Solution of Algebraic Riccati Equation for optimal control using Non-Square estimator

The Algebraic Riccati Equation (ARE) has increasingly played its role for the optimal control theory [1], [2]. Adaptive filters have been a widely used technique in the context of real time solution for ARE [3]. The least mean square (LMS) and the recursive least square (RLS) are among the most well known filters [4], [5]. Nevertheless, these algorithms have a lower learning rate for multivariable systems. The present study proposes to solve ARE using an adaptive filter. Unlike the RLS, it uses not only one error potency, but the sum of the pair error potencies. Such algorithm will be called Recursive Least Non-Squares (RLNS) and evaluated in two multivariable systems. The first is a first-order electrical circuit, and the second is a 6^th order wind generator. The simulations show a convergence velocity for the RLNS algorithm of up to 70% faster than the RLS.