(494a) Convex Optimization for Model Predictive Control

In this paper we describe how convex optimization technology can be used to improve system identification and predictive control of linear systems. In particular we demonstrate the benefits obtainable using other fitting and performance criteria than the l2-norm. In addition we demonstrate how such extended convex programs can be solved as efficiently as standard l2-norm problems. Standard solvers for convex quadratic programs and linear programs are often at least one-order of magnitude slower than customized solvers.

l1- and Huber-regression can be used for improved system identification in systems with outliers. Outliers is a common problem for automatic system identification in embedded applications such as the artificial pancreas. For such systems, Huber- and l1-regression improves parameter estimation and prediction accuracy compared to l2-regressison. In an artificial pancreas (or beta-cell), ARX models for blood glucose prediction can be identified in unsupervised learning mode for an individual type-1 diabetic without human intervention. These ARX models are based on continuous glucose measurements, insulin injections, and physical activity measurements. The blood glucose concentration can be predicted with good accuracy and is applicable in a predictive controller adjusting the insulin injections.

Model Predictive Controllers consists of a state estimator and a regulator. To have steady-state offset free control, the state estimator must have integrators. In Generalized Predictive Control (GPC) this is achieved by formulating ARX and ARMAX models in delta-variables. In state-space based MPC steady-state offset free control is achieved by augmenting the model with integrators. We demonstrate how the state estimator can efficiently be expressed as a moving horizon estimator using a Huber-regression criterion such that steady-state offset is avoided. This formulation provides state estimates with lower covariance than in GPC and state space based MPC.

The model used in predictive control is almost never accurate for real systems. Furthermore, its prediction accuracy decreases over time as the plant changes due to wear. Such systems in which the model and the plant are different may be controlled robustly using an l2-penalty function with a dead-zone rather than a pure l2-penalty function. The improved performance achievable using an l2-penalty function with a dead-zone is significant.

Finally, we describe how Schur-complement and structure exploiting techniques may be used in primal-dual interior point algorithms for solution of the above convex optimization problems.