A Genetic Algorithm Compared with a Gradient-Based Method for the Solution of an Active-Control Model Problem

Nathalie Marco (1) , Cyril Godart , Jean-Antoine Desideri , Bertrand Mantel , Jacques Périaux

1 SINUS - Numerical Simulation for the Engineering Sciences

In this study, a linear active-control model problem is employed to conduct a preliminary performance comparison between a genetic algorithm and a classical optimization method based on the evaluation of a gradient of functional. For this purpose, we consider a system modeled by the heat equation in one space dimension controled by a source term. The cost functional is a quadratic form of the distance between the final state and a prescribed function augmented of a penalty involving the control quadratically. The problem is first solved by a direct identification of the «optimal-control law» from the solution of a Riccati system. A simple genetic algorithm is implemented afterwards and compared.

Mots clés: OPTIMAL CONTROL; HEAT EQUATION; OBJECTIVE FUNCTIONAL; RICCATIEQUATION; OPTIMAL CONTROL LAW; SPECTRAL APPROXIMATION; GENETIC ALGORITHM

Domaines: Autre [cs.OH]

Nathalie Marco, Cyril Godart, Jean-Antoine Desideri, Bertrand Mantel, Jacques Périaux. A Genetic Algorithm Compared with a Gradient-Based Method for the Solution of an Active-Control Model Problem. RR-2948, INRIA. 1996. ⟨inria-00073751⟩