Legendre-type optimality conditions for a variational problem with inequality state constraints

1999 ◽  
Vol 84 (2) ◽  
pp. 421-434 ◽  
Author(s):  
Sayuri Koga ◽  
Hidefumi Kawasaki
Keyword(s):  
Variational Problem ◽  
Optimality Conditions ◽  
State Constraints ◽  
Inequality State

Maximum Correntropy Criterion Constrained Kalman Filter

2017 ◽  
Author(s):  
Seyed Fakoorian ◽  
Mahmoud Moosavi ◽  
Reza Izanloo ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Constraints ◽  
Statistical Information ◽  
Second Order ◽  
System Model ◽  
Error Covariance ◽  
Inequality State ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

Optimality conditions for infinite horizon control problems with state constraints

2009 ◽  
Vol 71 (12) ◽  
pp. e1788-e1795 ◽  
Author(s):  
Valeriano Antunes de Oliveira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimality Conditions ◽  
State Constraints ◽  
Infinite Horizon ◽  
Control Problems ◽  
Infinite Horizon Control
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