Predictor-Corrector Continuation Method for Optimal Control Problems

1998 ◽  
pp. 223-232 ◽  
Author(s):  
Ernst Grigat ◽  
Gottfried Sachs
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Continuation Method ◽  
Control Problems ◽  
Predictor Corrector

An Indirect Method for Solving Non-Linear Optimal Control Problems in Power Systems-Part 2

1974 ◽  
Vol 11 (4) ◽  
pp. 313-321 ◽  
Author(s):  
O. P. Malik ◽  
B. K. Mukhopadhyay ◽  
P. Subramaniam
Keyword(s):  
Optimal Control ◽  
Power Systems ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Continuation Method ◽  
Hybrid Approach ◽  
Control Problems ◽  
Linear Optimal Control ◽  
Non Linear ◽  
Linear Optimal Control Problems

This paper describes the application of quasilinearization algorithm and its various modifications to solve the non-linear optimal control problems in power systems. Results obtained by this indirect numerical technique are compared to those obtained by other, direct methods. It is shown that a proposed hybrid approach, in conjunction with the continuation method, can be considered as an effective iterative procedure for most practical problems in power systems.

An Indirect Method for Solving Non-Linear Optimal Control Problems in Power Systems-Part 1

1974 ◽  
Vol 11 (3) ◽  
pp. 273-282
Author(s):  
O. P. Malik ◽  
B. K. Mukhopadhyay ◽  
P. Subramaniam
Keyword(s):  
Optimal Control ◽  
Power Systems ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Continuation Method ◽  
Hybrid Approach ◽  
Control Problems ◽  
Linear Optimal Control ◽  
Non Linear ◽  
Linear Optimal Control Problems

This paper describes the application of quasilinearization algorithm and its various modifications to solve the non-linear optimal control problems in power systems. Results obtained by this indirect numerical technique are compared to those obtained by other, direct methods. It is shown that a proposed hybrid approach, in conjunction with the continuation method, can be considered as an effective iterative procedure for most practical problems in power systems.

Indirect Solution of Inequality Constrained and Singular Optimal Control Problems Via a Simple Continuation Method

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Brian C. Fabien
Keyword(s):  
Optimal Control ◽  
Original Problem ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Continuation Method ◽  
Singular Control ◽  
Inequality Constraints ◽  
Control Problems ◽  
Quadratic Loss ◽  
State Variable

This paper develops a simple continuation method for the approximate solution of optimal control problems. The class of optimal control problems considered include (i) problems with bounded controls, (ii) problems with state variable inequality constraints (SVIC), and (iii) singular control problems. The method used here is based on transforming the state variable inequality constraints into equality constraints using nonnegative slack variables. The resultant equality constraints are satisfied approximately using a quadratic loss penalty function. Similarly, singular control problems are made nonsingular using a quadratic loss penalty function based on the control. The solution of the original problem is obtained by solving the transformed problem with a sequence of penalty weights that tends to zero. The penalty weight is treated as the continuation parameter. The paper shows that the transformed problem yields necessary conditions for a minimum that can be written as a boundary value problem involving index-1 differential–algebraic equations (BVP-DAE). The BVP-DAE includes the complementarity conditions associated with the inequality constraints. It is also shown that the necessary conditions for optimality of the original problem and the transformed problem differ by a term that depends linearly on the algebraic variables in the DAE. Numerical examples are presented to illustrate the efficacy of the proposed technique.

A Simple Continuation Method for the Solution of Optimal Control Problems With State Variable Inequality Constraints

2013 ◽  
Author(s):  
Brian C. Fabien
Keyword(s):  
Optimal Control ◽  
Pure State ◽  
Original Problem ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Continuation Method ◽  
Inequality Constraints ◽  
Control Problems ◽  
State Variable ◽  
Variable Inequality

This paper develops a simple continuation method for the approximate solution of optimal control problems with pure state variable inequality constraints. The method is based on transforming the inequality constraints into equality constraints using nonnegative slack variables. The resultant equality constraints are satisfied approximately using a quadratic loss penalty function. The solution of the original problem is obtained by solving the transformed problem with a sequence of penalty weights that tends to zero. The penalty weight is treated as the continuation parameter. The necessary conditions for a minimum are written as a boundary value problem involving index-1 differential-algebraic equations (BVP-DAE). The BVP-DAE include the complementarity conditions associated with the inequality constraints. The paper shows that the necessary conditions for optimality of the original problem and the transformed problems are remarkably similar. In particular, the BVP-DAE for each problem differ by a linear term related to the Lagrange multipliers associated with the state variable inequality constraints. Numerical examples are presented to illustrate the efficacy of the proposed technique. Specifically, the paper presents results for; (1) the optimal control of a simplified model of a gantry crane system, (2) the optimal control of a rigid body moving in the vertical plane, and (3) the trajectory optimization of a planar two-link robot. All problems include pure state variable inequality constraints.

Stabilized continuation method for solving optimal control problems

1994 ◽  
Vol 17 (5) ◽  
pp. 950-957 ◽  
Author(s):  
Toshiyuki Ohtsuka ◽  
Hironori Fujii
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Continuation Method ◽  
Control Problems
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