Robust periodic economic MPC for linear systems

Broomhead, Timothy; Manzie, Chris; Shekhar, Rohan C.; Hield, Peter

doi:10.1016/j.automatica.2015.06.034

Cited by 38 publications

(31 citation statements)

References 19 publications

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“…As was discussed in [120], just transferring robust MPC approaches from a stabilizing to an economic context might not result in an optimal performance, and hence novel approaches have to be developed. Some robust and stochastic economic MPC schemes can, e.g., be found in [111], [120]- [126]. Some of these references focus on applications, while others establish theoretical properties such as closed-loop performance and convergence guarantees in the presence of disturbances.…”

Section: Further Resultsmentioning

confidence: 99%

“…Here, constraints based on a known control Lyapunov function are added to the repeatedly solved optimization problem to ensure that the system stays within a certain stability region or converges there. Economic MPC using a generalized terminal constraint was, e.g., considered in [101], [108]- [111]. Here, the predicted terminal state is not required to be equal to the optimal steadystate or periodic orbit, but only to some (arbitrary) steadystate [108]- [110] or periodic orbit [101], [111].…”

Section: Further Resultsmentioning

confidence: 99%

“…Economic MPC using a generalized terminal constraint was, e.g., considered in [101], [108]- [111]. Here, the predicted terminal state is not required to be equal to the optimal steadystate or periodic orbit, but only to some (arbitrary) steadystate [108]- [110] or periodic orbit [101], [111]. Advantages compared to "standard" terminal constraints are that the optimal steady-state/periodic orbit need not be known a priori, and the feasible set can be larger.…”

Section: Further Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Economic and Distributed Model Predictive Control: Recent Developments in Optimization-Based Control

Müller

Allgöwer

2017

SICE Journal of Control, Measurement, and System Integration

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Section: Further Resultsmentioning

confidence: 99%

Section: Further Resultsmentioning

confidence: 99%

Section: Further Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Economic and Distributed Model Predictive Control: Recent Developments in Optimization-Based Control

Müller

Allgöwer

2017

SICE Journal of Control, Measurement, and System Integration

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“…Robust MPC is proposed to track periodic trajectories online, where a local control law is used to refine the constraints to guarantee the recursive feasibility in a closed loop. In recent years, several developments on adjusting the robustness of economic MPC have been studied, where the strong terminal constraint and cost are also used to enforce the periodicity. In our work, we consider a pure economic cost function without using terminal constraint and terminal cost function.…”

Section: Introductionmentioning

confidence: 99%

Robust economic model predictive control based on a periodicity constraint

Wang

Peña

Puig

et al. 2019

Intl J Robust & Nonlinear

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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

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“…Assumption 2 (Robustness): The robustness of the EMPC controller can be realized by means of an appropriate constraint tightening technique (see [12], [13], [14] and [15]). Therefore, the tightened constraints on system states and control inputs can be formulated as follows:…”

Section: B Empc Optimization Statementmentioning

confidence: 99%

Fault-tolerant periodic economic model predictive control of differential-algebraic-equation systems

Wang

Puig

Cembraño

2016

2016 3rd Conference on Control and Fault-Tolerant Systems (SysTol)

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Abstract-This paper addresses a fault-tolerant periodic economic model predictive control (MPC) strategy for differentialalgebraic-equation (DAE) systems. Fault tolerance evaluation of the proposed economic MPC strategy uses set computations and a performance degradation analysis. By means of the set computations, the feasible solution set (including system states and control inputs) can be determined as well as the admissible performance set can be obtained when system reconfiguration or fault accommodation strategies are used. The proposed control strategy allows to carry out an analysis of performance degradation by using the feasible and admissible performance set. As a result, if the performance degradation is accepted, the economic MPC controller can be applied using system reconfiguration or fault accommodation. Finally, the proposed fault-tolerant MPC strategy is verified through an illustrative example.

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Robust periodic economic MPC for linear systems

Cited by 38 publications

References 19 publications

Economic and Distributed Model Predictive Control: Recent Developments in Optimization-Based Control

Economic and Distributed Model Predictive Control: Recent Developments in Optimization-Based Control

Robust economic model predictive control based on a periodicity constraint

Fault-tolerant periodic economic model predictive control of differential-algebraic-equation systems

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