scholarly journals A Study on Numerical Solutions of Hamilton-Jacobi-Bellman Equations Based on Successive Approximation Approach

2020 ◽  
Vol 13 (3) ◽  
pp. 157-163
Author(s):  
Ichiro MARUTA ◽  
Shuhei NISHIDA ◽  
Kenji FUJIMOTO
Keyword(s):  
Successive Approximation ◽  
Numerical Solutions ◽  
Approximation Approach ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Successive Approximation Approach

A Method for Numerical Solutions to Problems with Pipes under Unknown Forces and Constraint Conditions

2009 ◽  
Vol 419-420 ◽  
pp. 841-844
Author(s):  
Dong Yan Shi ◽  
Ku Ang Xia ◽  
Hua Chun Lin
Keyword(s):  
High Temperature ◽  
Successive Approximation ◽  
Numerical Solutions ◽  
Fluid Pressure ◽  
Constraint Condition ◽  
Approximation Approach ◽  
Evaluation Scheme ◽  
Successive Approximation Approach ◽  
The Relationship

For the solutions to engineering equipment with pipes, unknown forces and unclear constraint conditions on the pipes result in the analysis limitation due to the high temperature and fluid pressure to pipes. In this paper, a new method for determining the loads is established to problems with many pipes. In the method, based on the combination of FEM and Successive Approximation Approach, pipes forces on the equipment are analyzed. By the analysis of suitable forces, the relationship between forces and stress can be obtained. The cycling process of “loading-solving-determining-adjusting” is carried out to approaching destinations based on hundreds of numerical results. Moreover, an evaluation scheme is built to evaluate groups of forces and guarantee equipment to work normally under some certain forces. The constraint condition from groups of forces can be also confirmed. A case study gave the verification of the method.

A Successive Approximation Approach of Nonlinear Optimal Control with R-Rank Persistent Disturbances

2011 ◽  
Vol 130-134 ◽  
pp. 1862-1866
Author(s):  
Shi Yong Ma
Keyword(s):  
Optimal Control ◽  
Successive Approximation ◽  
Nonlinear Optimal Control ◽  
Suboptimal Control ◽  
Control Law ◽  
Approximation Approach ◽  
Nonlinear Compensation ◽  
Successive Approximation Approach ◽  
Feedback Optimal Control ◽  
Persistent Disturbances

A new feedforward and feedback optimal control law for a class of nonlinear systems with persistent disturbances is presented in this paper. By using a successive approximation approach (SAA), the original nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of analytical linear feedforward and feedback terms and a nonlinear compensation term which is the limit of the solution sequence for the adjoint vector differential equations. By using the finite-step iteration of nonlinear compensation sequence, we can obtain a feedforward and feedback suboptimal control law. A disturbance observer is designed to get a physically realizable controller. Simulation examples show the effectiveness of the approach.

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