On stability of multiobjective NMPC with objective prioritization

He, Defeng; Wang, Lei; Sun, Jing

doi:10.1016/j.automatica.2015.04.024

Cited by 63 publications

(49 citation statements)

References 36 publications

(45 reference statements)

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“…When m =1, it becomes a monotonic Lyapunov function, which is similar to the aforementioned works. () As shown in the works of Geromel and Colaneri, Chesi et al, and Dehghan and Ong, the condition in can be considered as a sufficient condition for stability.…”

Section: Economic Mpc With Lyapunov‐based Constraintsmentioning

confidence: 96%

“…One method to ensure the stability of economic MPC is to use Lyapunov‐based constraints. () The idea follows from the standard MPC arguments on recursive feasibility and stability . However, it is not necessary to construct a monotonic Lyapunov function to guarantee stability as the induced Lyapunov‐based constraints will become restrictive and potentially undermine economic performance.…”

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

“…In the second mode, suitable Lyapunov‐based constraints are used to drive the state of the system to the desired steady state, and the Lyapunov function is monotonically decreasing. Similar techniques have also been used in discrete‐time systems,() which refer to the Lyapunov‐based constraint as the stabilizing or contractive constraint. These constraints will enforce a Lyapunov decrease and steer the state to the desired set‐point.…”

Section: Introductionmentioning

confidence: 99%

“…However, it may be conservative to require that the Lyapunov function is monotonically decreasing. To reduce the conservatism, the Lyapunov‐based constraints used in the works of He et al, Zavala, and He et al can be relaxed so that only nonmonotonic Lyapunov functions are needed to achieve asymptotic stability. Nonmonotonic Lyapunov functions are often used in the stability analysis of switched and uncertain systems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Economic MPC of nonlinear systems with nonmonotonic Lyapunov functions and its application to HVAC control

Wang

2018

Intl J Robust & Nonlinear

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Summary This paper proposes a Lyapunov‐based economic model predictive control (MPC) scheme for nonlinear systems with nonmonotonic Lyapunov functions. Relaxed Lyapunov‐based constraints are used in the MPC formulation to improve the economic performance. These constraints will enforce a Lyapunov decrease after every few steps. Recursive feasibility and asymptotical convergence to the steady state can be achieved using Lyapunov‐like stability analysis. The proposed economic MPC can be applied to minimize energy consumption in heating ventilation and air conditioning control of commercial buildings. The Lyapunov‐based constraints in the online MPC problem enable the tracking of the desired set‐point temperature. The performance is demonstrated by a virtual building composed of 2 adjacent zones.

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Section: Economic Mpc With Lyapunov‐based Constraintsmentioning

confidence: 96%

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Economic MPC of nonlinear systems with nonmonotonic Lyapunov functions and its application to HVAC control

Wang

2018

Intl J Robust & Nonlinear

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“…In fact, due to the reference point method, the objective function is always convex [109] which can be exploited during the optimization. Alternative scalarization methods are the -constraint method [136] or lexocographic ordering [137]. A disadvantage of a priori scalarization is that it is often difficult to select the scalarization parameter in such a way that a desired trade-off solution is obtained, and the remedy proposed in [134] is only applicable to a specific class of problems.…”

Section: Online Multiobjective Optimizationmentioning

confidence: 99%

A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

Peitz¹,

Dellnitz²

2018

Preprint

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Abstract:Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto optimal solutions have led to a wide range of new applications related to optimal and feedback control which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview over recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

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Parametric control to linear time‐varying systems based on dynamic compensator and multi‐objective optimization

Zhang

Duan

2019

Asian Journal of Control

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This paper investigates the parametric approach for linear time-variant systems by using dynamic compensator and multi-objective optimization. Based on the solution to a class of generalized Sylvester matrix equations, the generally completely parametrized expression of the dynamic compensator is established, meanwhile, the completely parametric forms of left and right closed-loop eigenvectors and two groups of arbitrary parameters are obtained. With the proposed parametric approach, the closed-loop system can be transformed into a linear time-invariant one with expected eigenstructure. Simultaneously, it also considers a novel technique to multi-objective optimization design for linear time-varying systems. Multiple performance objectives, including the overall sensitivity function, H 2 norm and H ∞ norm, are formulated by two groups of arbitrary parameters. Based on these performance objectives, the robustness criteria is expressed by a comprehensive objective function which includes each performance objective weighted. By utilizing the degrees of freedom in parameters to optimize the comprehensive objective function, an optimized dynamic compensator can be obtained to satisfy the robustness criteria. Finally, an example of spacecraft rendezvous problem is presented to illustrate the effectiveness of the proposed approach.

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On stability of multiobjective NMPC with objective prioritization

Cited by 63 publications

References 36 publications

Economic MPC of nonlinear systems with nonmonotonic Lyapunov functions and its application to HVAC control

Economic MPC of nonlinear systems with nonmonotonic Lyapunov functions and its application to HVAC control

A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

Parametric control to linear time‐varying systems based on dynamic compensator and multi‐objective optimization

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