Optimal control by weighted least squares generalized support vector machines

We introduced the use of weighted least squares generalized support vector machines (SVMs) for the optimal control of nonlinear systems. The problem is formulated in such a way that it incorporates the N-stage optimal control problem as well as a generalized support vector machine approach for mapping the state space into the action space. The solution is characterized by a set of nonlinear equations. Weighted least squares generalized SVMs are generalized SVMs version which kernel may not satisfy Mercer´s condition. In the weighted least squares generalized SVMs formulations one works with equality instead of inequality constraints and a least squares cost function. The using of the least squares cost function without regularization makes the solutions of least squares generalized SVMs less robust. The weighted least squares generalized SVMs overcome this drawback. Numerical simulation demonstrates the validity of this methodology.