CLF-based nonlinear control with polytopic input constraints

This paper presents a practical method for generating high-performance control laws which are guaranteed to be stabilizing in the presence of known input constraints. We address the class of smooth non-linear systems which are affine in the control with non-smooth (rectangular or polytopic) actuator constraints and a known control Lyapunov function. We present a result which uses a complete state-dependent description of the stabilizing control value set to generate, point-wise, the set of input values which contains all the (Lyapunov) stabilizing control values that simultaneously obey the input constraints. The vertex enumeration algorithm is then used to derive a complete parameterization of this set, and a nonlinear program is employed to select a high-performance control from this feasible and stabilizing control set for an illustrative example.