scholarly journals On stability zones for discrete-time periodic linear Hamiltonian systems

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Vladimir Răsvan
Keyword(s):  
Hamiltonian Systems ◽  
Discrete Time ◽  
Periodic Linear ◽  
Linear Hamiltonian Systems ◽  
Time Periodic

DISCRETE PROCEDURE OF OPTIMAL STABILIZATION FOR PERIODIC LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

2018 ◽  
pp. 891-906
Author(s):  
Roman Ivanovich Shevchenko ◽  
Yuri Filippovich Dolgii
Keyword(s):  
Differential Equations ◽  
Discrete Time ◽  
Periodic Problem ◽  
Optimal Stabilization ◽  
Systems Of Differential Equations ◽  
Special Procedure ◽  
Periodic Linear ◽  
System States ◽  
Linear Periodic Systems ◽  
Time Periodic

We propose procedure to solve the optimal stabilization problem for linear periodic systems of differential equations. Stabilizing controls, formed as a feedback, are defined by the system states at the fixed instants of time. Equivalent discrete-time linear periodic problem of optimal stabilization is considered. We propose a special procedure for the solution of discrete periodic Riccati equation. We investigate the relation between continuous-time and discrete-time periodic optimal stabilization problems. The proposed method is used for stabilization of mechanical systems.

scholarly journals On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Nina Xue ◽  
Wencai Zhao
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Linear Hamiltonian System ◽  
Constant Matrix ◽  
Change Of Variables ◽  
Periodic Linear ◽  
Multiple Eigenvalues ◽  
Linear Hamiltonian Systems ◽  
Constant Coefficients ◽  
Exponentially Small

In this paper, we consider the effective reducibility of the quasi-periodic linear Hamiltonian system x˙=A+εQt,εx, ε∈0,ε0, where A is a constant matrix with possible multiple eigenvalues and Q(t,ε) is analytic quasi-periodic with respect to t. Under nonresonant conditions, it is proved that this system can be reduced to y˙=A⁎ε+εR⁎t,εy, ε∈0,ε⁎, where R⁎ is exponentially small in ε, and the change of variables that perform such a reduction is also quasi-periodic with the same basic frequencies as Q.

Ornithopter Trajectory Generation With Stabilization

2008 ◽  
Author(s):  
John M. Dietl ◽  
Ephrahim Garcia
Keyword(s):  
Feedback Control ◽  
Discrete Time ◽  
Trajectory Generation ◽  
Flight Dynamics ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Flight Stabilization ◽  
Rate Feedback ◽  
Periodic Linear ◽  
Time Periodic

Ornithopter flight dynamics and a method for developing flight trajectories are described. These are used to study the unstable modes in hovering ornithopter flight. Stabilization is accomplished through three strategies: pitch-rate feedback control, linear quadratic regulator, and discrete-time periodic linear quadratic regulator. The discrete time controller is the only controller tested that was capable of stabilizing position of the vehicle in hover.

Parallel Algorithms for LQ Optimal Control of Discrete-Time Periodic Linear Systems

2002 ◽  
Vol 62 (2) ◽  
pp. 306-325 ◽  
Author(s):  
Peter Benner ◽  
Ralph Byers ◽  
Rafael Mayo ◽  
Enrique S Quintana-Ortı́ ◽  
Vicente Hernández
Keyword(s):  
Optimal Control ◽  
Parallel Algorithms ◽  
Linear Systems ◽  
Discrete Time ◽  
Periodic Linear ◽  
Lq Optimal Control ◽  
Time Periodic
Sign in / Sign up

Export Citation Format

Share Document