Nonlinear Output-Feedback Model Predictive Control with Moving Horizon Estimation: Illustrative Examples

We review a recently introduced method to efficiently solve online optimization problems that appear in output-feedback model predictive control (MPC) and moving-horizon state estimation (MHE). The novel feature of this approach is that it solves both the MPC and MHE problems simultaneously as a single min-max optimization. Like in the more common state-feedback MPC, this approach allows one to incorporate explicit constraints on the control input and state. In addition, it allows one to incorporate any known constraints on disturbances and noise. Under appropriate assumptions that ensure controllability and observability of the nonlinear process to be controlled, we give results showing that the state of the system remains bounded and establish bounds on the tracking error for trajectory tracking problems. The min-max optimization that arises in our approach can be solved using a primal-dual-like interiorpoint method, developed especially for this purpose. Under appropriate convexity assumptions, this method is guaranteed to terminate at a global solution. However, simulation results show that it also converges rapidly in many problems that are severely nonconvex. This report includes a few representative examples that demonstrate the applicability of the approach in systems that are high-dimensional, nonlinear in their dynamics and/or measurements, and that have significant dynamic uncertainty. For all these examples, the interior-point method solver takes on average less than 6 ms to compute the control signal on a regular laptop computer.