Bounded Finite Time Control for Planar Feedback Linearizable Systems: Application to a Continuous Stirred Tank Reactor

In this work, we consider nonlinear SISO affine systems in the plane which admit complete linearization and where it is important to reach fast (in a finite time) a target point at the price of more control effort than the one demanded by a bounded asymptotic control. Departing from system equivalence to a linear controllable form and suboptimal time control for bounded linear systems, we derive a bounded finite time control which is smooth except at the target point and is an approximation to the optimal control. The resulting control has state-dependent gains. The control technique is applied to a chemical reactor where the target point is an open-loop unstable equilibrium point.