70 research outputs found
Using nonlinear model predictive control for dynamic decision problems in economics
Gruene L, Semmler W, Stieler M. Using nonlinear model predictive control for dynamic decision problems in economics. Journal of Economic Dynamics and Control. 2015;60:112-133.This paper presents a new approach to solve dynamic decision models in economics. The proposed procedure, called Nonlinear Model Predictive Control (NMPC), relies on the iterative solution of optimal control problems on finite time horizons and is well established in engineering applications for stabilization and tracking problems. Only quite recently, extensions to more general optimal control problems including those appearing in economic applications have been investigated. Like Dynamic Programming (DP), NMPC does not rely on linearization techniques but uses the full nonlinear model and in this sense provides a global solution to the problem. However, unlike DP, NMPC only computes one optimal trajectory at a time, thus avoids to grid the state space and for this reason the computational demand grows much more moderately with the space dimension than for DP. In this paper we explain the basic idea of NMPC, give a proof concerning the accuracy of NMPC for discounted optimal control problems, present implementational details, and demonstrate the ability of NMPC to solve dynamic decision problems in economics by solving low and high dimensional examples, including models with multiple equilibria, tracking and stochastic problems. (C) 2015 Elsevier B.V. All rights reserved
NMPC in Active Subspaces: Dimensionality Reduction with Recursive Feasibility Guarantees
Dimensionality reduction of decision variables is a practical and classic
method to reduce the computational burden in linear and Nonlinear Model
Predictive Control (NMPC). Available results range from early move-blocking
ideas to singular-value decomposition. For schemes more complex than
move-blocking it is seemingly not straightforward to guarantee recursive
feasibility of the receding-horizon optimization. Decomposing the space of
decision variables related to the inputs into active and inactive complements,
this paper proposes a general framework for effective feasibility-preserving
dimensionality reduction in NMPC. We show how -- independently of the actual
choice of the subspaces -- recursive feasibility can be established. Moreover,
we propose the use of global sensitivity analysis to construct the active
subspace in data-driven fashion based on user-defined criteria. Numerical
examples illustrate the efficacy of the proposed scheme. Specifically, for a
chemical reactor we obtain a significant reduction by factor at a
closed-loop performance decay of less than .Comment: 10 page
On the Design of Economic NMPC Based on an Exact Turnpike Property
We discuss the design of sampled-data economic nonlinear model predictive control schemes for continuous-time systems. We present novel sufficient convergence conditions that do not require any kind of terminal constraints nor terminal penalties. Instead, the proposed convergence conditions are based on an exact turnpike property of the underlying optimal control problem. We prove that, in the presence of state constraints, the existence of an exact turnpike implies recursive feasibility of the optimization. We draw upon the example of optimal fish harvest 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
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
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