Passive adaptive control of non‐linear systems

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Abstract
We develop a new recursive procedure for the design of adaptive controllers for non‐linear systems with unknown parameters and unmeasured states. The use of novel nonlinear damping terms endows the closed‐loop systems with the remarkable property of boundedness for arbitrary parametric uncertainty even when the adaptation is switched off. The combination of these nonlinear terms with interlacing functions produces ‘damped interlacing’, which results in new passivity and transient performance properties. Damped interlacing allows us to construct a full Lyapunov function that encompasses all the variables of the adaptive system.