Performance of Sensitivity based NMPC Updates in Automotive Applications

In this work we consider a half car model which is subject to unknown but measurable disturbances. To control this system, we impose a combination of model predictive control without stabilizing terminal constraints or cost to generate a nominal solution and sensitivity updates to handle the disturbances. For this approach, stability of the resulting closed loop can be guaranteed using a relaxed Lyapunov argument on the nominal system and Lipschitz conditions on the open loop change of the optimal value function and the stage costs. For the considered example, the proposed approach is realtime applicable and corresponding results show significant performance improvements of the updated solution with respect to comfort and handling properties.Comment: 6 pages, 2 figure

Model order reduction approaches for infinite horizon optimal control problems via the HJB equation

We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this report we focus on the infinite horizon optimal control problem with quadratic cost functionals. We compare several model reduction methods such as Proper Orthogonal Decomposition, Balanced Truncation and a new algebraic Riccati equation based approach. Finally, we present numerical examples and discuss several features of the different methods analyzing advantages and disadvantages of the reduction methods

Why the Realist-Instrumentalist Debate about Rational Choice Rests on a Mistake

Within the social sciences, much controversy exists about which status should be ascribed to the rationality assumption that forms the core of rational choice theories. Whilst realists argue that the rationality assumption is an empirical claim which describes real processes that cause individual action, instrumentalists maintain that it amounts to nothing more than an analytically set axiom or ‘as if’ hypothesis which helps in the generation of accurate predictions. In this paper, I argue that this realist-instrumentalist debate about rational choice theory can be overcome once it is realised that the rationality assumption is neither an empirical description nor an ‘as if’ hypothesis, but a normative claim

Grid refinement in the construction of Lyapunov functions using radial basis functions

Lyapunov functions are a main tool to determine the domain of attraction of equilibria in dynamical systems. Recently, several methods have been presented to construct a Lyapunov function for a given system. In this paper, we improve the construction method for Lyapunov functions using Radial Basis Functions. We combine this method with a new grid refinement algorithm based on Voronoi diagrams. Starting with a coarse grid and applying the refinement algorithm, we thus manage to reduce the number of data points needed to construct Lyapunov functions. Finally, we give numerical examples to illustrate our algorithms