| The 9th Mediterranean Conference on Control and Automation (2001) | |||||||||||||||
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| We briefly review selected results in nonlinear and adaptive control, focusing on constructive concepts and design procedures: control Lyapunov functions, feedback passivation, robust and adaptive backstepping. For a more extensive discussion see Kokotović and Arcak (2001). 1 Control Lyapunov Functions Early nonlinear concepts have been descriptive. Their ’feedback activation ’ began only recently, when some local properties were replaced with new concepts applicable to large regions of the state space. The main effort of activation is to make new concepts dependent on, and transformable by feedback control. A prominent example is the concept of control Lyapunov function (CLF) whose derivative depends on the control and can be made negative by feedback. This seemingly obvious concept, introduced by Artstein (1983) and Sontag (1983), made a tremendous impact on stabilization theory, which, at the end of the 1970’s was stagnant. It converted stability descriptions into tools for solving stabilization tasks. One way to stabilize a nonlinear system is to select a Lyapunov function V (x) and then try to find a feedback control u(x) that renders ˙ V (x, u(x)) negative definite. With an arbitrary choice of | |||||||||||||||
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