2011 Fiscal Year Final Research Report
On the optimal control for control systems on manifolds
| Project/Area Number |
21760334
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Control engineering
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| Research Institution | Shimane University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 非線形制御 / 最適制御 / 数値解法 / Hamilton-Jacobi-Bellman方程式 / 制御 / Lyapunov関数 |
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| Research Abstract |
This study deals with the global asymptotic stabilization problem and the optimal control problem of nonlinear control system such that the state space is diffeomorphic to a manifold. First, we have investigated a relationship between a stabilizability and a control Lyapunov function. We have shown sufficient conditions for semiconcavity of control Lyapunov functions that are solutions of the Hamilton-Jacobi-Bellman equation of nonlinear optimal regulator problem. Moreover, we have proposed the algorithms for searching the function by using a neural networks and solving the HJB equation.
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