Time-Optimal Output Transition for Minimum-Phase Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Jennifer Haggerty ◽  
Tarunraj Singh
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Control Problem ◽  
Minimum Phase ◽  
Transition Control ◽  
Optimal Output ◽  
Time Optimal ◽  
Phase Systems ◽  
Poles And Zeros ◽  
Double Integrator

The time-optimal output transition control problem for stable or marginally stable systems with minimum-phase zeros is discussed in this paper. A double integrator system with a real left-half plane zero is used to illustrate the development of the time-optimal output transition controller. It is shown that an exponentially decaying postactuation control profile is necessary to maintain the output at the desired final location. It is shown that the resulting solution to the output transition time-optimal control profile can be generated by a time-delay filter whose zeros and poles cancels the poles and zeros of the system to be controlled. The design of the time-optimal output transition problem is generalized and illustrated on the benchmark floating oscillator problem.

Solution of Finite-Time LQP Optimal Control Problems for Discrete-Time Systems

1982 ◽  
Vol 104 (2) ◽  
pp. 151-157 ◽  
Author(s):  
M. J. Grimble ◽  
J. Fotakis
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Time ◽  
Time Optimal Control ◽  
Infinite Time ◽  
Time Problem ◽  
Z Domain ◽  
Time Optimal ◽  
Time Optimal Control Problem

The deterministic discrete-time optimal control problem for a finite optimization interval is considered. A solution is obtained in the z-domain by embedding the problem within a equivalent infinite time problem. The optimal controller is time-invariant and may be easily implemented. The controller is related to the solution of the usual infinite time optimal control problem due to Wiener. This new controller should be of value in self-tuning control laws where a finite interval controller is particularly important.

scholarly journals Near Optimality of Linear Delayed Doubly Stochastic Control Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jie Xu ◽  
Ruiqiang Lin
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Control Problem ◽  
Delay System ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
The Maximum Principle ◽  
Doubly Stochastic ◽  
Convex Control ◽  
Near Optimality

In this paper, we study a kind of near optimal control problem which is described by linear quadratic doubly stochastic differential equations with time delay. We consider the near optimality for the linear delayed doubly stochastic system with convex control domain. We discuss the case that all the time delay variables are different. We give the maximum principle of near optimal control for this kind of time delay system. The necessary condition for the control to be near optimal control is deduced by Ekeland’s variational principle and some estimates on the state and the adjoint processes corresponding to the system.

scholarly journals A minimal time optimal control for a drone landing problem

2021 ◽  
Author(s):  
Filippo Gazzola ◽  
Elsa Maria Marchini
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Aerospace Engineering ◽  
Time Optimal Control ◽  
Height Velocity ◽  
The Moon ◽  
Piecewise Constant ◽  
Time Optimal

We study a variant of the classical safe landing optimal control problem in aerospace engineering, introduced by Miele in 1962, where the target was to land a spacecraft on the moon by minimizing the consumption of fuel. A more modern model consists in replacing the spacecraft by a hybrid gas-electric drone. Assuming that the drone has a failure and that the thrust (representing the control) can act in both vertical directions, the new target is to land safely by minimizing time, no matter of what the consumption is. In dependence of the initial data (height, velocity, and fuel), we prove that the optimal control can be of four different kinds, all being piecewise constant. Our analysis covers all possible situations, including the nonexistence of a safe landing strategy due to the lack of fuel or for heights/velocities for which also a total braking is insufficient to stop the drone.

scholarly journals The Time-Optimal Control Problem of a Kind of Petrowsky System

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 311
Author(s):  
Dongsheng Luo ◽  
Wei Wei ◽  
Hongyong Deng ◽  
Yumei Liao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Null Controllability ◽  
Time Optimal Control ◽  
Necessary Condition ◽  
Vibration System ◽  
Time Optimal ◽  
Time Optimal Control Problem

In this paper, we consider the time-optimal control problem about a kind of Petrowsky system and its bang-bang property. To solve this problem, we first construct another control problem, whose null controllability is equivalent to the controllability of the time-optimal control problem of the Petrowsky system, and give the necessary condition for the null controllability. Then we show the existence of time-optimal control of the Petrowsky system through minimum sequences, for the null controllability of the constructed control problem is equivalent to the controllability of the time-optimal control of the Petrowsky system. At last, with the null controllability, we obtain the bang-bang property of the time-optimal control of the Petrowsky system by contradiction, moreover, we know the time-optimal control acts on one subset of the boundary of the vibration system.

scholarly journals A time optimal control problem for the collision-free robot motion planning

PAMM ◽  
2011 ◽  
Vol 11 (1) ◽  
pp. 725-726
Author(s):  
Chantal Landry ◽  
Matthias Gerdts ◽  
René Henrion ◽  
Dietmar Hömberg
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Motion Planning ◽  
Control Problem ◽  
Time Optimal Control ◽  
Robot Motion ◽  
Robot Motion Planning ◽  
Time Optimal ◽  
Time Optimal Control Problem
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