Adaptive control of nonlinearly parameterized systems

Studies adaptive control of nonlinearly parameterized systems with uncontrollable linearization. Using a parameter separation technique and the tool of adding a power integrator, we develop a feedback domination design approach for the explicit construction of a C^∞ adaptive controller which solves the longstanding open problem of global adaptive regulation. A significant feature of our adaptive regulator is its minimal-order property, namely, no matter how big the number of unknown parameters is, the order of the dynamic compensator is identical to one, and is therefore minimal. As an important consequence, global state regulation of feedback linearizable systems with nonlinear parameterization is solved by one-dimensional adaptive controllers, without imposing any convex or concave condition on the parameters