Infinite-horizon periodic minimax control problem

1993 ◽  
Vol 79 (2) ◽  
pp. 397-404 ◽  
Author(s):  
C. Piccardi
Keyword(s):  
Control Problem ◽  
Infinite Horizon ◽  
Minimax Control

scholarly journals Intrinsic Optimal Control for Mechanical Systems on Lie Group

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Chao Liu ◽  
Shengjing Tang ◽  
Jie Guo
Keyword(s):  
Optimal Control ◽  
Analytical Solution ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Lie Group ◽  
Control Method ◽  
Geodesic Distance ◽  
Infinite Horizon ◽  
Mechanical Systems ◽  
Programming Approach

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

scholarly journals Backward StochasticH2/H∞Control: Infinite Horizon Case

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zhen Wu ◽  
Qixia Zhang
Keyword(s):  
Control Problem ◽  
Infinite Horizon ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Current State ◽  
Exogenous Disturbance ◽  
History Of ◽  
Entire History ◽  
Necessary And Sufficient ◽  
Horizon Case

The mixedH2/H∞control problem is studied for systems governed by infinite horizon backward stochastic differential equations (BSDEs) with exogenous disturbance signal. A necessary and sufficient condition for the existence of a unique solution to theH2/H∞control problem is derived. The equivalent feedback solution is also discussed. Contrary to deterministic or stochastic forward case, the feedback solution is no longer feedback of the current state; rather, it is feedback of the entire history of the state.

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