scholarly journals Mean-Field Leader-Follower Games with Terminal State Constraint

2020 ◽  
Vol 58 (4) ◽  
pp. 2078-2113 ◽  
Author(s):  
Guanxing Fu ◽  
Ulrich Horst
Keyword(s):  
Mean Field ◽  
State Constraint ◽  
Terminal State ◽  
Terminal State Constraint

Robust Control with a Terminal State Constraint

1995 ◽  
Vol 28 (8) ◽  
pp. 373-376
Author(s):  
A.V. Savkin ◽  
I.R. Petersen
Keyword(s):  
Robust Control ◽  
State Constraint ◽  
Terminal State ◽  
Terminal State Constraint

Robust control with a terminal state constraint

Automatica ◽  
1996 ◽  
Vol 32 (7) ◽  
pp. 1001-1005 ◽  
Author(s):  
Andrey V. Savkin ◽  
Ian R. Petersen
Keyword(s):  
Robust Control ◽  
State Constraint ◽  
Terminal State ◽  
Terminal State Constraint

scholarly journals Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Yuefen Chen ◽  
Minghai Yang
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
State Constraint ◽  
Terminal State ◽  
Necessary Condition ◽  
Lagrangian Multiplier ◽  
Lq Optimal Control ◽  
System States ◽  
Lq Problem ◽  
Terminal State Constraint

Uncertainty theory is a branch of mathematics for modeling human uncertainty based on the normality, duality, subadditivity, and product axioms. This paper studies a discrete-time LQ optimal control with terminal state constraint, whereas the weighting matrices in the cost function are indefinite and the system states are disturbed by uncertain noises. We first transform the uncertain LQ problem into an equivalent deterministic LQ problem. Then, the main result given in this paper is the necessary condition for the constrained indefinite LQ optimal control problem by means of the Lagrangian multiplier method. Moreover, in order to guarantee the well-posedness of the indefinite LQ problem and the existence of an optimal control, a sufficient condition is presented in the paper. Finally, a numerical example is presented at the end of the paper.

scholarly journals Continuity of the value function for deterministic optimal impulse control with terminal state constraint

2021 ◽  
Author(s):  
Yue Zhou ◽  
Xinwei Feng ◽  
Jiongmin Yong
Keyword(s):  
Viscosity Solution ◽  
Impulse Control ◽  
Value Function ◽  
State Constraint ◽  
Terminal State ◽  
Dynamic Programming Principle ◽  
Hamilton Jacobi Bellman ◽  
Optimal Impulse ◽  
The Value Function ◽  
Terminal State Constraint

Deterministic optimal impulse control problem with terminal state constraint is considered. Due to the appearance of the terminal state constraint, the value function might be discontinuous in general. The main contribution of this paper is the introduction of an intrinsic condition under which the value function is proved to be continuous. Then by a Bellman dynamic programming principle, the corresponding Hamilton-Jacobi-Bellman type quasi-variational inequality (QVI, for short) is derived. The value function is proved to be a viscosity solution to such a QVI. The issue of whether the value function is characterized as the unique viscosity solution to this QVI is carefully addressed and the answer is left open challengingly.

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