Utilizing null controllable regions to stabilize input-constrained nonlinear systems

- An algorithm is proposed to address the problem of constructing the null controllable region (NCR) for nonlinear systems.
- The NCR is utilized to develop a constructive procedure for constrained control Lyapunov function (CCLF).
- The CCLF is embedded in a Lyapunov-based MPC formulation.
- The MPC formulation is guaranteed to be feasible and stabilizing from the entire NCR.
- Simulation results are used to illustrate the approach.

In this paper, we present a method for control of input-constrained nonlinear systems that offers guaranteed stabilization from the entire null controllable region (NCR). The controller achieves stabilization by using a constrained control Lyapunov function (CCLF) based on this NCR. Prior to online implementation, the level sets the CCLF are constructed using an iterative algorithm. The algorithm works by using an invariance principle to expand an initial quadratic Lyapunov function-based region of attraction. The level sets of this CCLF are then utilized in the control calculations, and in particular, an MPC is formulated that requires the system to go to lower level sets of the CCLF. The proposed MPC thus achieves stabilization from the entire NCR. The proposed approach is first corroborated against existing results for linear systems using two- and three-dimensional linear systems examples. Subsequently, the implementation is shown for two and three dimensional nonlinear systems.