On generalized terminal state constraints for model predictive control

This manuscript contains technical results related to a particular approach for the design of Model Predictive Control (MPC) laws. The approach, named "generalized" terminal state constraint, induces the recursive feasibility of the underlying optimization problem and recursive satisfaction of state and input constraints, and it can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to existing approaches, given the same computational complexity. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by three examples.Comment: Part of the material in this manuscript is contained in a paper accepted for publication on Automatica and it is subject to Elsevier copyright. The copy of record is available on http://www.sciencedirect.com

Implementation of an economic MPC with robustly optimal steady-state behavior

Designing an economic model predictive control (EMPC) algorithm that asymptotically achieves the optimal performance in presence of plant-model mismatch is still an open problem. Starting from previous work, we elaborate an EMPC algorithm using the offset-free formulation from tracking MPC algorithms in combination with modifier-adaptation technique from the real-time optimization (RTO) field. The augmented state used for offset-free design is estimated using a Moving Horizon Estimator formulation, and we also propose a method to estimate the required plant steady-state gradients using a subspace identification algorithm. Then, we show how the proposed formulation behaves on a simple illustrative example

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

Economic receding horizon control without terminal constraints

International audienceWe consider a receding horizon control scheme without terminal constraints in which the stage cost is de ned by economic criteria, i.e., not necessarily linked to a stabilization or tracking problem. We analyze the performance of the resulting receding horizon controller with a particular focus on the case of optimal steady states for the corresponding averaged in nite horizon problem. Using a turnpike property and suitable controllability properties we prove near optimal performance of the controller and convergence of the closed loop solution to a neighborhood of the optimal steady state. Several examples illustrate our ndings numerically and show how to verify the imposed assumptions

Model Predictive Control of a Nonlinear Aeroelastic System Using Volterra Series Representations

The purpose of this study is to investigate the potential effectiveness of using a Volterra-based Model Predictive Control strategy to control a nonlinear aeroelastic system. Model Predictive Control (MPC), also known as Receding Horizon Control (RHC), entails computing optimal control inputs over a finite time horizon, applying a portion of the computed optimal control sequence, and then repeating the process over the next time horizon. The Volterra series provides input-output models of a dynamical system in terms of a series of integral operators of increasing order, where the first-order Volterra operator models the linear dynamics and the higher-order operators model the nonlinear dynamics. In this thesis, Volterra-based Model Predictive Control is applied to simulated linear and nonlinear pitch-plunge aeroelastic systems. A linear MPC controller based on a first-order Volterra model is used to control the linear aeroelastic system, and the results are compared to those obtained using a standard LQR controller and a LQR-based MPC strategy. The controller is implemented for regulator and tracking cases for a free-stream velocity of 6 m/s, a condition for which the open-loop linear system is stable, and a free-stream velocity of 12.5 m/s, which corresponds to an unstable flutter condition. Nonlinear MPC controllers, using second- and third-order Volterra models, are then used to control the nonlinear aeroelastic system for regulator and tracking cases at the stable flight condition. The stability and performance of the linear and nonlinear Volterra-based MPC strategies are discussed, and a detailed analysis of the effect of different parameters such as the optimization horizon, control horizon and control discretization, is provided. The results show that the linear MPC controller is able to successfully track a reference input for the stable condition and stabilizes the system at the unstable flutter condition. It is also shown that the incorporation of the second- and third-order Volterra kernels in the nonlinear MPC controller provides superior performance on the nonlinear aeroelastic system compared to the results obtained using only a linear model