Economic MPC with periodic terminal constraints of nonlinear differential-algebraic-equation systems: Application to drinking water networks

© 2026 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this paper, an Economic Model Predictive Control (EMPC) strategy with periodic terminal constraints is addressed for nonlinear differential-algebraic-equation systems with an application to Drinking Water Networks (DWNs). DWNs have some periodic behaviours because of the daily seasonality of water demands and electrical energy price. The periodic terminal constraint and economic terminal cost are implemented in the EMPC controller design for the purpose of achieving convergence. The feasibility of the proposed EMPC strategy when disturbances are considered is guaranteed by means of soft constraints implemented by using slack variables. Finally, the comparison results in a case study of the D-Town water network is provided by applying the EMPC strategy with or without periodic terminal constraints.Accepted versio

Nonlinear predictive control applied to steam/water loop in large scale ships

In steam/water loop for large scale ships, there are mainly five sub-loops posing different dynamics in the complete process. When optimization is involved, it is necessary to select different prediction horizons for each loop. In this work, the effect of prediction horizon for Multiple-Input Multiple-Output (MIMO) system is studied. Firstly, Nonlinear Extended Prediction Self-Adaptive Controller (NEPSAC) is designed for the steam/water loop system. Secondly, different prediction horizons are simulated within the NEPSAC algorithm. Based on simulation results, we conclude that specific tuning of prediction horizons based on loop’s dynamic outperforms the case when a trade-off is made and a single valued prediction horizon is used for all the loops

Risks to price stability, the zero lower bound and forward guidance: a real-time assessment : [Version August 14, 2013]

This paper employs stochastic simulations of the New Area-Wide Model—a microfounded open-economy model developed at the ECB—to investigate the consequences of the zero lower bound on nominal interest rates for the evolution of risks to price stability in the euro area during the recent financial crisis. Using a formal measure of the balance of risks, which is derived from policy-makers’ preferences about inflation outcomes, we first show that downside risks to price stability were considerably greater than upside risks during the first half of 2009, followed by a gradual rebalancing of these risks until mid-2011 and a renewed deterioration thereafter. We find that the lower bound has induced a noticeable downward bias in the risk balance throughout our evaluation period because of the implied amplification of deflation risks. We then illustrate that, with nominal interest rates close to zero, forward guidance in the form of a time-based conditional commitment to keep interest rates low for longer can be successful in mitigating downside risks to price stability. However, we find that the provision of time-based forward guidance may give rise to upside risks over the medium term if extended too far into the future. By contrast, time-based forward guidance complemented with a threshold condition concerning tolerable future inflation can provide insurance against the materialisation of such upside risks

Optimal operation of combined heat and power systems: an optimization-based control strategy

The use of decentralized Combined Heat and Power (CHP) plants is increasing since the high levels of efficiency they can achieve. Thus, to determine the optimal operation of these systems in dynamic energy-market scenarios, operational constraints and the time-varying price profiles for both electricity and the required resources should be taken into account. In order to maximize the profit during the operation of the CHP plant, this paper proposes an optimization-based controller designed according to the Economic Model Predictive Control (EMPC) approach, which uses a non-constant time step along the prediction horizon to get a shorter step size at the beginning of that horizon while a lower resolution for the far instants. Besides, a softening of related constraints to meet the market requirements related to the sale of electric power to the grid point is proposed. Simulation results show that the computational burden to solve optimization problems in real time is reduced while minimizing operational costs and satisfying the market constraints. The proposed controller is developed based on a real CHP plant installed at the ETA research factory in Darmstadt, Germany.Peer ReviewedPostprint (author's final draft

Adaptive Horizon Model Predictive Control and Al'brekht's Method

A standard way of finding a feedback law that stabilizes a control system to an operating point is to recast the problem as an infinite horizon optimal control problem. If the optimal cost and the optmal feedback can be found on a large domain around the operating point then a Lyapunov argument can be used to verify the asymptotic stability of the closed loop dynamics. The problem with this approach is that is usually very difficult to find the optimal cost and the optmal feedback on a large domain for nonlinear problems with or without constraints. Hence the increasing interest in Model Predictive Control (MPC). In standard MPC a finite horizon optimal control problem is solved in real time but just at the current state, the first control action is implimented, the system evolves one time step and the process is repeated. A terminal cost and terminal feedback found by Al'brekht's methoddefined in a neighborhood of the operating point is used to shorten the horizon and thereby make the nonlinear programs easier to solve because they have less decision variables. Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon length of Model Predictive Control (MPC) as needed. Its goal is to achieve stabilization with horizons as small as possible so that MPC methods can be used on faster and/or more complicated dynamic processes.Comment: arXiv admin note: text overlap with arXiv:1602.0861

The potential of fractional order distributed MPC applied to steam/water loop in large scale ships

The steam/water loop is a crucial part of a steam power plant. However, satisfying control performance is difficult to obtain due to the frequent disturbance and load fluctuation. A fractional order model predictive control was studied in this paper to improve the control performance of the steam/water loop. Firstly, the dynamic of the steam/water loop was introduced in large-scale ships. Then, the model predictive control with an extended prediction self adaptive controller framework was designed for the steam/water loop with a distributed scheme. Instead of an integer cost function, a fractional order cost function was applied in the model predictive control optimization step. The superiority of the fractional order model predictive control was validated with reference tracking and load fluctuation experiments

Distributed model predictive control of steam/water loop in large scale ships

In modern steam power plants, the ever-increasing complexity requires great reliability and flexibility of the control system. Hence, in this paper, the feasibility of a distributed model predictive control (DiMPC) strategy with an extended prediction self-adaptive control (EPSAC) framework is studied, in which the multiple controllers allow each sub-loop to have its own requirement flexibility. Meanwhile, the model predictive control can guarantee a good performance for the system with constraints. The performance is compared against a decentralized model predictive control (DeMPC) and a centralized model predictive control (CMPC). In order to improve the computing speed, a multiple objective model predictive control (MOMPC) is proposed. For the stability of the control system, the convergence of the DiMPC is discussed. Simulation tests are performed on the five different sub-loops of steam/water loop. The results indicate that the DiMPC may achieve similar performance as CMPC while outperforming the DeMPC method

A Novel Formulation of Economic Model Predictive Control for Periodic Operations

This paper proposes a novel formulation of economic model predictive control (MPC) for linear systems with periodic operations. In this economic MPC design, the optimal periodic trajectory from an economic point of view is unknown, hence it is not possible to follow a standard control strategy in which the MPC uses this trajectory to define a terminal constraint to guarantee closed-loop convergence. The economic cost function is optimized with a periodicity constraint at each time step considering all periodic trajectories in a period including the current state. The recursive feasibility and closed-loop convergence to the optimal periodic trajectory are analyzed using the Karush-Kuhn-Tucker conditions. Finally, two simulations are provided to demonstrate the main results.Agencia Estatal de Investigación DPI2013-48243-C2Agencia Estatal de Investigación DPI2016-76493- C3Ministerio de Ciencia, Innovación y Universidades MDM-2016-065