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- Exploring a multi-objective approach for optimal control problems via a direct multiple shooting methodPublication . Ramadas, Gisela C. V.; Fernandes, Edite M. G. P.; Rocha, Ana Maria A. C.; Costa, M. Fernanda P.This paper explores the use of a multi-objective approach through the implementation of a numerical direct multiple shooting (MS) method to solve optimal control problems (OCP). When a direct MS method is used to solve the OCP, a set of `continuity constraints' emerges and should be satisfied together with the other algebraic mixed states and control constraints. To minimize the objective function and satisfy all the constraint conditions, the finite-dimensional optimization problem is reformulated as a multi-objective problem with three objectives to be optimized. An illustrative example is included to show that the present methodology is worth pursuing.
- On metaheuristics for solving the parameter estimation problem in dynamic systems: A comparative studyPublication . Ramadas, Gisela C. V.; Fernandes, Edite M. G. P.; Ramadas, António M. V.; Rocha, Ana Maria A. C.; Costa, M. Fernanda P.This paper presents an experimental study that aims to compare the practical performance of well-known metaheuristics for solving the parameter estimation problem in a dynamic systems context. The metaheuristics produce good quality approximations to the global solution of a finite small-dimensional nonlinear programming problem that emerges from the application of the sequential numerical direct method to the parameter estimation problem. Using statistical hypotheses testing, significant differences in the performance of the metaheuristics, in terms of the average objective function values and average CPU time, are determined. Furthermore, the best obtained solutions are graphically compared in relative terms by means of the performance profiles. The numerical comparisons with other results in the literature show that the tested metaheuristics are effective in achieving good quality solutions with a reduced computational effort.
- A Multiple Shooting Descent-based Filter Method for Optimal ControlPublication . Ramadas, Gisela C. V.; Fernandes, Edite M. G. P.; Rocha, Ana Maria A. C.; Costa, M. Fernanda P.A direct multiple shooting (MS) method is implemented to solve optimal control problems (OCP) in the Mayer form. The use of an MS method gives rise to the so-called ‘continuity conditions’ that must be satisfied together with general algebraic equality and inequality constraints. The resulting finite nonlinear optimization problem is solved by a first-order descent method based on the filter methodology. In the equivalent tri-objective problem, the descent method aims to minimize the objective function, the violation of the ‘continuity conditions’ and the violation of the algebraic constraints simultaneously. The preliminary numerical experiments carried out with a set of benchmark OCP are encouraging.