Nonlinear control of static systems with unsupervised learning of the initial conditions

We propose an algorithm for adaptive control of nonlinear multiple-input, multiple-output (MIMO) static systems. The advantage of the proposed method lies in its easy on-line implementation and reliable performance that is due to an intelligent algorithm for handling the initial conditions. We represent the nonlinear system with a piecewise linear model-a variable matrix of first order changes (i.e. the Jacobian matrix). In order to achieve global optimality for different initial conditions, an enhanced method involving on-line learning a fuzzy rule-base for determining a set of “good” initial conditions is developed. The knowledge in the rule-base (so as to determine a “good” initial input change) is extracted by on-line analyzing the relationship between the error signal, and the controller response. The algorithm continuously evaluates this information, and updates the rule-base model by using an unsupervised learning scheme. The rule-base provides the “optimal” estimates for the Jacobian and initial control settings anytime the control algorithm starts from new initial conditions