ON THE NULL-CONTROLLABILITY SET, MINIMAL TIME FUNCTION AND TIME OPTIMAL CONTROL OF FINITE DIMENSIONAL SYSTEMS

1994 ◽  
pp. 325-344
Author(s):  
SHOUCHUAN HU ◽  
V. LAKSHMIKANTHAM ◽  
NIKOLAOS S. PAPAGEORGIOU
Keyword(s):  
Optimal Control ◽  
Null Controllability ◽  
Time Function ◽  
Time Optimal Control ◽  
Minimal Time Function ◽  
Minimal Time ◽  
Finite Dimensional ◽  
Time Optimal

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.

Modified bang‐bang controller for maximal and minimal time optimal control problems

2019 ◽  
Vol 22 (5) ◽  
pp. 1827-1839
Author(s):  
Kyung‐Tae Lee ◽  
Sang‐Young Oh ◽  
Ho‐Lim Choi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Time Optimal Control ◽  
Control Problems ◽  
Minimal Time ◽  
Time Optimal

Frequency Domain Approach to Solve the Time-Optimal Control of a Distributed Parameter System

1995 ◽  
Author(s):  
Hasan Alli ◽  
Tarunraj Singh
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Time Optimal Control ◽  
Distributed Parameter ◽  
Dimensional System ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Finite Dimensional ◽  
Time Optimal ◽  
Frequency Domain Approach

Abstract In this paper, the time-optimal control of the wave equation is derived in closed form. A frequency domain approach is used to obtain the time-optimal solution which is bang-off-bang. The system studied in this paper is a uniform flexible rod with a control input at each end, whose dynamics in axial vibration is represented by the wave equation. In order to verify the optimality of the control profile derived for the distributed parameter system, the system is discretized in space and a series of time-optimal control problems are solved for the finite dimensional model, with increasing number of flexible modes. In the limit, the controllers show the convergence of the first and final switch of the bang-bang controller of the finite dimensional system to the first and final switch of the bang-off-bang controller of the distributed parameter system, in addition to the convergence of the maneuver time. The number of switches in between the first and final switch is a function of the order of the finite dimensional system. The maneuver time of the distributed parameter system is compared to that of an equivalent rigid system and the coincidence of the time-optimal controller for the flexible and rigidized systems is illustrated for certain maneuvers.

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