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We consider the control of nonlinear systems having imprecise models. Model imprecision may come from actual uncertainty about the plant (e.g., unknown plant parameters), or from the purposeful choice of a simplified representation of the system's dynamics (e.g., modeling friction as linear, or neglecting structural modes in a reasonably rigid mechanical system). From a control point of view, modeling inaccuracies can be classified into two major kinds:

• structured (or parametric) uncertainties
• unstructured uncertainties (or unmodeled dynamics)

The first kind corresponds to inaccuracies on the terms actually included in the model, while the second kind corresponds to inaccuracies on (i.e., underestimation of) the system order.

Modeling inaccuracies can have strong adverse effects on nonlinear control systems. Therefore, any practical design must address them explicitly. Two major and complementary approaches to dealing with model uncertainty are robust control and adaptive control. The typical structure of a robust controller is composed of a nominal part, similar to a feedback linearizing or inverse control law, and of additional terms aimed at dealing with model uncertainty.

A simple approach to robust control is the so-called sliding control methodology. Intuitively, it is based on the remark that it is much easier to control lst-order systems (i.e., systems described by lst-order differential equations), be they nonlinear or uncertain, than it is to control general n-th-order systems (i.e., systems described by n-th-order differential equations). Accordingly, a notational simplification is introduced, which, in effect, allows nth-order problems to be replaced by equivalent lst-order problems. It is then easy to show that, for the transformed problems, "perfect" performance can in principle be achieved in the presence of arbitrary parameter inaccuracies. Such performance, however, is obtained at the price of extremely high control activity. This is typically at odds with the other source of modeling uncertainty, namely the presence of neglected dynamics, which the high control activity may excite. This leads us to a modification of the control laws which, given the admissible control activity, is aimed at achieving an effective trade-off between tracking performance and parametric uncertainty. Furthermore, in some specific applications, particularly those involving the control of electric motors, the unmodified control laws can be used directly.

For the class of systems to which it applies, sliding controller design provides a systematic approach to the problem of maintaining stability and consistent performance in the face of modeling imprecisions. Furthermore, by allowing the trade-offs between modeling and performance to be quantified in a simple fashion, it can illuminate the whole design process. Sliding control has been successfully applied to robot manipulators, underwater vehicles, automotive transmissions and engines, high-performance electric motors, and power systems.

-- from Slotine, Jean-Jacques E., and Weiping Li. Applied nonlinear control. Vol. 199. No. 1. Englewood Cliffs, NJ: Prentice hall, 1991.

The tutorial slides are available in this repository: https://github.com/SMARTlab-Purdue/robust-control-tutorial/blob/master/robustControl_nonlinearSystems_tmina.pdf