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 nonlinear 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.