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.

Well-Ordered and Non-Well-Ordered Lower and Upper Solutions for Periodic Planar Systems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alessandro Fonda ◽  
Giuliano Klun ◽  
Andrea Sfecci
Keyword(s):  
Differential Equations ◽  
Detailed Analysis ◽  
Topological Degree ◽  
Phase Plane ◽  
Periodic Problem ◽  
Lower And Upper Solutions ◽  
Systems Of Differential Equations ◽  
Planar Systems

Abstract The aim of this paper is to extend the theory of lower and upper solutions to the periodic problem associated with planar systems of differential equations. We generalize previously given definitions and we are able to treat both the well-ordered case and the non-well-ordered case. The proofs involve topological degree arguments, together with a detailed analysis of the solutions in the phase plane.

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.

scholarly journals Design of an optimal preview controller for linear discrete-time periodic systems

2021 ◽  
pp. 014233122110025
Author(s):  
Mengyuan Sun ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Tracking Control ◽  
Reference Signal ◽  
Periodic Systems ◽  
Augmented System ◽  
The Difference ◽  
System States ◽  
Ordinary Time ◽  
Time Periodic

In this paper, the preview tracking control problem for linear discrete-time periodic systems is considered. First, to overcome the difficulty arising from periodicity of the system, the linear discrete-time periodic system is transformed into an ordinary time-invariant system by lifting method. Secondly, the difference between a system state and its steady-state value is used to derive an augmented system instead of the usual difference between system states. Then, the preview controller for the augmented system is proposed by the preview control theory, which solves the preview tracking control problem for the periodic systems. Moreover, an integrator is introduced to ensure that the output can track the reference signal without static error. Finally, the obtained results are illustrated by the simulation examples.

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