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

Álamo

2016 IEEE Conference on Control Applications (CCA)

et al. 2016

Self Cite

Abstract-In this paper, a periodic economic model predictive control (EMPC) strategy with nonlinear algebraic constraint relaxations for water distribution networks (WDNs) is presented. A WDN is usually modeled by a series of differentialalgebraic equations. When the hydraulic pressure/head and flow relations in the interconnected pipes are considered, the nonlinear algebraic equations will appear in the control-oriented model of WDNs. Specifically, two types of nonlinear algebraic equations are studied in terms of unidirectional and bidirectional flows in pipes. These nonlinear algebraic constraints are iteratively relaxed by a series of linear constraints. Therefore, the proposed EMPC strategy can be implemented by solving an optimization problem using the linear programming technique. Finally, the EMPC strategy with nonlinear algebraic constraint relaxations is verified in the Richmond water network. The comparison results of applying nonlinear EMPC strategy are also provided. The proposed nonlinear-constraint relaxation technique turns out to be much faster than the one obtained by a standard nonlinear optimization solver.

“…The detailed definitions of these functions can be found in [1]. λ 1 , λ 2 and λ 3 are fixed weights for each objective.…”

Section: Case Study: Richmond Water Networkmentioning

confidence: 99%

“…The cost function for the Richmond water network includes mainly includes three parts [1]: the economic term, the safety term and the smoothness term, which can be formulated as follows:…”

Section: Case Study: Richmond Water Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Periodic economic model predictive control with nonlinear-constraint relaxation for water distribution networks

Álamo

2016 IEEE Conference on Control Applications (CCA)

et al. 2016

Self Cite

“…Descriptor systems may contain static relations between system variables. Due to their powerful modeling capability, descriptor systems are encountered in diverse applications such as electrical circuits (Dai, 1989), water networks (Wang et al, 2016) and chemical processes (Kumar and Daoutidis, 1995). Therefore, control analysis and synthesis problems for descriptor systems have attracted considerable attention during the past decades (Duan, 2010).…”

Section: Introductionmentioning

confidence: 99%

Zonotopic Fault Estimation Filter Design for Discrete-time Descriptor Systems

et al. 2017

IFAC-PapersOnLine

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This paper considers actuator-fault estimation for discrete-time descriptor systems with unknown but bounded system disturbance and measurement noise. A zonotopic fault estimation filter is designed based on the analysis of fault detectability indexes. To ensure estimation accuracy, the filter gain in the zonotopic fault estimation filter is optimized through the zonotope minimization. The designed zonotopic filter not only can estimate fault magnitudes, but it also provides fault estimation results in an interval, i.e. the upper and lower bounds of fault magnitudes. Moreover, the proposed fault estimation filter has a non-singular structure and hence is easy to implement. Finally, simulation results are provided to illustrate the effectiveness of the proposed method.

Robust economic model predictive control based on a periodicity constraint

Peña

Intl J Robust & Nonlinear

et al. 2019

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This paper proposes robust economic model predictive control based on a periodicity constraint for linear systems subject to unknown-but-bounded additive disturbances. In this economic MPC design, a periodic steady-state trajectory is not required and thus assumed unknown, which precludes the use of enforcing terminal state constraints as in other standard economic formulations. Instead, based on the desired periodicity of system operation, we optimize the economic performance over a set of periodic trajectories that include the current state. To achieve robust constraint satisfaction, we use a tube-based technique in the economic MPC formulation. The mismatches between the nominal model and the closed-loop system with perturbations are limited using a local control law. With the proposed robust tube-based strategy, recursive feasibility is guaranteed. Moreover, under a convexity assumption, the closed-loop convergence of the closed-loop system is analyzed, and an optimality certificate is provided to check if the closed-loop trajectory reaches a neighborhood of the optimal nominal periodic steady trajectory using Karush-Kuhn-Tucker optimality conditions. Finally, through numerical examples, we show the effectiveness of the proposed approach.KEYWORDS convex optimization, economic MPC, linear uncertain systems, periodic operation 3296