Exact slow-fast decomposition of a class of non-linear singularly perturbed optimal control problems via invariant manifolds

1999 ◽  
Vol 72 (17) ◽  
pp. 1609-1618 ◽  
Author(s):  
E. Fridman
Keyword(s):  
Optimal Control ◽  
Invariant Manifolds ◽  
Optimal Control Problems ◽  
Singularly Perturbed ◽  
Control Problems ◽  
Non Linear ◽  
Fast Decomposition

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.

The approximate solution of non-linear time-delay fractional optimal control problems by embedding process

2018 ◽  
Vol 36 (3) ◽  
pp. 713-727 ◽  
Author(s):  
E Ziaei ◽  
M H Farahi
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Fractional Derivative ◽  
Optimal Control Problems ◽  
Linear Time ◽  
Control Problems ◽  
Linear Dynamical Systems ◽  
Fractional Optimal Control ◽  
Non Linear ◽  
Fractional Optimal Control Problems

Abstract In this paper, a class of time-delay fractional optimal control problems (TDFOCPs) is studied. Delays may appear in state or control (or both) functions. By an embedding process and using conformable fractional derivative as a new definition of fractional derivative and integral, the class of admissible pair (state, control) is replaced by a class of positive Radon measures. The optimization problem found in measure space is then approximated by a linear programming problem (LPP). The optimal measure which is representing optimal pair is approximated by the solution of a LPP. In this paper, we have shown that the embedding method (embedding the admissible set into a subset of measures), successfully can be applied to non-linear TDFOCPs. The usefulness of the used idea in this paper is that the method is not iterative, quite straightforward and can be applied to non-linear dynamical systems.

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