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Convex MPC - Convex Dynamic Programming for Applications in Robust Model Predictive Control and State Estimation

From 01-01-2008 to 31-12-2011

Description

The project shall explore a large but partly unexplored class of nonlinear optimal control systems that are connected by the fact that their dynamic programming (DP) cost-to-go is convex. Of this class the classical linear quadratic regulator (LQR), a linear control law, and the linear model predictive controller (MPC), a nonlinear control law, are the two best-known examples.

Full exploitation of convexity for more general control systems in this class will lead to new and computational efficient “convex dynamic programming” methods. These can be used for exact and approximate computation of optimization based feedback controllers that are applicable not only to linear but also to special nonlinear and in particular to uncertain systems. This last fact will allow us to apply the new methods to the emerging
control technique of robust model predictive control, originally due to Witsenhausen
where a dynamic min-max game with nature as the controller’s adverse player needs to be solved, and which is computationally considerably more demanding than classical MPC.

The project shall investigate the two major questions: (a) What problem classes are covered by convex dynamic programming? and (b) How to represent and compute the convex cost-to-go efficiently? Finally, the concepts shall be transferred to the problem of state estimation, which in a Bayesian framework deals with probability densities instead of cost-to-go functions. The negative logarithm of these densities is in many cases convex, and can thus again be treated by convexity-based computational methods. The Kalman filter with its multidimensional Gaussian probability distribution is again only the simplest case of a considerably larger class of “convex filters”.

The outcome of the project will be a sound theoretical framework for the understanding of control and estimation systems based on “convex dynamic programming”, along with new and efficient open-source algorithms ready for use in practical applications.