In Chap. 2, we introduced Lyapunov theory as a tool to design controllers enforcing stability of nonlinear control systems. In this chapter, we extend these ideas to nonlinear control systems with uncertain dynamics. We focus on the case where the uncertainty enters the system in a structured manner through uncertain parameters. Such a situation occurs when the structure of the vector fields are known, but certain physical attributes of the system (e.g., inertia and damping properties) under consideration are unknown. The dynamics of many relevant systems, especially those in robotics, obey such an assumption. We argue that exploiting this structure, rather than treating uncertainties as a “black box,” allows for the development of efficient learning-based approaches to control with strong guarantees of correctness. We provide an introduction to adaptive nonlinear control in Sect. 4.1, where stabilization does not necessarily require convergence of the unknown parameters to their true values. Next, we present two methods that enforce both stability and parameter convergence in Sect. 4.2 and show how convergence can be guaranteed to be exponential in Sect. 4.3. We conclude with final remarks and suggestions for further readings in Sect. 4.4.
Adaptive Control Lyapunov Functions
synth. Lectures on Computer sci.
2023-05-16
20 pages
Article/Chapter (Book)
Electronic Resource
English
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