Globally stabilizing adaptive control design for nonlinearly-parameterized systems

In this paper, a new adaptive control design is proposed for nonlinear systems that are possibly non-affine and contain nonlinearly parameterized unknowns. The proposed control is not based on certainty equivalence principle, which forms the foundation of existing and standard adaptive control designs. Instead, a biasing vector function is introduced into parameter estimate, it links the system dynamics to estimation error dynamics, and its choice leads to a new Lyapunov-based design so that affine or non-affine systems with nonlinearly parameterized unknowns can be controlled by adaptive estimation. Explicit conditions are found for achieving global asymptotic stability of the state, and the convergence condition for parameter estimation is also found. The conditions are illustrated by several examples and classes of systems. Besides global stability, the proposed adaptive control has the unique feature that it does not contains no robust control part which typically overpowers unknown dynamics, is conservative, and also interferes with parameter estimation.