Lesson plan
Feedback linearization
Feedback linearization is a common strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied to nonlinear control systems of the form where x(t) \in \mathbb{R}^n is the state, u_1(t), \ldots, u_m(t) \in \mathbb{R} are the inputs. The approach involves transforming a nonlinear control system into an equivalent linear control system through a change of variables and a suitable control input. In particular, one seeks a change of coordinates z = \Phi(x) and control input u = a(x) + b(x)\,v, so that the dynamics of x(t) in the coordinates z(t) take the form of a linear, controllable control system, An outer-loop control strategy for the resulting linear control system can then be applied to achieve the control objective. Typically, feedback linearization is applied to unconstrained systems, as the required nonlinear transformations can make simple state constraints significantly more complicated in the new coordinate system.
Article summary
Feedback linearization is a common strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied to nonlinear control systems of the form where x(t) \in \mathbb{R}^n is the state, u_1(t), \ldots, u_m(t) \in \mathbb{R} are the inputs. The approach involves transforming a nonlinear control system into an equivalent linear control system through a change of variables and a suitable control input. In particular, one seeks a change of coordinates z = \Phi(x) and control input u = a(x) + b(x)\,v, so that the dynamics of x(t) in the coordinates z(t) take the form of a linear, controllable control system, An outer-loop control strategy for the resulting linear control system can then be applied to achieve the control objective. Typically, feedback linearization is applied to unconstrained systems, as the required nonlinear transformations can make simple state constraints significantly more complicated in the new coordinate system.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.