On the Design of Economic NMPC Based on Approximate Turnpike Properties

We discuss the design of sampled-data economic nonlinear model predictive control schemes for continuous-time systems based on turnpike properties. In a recent paper we have shown that an exact turnpike property allows establishing finite-time convergence of the NMPC scheme to the optimal steady state, and also recursive feasibility, without using terminal penalties or terminal constraints. Herein, we extend our previous results to the more general case of approximate turnpikes. We establish sufficient conditions, based on a dissipativity assumption, that guarantee (i) convergence to a neighborhood of the optimal steady state, and (ii) recursive feasibility in the presence of state constraints. The proposed conditions do not rely on terminal regions or terminal penalties. A key step in our developments is the use of a storage function as a penalty on the initial condition in the NMPC scheme. We draw upon the example of a chemical reactor to illustrate our findings

A Gauss-Newton-Like Hessian Approximation for Economic NMPC

Economic Model Predictive Control (EMPC) has recently become popular because of its ability to control constrained nonlinear systems while explicitly optimizing a prescribed performance criterion. Large performance gains have been reported for many applications and closed-loop stability has been recently investigated. However, computational performance still remains an open issue and only few contributions have proposed real-time algorithms tailored to EMPC. We perform a step towards computationally cheap algorithms for EMPC by proposing a new positive-definite Hessian approximation which does not hinder fast convergence and is suitable for being used within the real-time iteration (RTI) scheme. We provide two simulation examples to demonstrate the effectiveness of RTI-based EMPC relying on the proposed Hessian approximation

Exponential Turnpike property for fractional parabolic equations with non-zero exterior data

We consider averages convergence as the time-horizon goes to infinity of optimal solutions of time-dependent optimal control problems to optimal solutions of the corresponding stationary optimal control problems. Control problems play a key role in engineering, economics and sciences. To be more precise, in climate sciences, often times, relevant problems are formulated in long time scales, so that, the problem of possible asymptotic behaviors when the time-horizon goes to infinity becomes natural. Assuming that the controlled dynamics under consideration are stabilizable towards a stationary solution, the following natural question arises: Do time averages of optimal controls and trajectories converge to the stationary optimal controls and states as the time-horizon goes to infinity? This question is very closely related to the so-called turnpike property that shows that, often times, the optimal trajectory joining two points that are far apart, consists in, departing from the point of origin, rapidly getting close to the steady-state (the turnpike) to stay there most of the time, to quit it only very close to the final destination and time. In the present paper we deal with heat equations with non-zero exterior conditions (Dirichlet and nonlocal Robin) associated with the fractional Laplace operator $(-\Delta)^s$ ($0<s<1$). We prove the turnpike property for the nonlocal Robin optimal control problem and the exponential turnpike property for both Dirichlet and nonlocal Robin optimal control problems

Jahresbericht 2015 / Institut für Angewandte Informatik (KIT Scientific Reports ; 7714)

Im Jahresbericht 2015 des Instituts für Angewandte Informatik (IAI) werden, nach einem kurzen Überblick über die Arbeiten, die Forschungsergebnisse dieses Jahres vorgestellt. Die Einordnung erfolgt entsprechend der Zuordnung der Vorhaben zu den Helmholtz-Programmen des Großforschungsbereichs des KIT. Es schließt sich ein Verzeichnis der im Berichtszeitraum erschienenen Publikationen an