Near-optimal control of nonlinear dynamical systems: A brief survey

Zhang, Yinyan; Li, Shuai; Liao, Liefa

doi:10.1016/j.arcontrol.2019.01.003

Cited by 50 publications

(37 citation statements)

References 136 publications

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“…This kind of technique was applied for practical purposes (such as the control of solar and desalination plants) in (Torrico et al, 2010;Ayala et al, 2011). A recent survey of near-optimal control of nonlinear proceses was delivered by Zhang et al (2019).…”

Section: Sub-optimal Methodsmentioning

confidence: 99%

“…To overlap the complexity of these "full-blown" NMPC procedures, many sub-optimal solutions have been presented, such as: a) approaches that overcome the nonlinearities via linearization along the prediction trajectory (Ayala et al, 2011); b) methods that manipulate the nature of the nonlinearities to represent them in some specific manner (as bilinearities or sector conditions, for instance) which may reduce complexity (Nguyen et al, 2016); and c) algorithms that parametrize the control inputs in finite discrete possibilities, solving a search algorithm to find the smallest J instead of the actual optimization procedure (Rathai et al, 2018;Alamir, 2012). A brief survey on these works has been recently performed by Zhang et al (2019).…”

Section: Nonlinear Model Predictive Controlmentioning

confidence: 99%

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Model predictive control design for linear parameter varying systems: A survey

Morato

Normey‐Rico

Sename

2020

Annual Reviews in Control

140

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Motivated by the fact that many nonlinear plants can be represented through Linear Parameter Varying (LPV) embedding, and being this framework very popular for control design, this paper investigates the available Model Predictive Control (MPC) policies that can be applied for such systems. This paper reviews the available works considering LPV MPC design, ranging from the sub-optimal, simplified, yet Quadratic Programming (QP) algorithms, the tube-based tools, the set-constrained procedures, the Nonlinear Programming procedures and the robust ones; the main features of the recent research body on this topic are examined. A simulation example is given comparing some of the important techniques. Finally, some suggestions are given for future investigation threads, seeking further applicability of these methods.

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Section: Sub-optimal Methodsmentioning

confidence: 99%

Section: Nonlinear Model Predictive Controlmentioning

confidence: 99%

Model predictive control design for linear parameter varying systems: A survey

Morato

Normey‐Rico

Sename

2020

Annual Reviews in Control

140

View full text Add to dashboard Cite

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“…It is important to mention that when a multivariable system is linearized at an operating point, the RGA, as well as the relative-order matrix or the NRGA for the same operating point, can provide different information on the type of inputoutput pairing to choose. This shows that the task of selecting loop pairings to control a multivariable non-linear system is complex due to the characteristics of these systems [16].…”

Section: Introductionmentioning

confidence: 99%

A Loop Pairing Method for Non-Linear Multivariable Control Systems Under a Multi-Objective Optimization Approach

et al. 2020

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In the multivariable control literature there are few techniques that face the problem of selecting suitable loop pairings in non-linear multivariable systems. Most techniques analyze the linearized system at a specific operating point. This paper proposes a new methodology to optimally and simultaneously select the loop pairings and the tuning of the parameters of the decentralized control by applying a multi-objective optimization approach directly on the non-linear system. The main contribution of this work is that the proposed methodology enables a detailed multi-dimensional analysis of the performances and trade-offs in the available loop pairings to control a multivariable non-linear system. The methodology is applied in this paper to three examples that analyze how the different types of loop pairings conflict. In one of the examples, the proposed methodology was applied first in the linearized system and later in the non-linear system. The results were contradictory and show how the application of loop pairing techniques for linear systems can be inaccurate when they are applied on a non-linear system previously linearized at an operating point. The following examples show that the operating point of a non-linear system, the design objectives of each multiobjective problem, as well as the designer's preferences have important roles in the selection of an optimal loop pairing. INDEX TERMS Multivariable control system, non-linear systems, loop pairing, decentralized control structures, multi-objective evolutionary optimization, Pareto front.

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“…Optimal control, as one of the approaches to solve this problem, has attracted some efforts throughout past several decades. The interested reader can refer to [1][2][3][4][5][6] for a concise introduction to more common non-linear optimal control techniques. Since analytic solutions of non-linear optimal control problems is not available, except for simple cases, seeking approximate solutions is a common practice.…”

Section: Introductionmentioning

confidence: 99%

Near optimal tracking control of a class of non‐linear systems and an experimental comparison

Asadi

Heydari

2020

IET Control Theory & Appl

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In this study, near optimal tracking of a class of non-linear systems is addressed. Adaptive (approximate) dynamic programming (ADP) approach is used to calculate the optimal control in closed form. ADP has been widely used to resolve optimal regulation and tracking problems of non-linear control systems. Despite advances in the so called supervised and unsupervised ADP techniques for optimal tracking, they have a main draw back. That is, the optimal controller needs to be recalculated for every particular reference trajectory. The main goal of this work is to address this issue for a class of non-linear systems. Finally, this approach is applied on a Delta robot and the performance of the method is analysed experimentally.

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Near-optimal control of nonlinear dynamical systems: A brief survey

Cited by 50 publications

References 136 publications

Model predictive control design for linear parameter varying systems: A survey

Model predictive control design for linear parameter varying systems: A survey

A Loop Pairing Method for Non-Linear Multivariable Control Systems Under a Multi-Objective Optimization Approach

Near optimal tracking control of a class of non‐linear systems and an experimental comparison

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