propose a class of linear time-varying state feedback…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…
Admissible perturbations (i.e., perturbations that do not change the Mironenko reflecting function of the system) are obtained for an autonomous three-dimensional quadratic generalized Langford system with five parameters. The obtained…
This paper proposes a novel nonlinear sliding mode state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output of interest…
We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…
We consider a general linear control system and a general quadratic cost, where the state evolves continuously in time and the control is sampled, i.e., is piecewise constant over a subdivision of the time interval. This is the framework of…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
We study the minimum-time damping of a physical pendulum by means of a bounded control. In the similar problem for a linear oscillator each optimal trajectory possesses a finite number of control switchings from the maximal to the minimal…
This paper is concerned with the design of a linear control law for linear systems with stationary additive disturbances. The objective is to find a state feedback gain that minimizes a quadratic stage cost function, while observing chance…
We present a methodology for bounding the error term of an asymptotic solution to a singularly perturbed optimal control (SPOC) problem whose exact solution is known to be computationally intractable. In previous works, reduced or…