Parameter-dependent stability conditions for quasi-LPV Model Predictive Control

Cisneros, Pablo S. G.; Werner, Herbert

doi:10.23919/acc.2017.7963735

Cited by 13 publications

(19 citation statements)

References 7 publications

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“…We give the construction for c = ∞ in (11), as used in the numerical examples. The cost (11) can be implemented by introducing non-negative slack variables ( , , ). Then, wc (X i , K i , Θ i ) ≤ i is equivalent to ∀i ∈ [0..N − 1]:…”

Section: Discussionmentioning

confidence: 99%

“…Both the controllers presented here and in [10,11] make use of a scheduling map to take into account the relationship between the state and scheduling variables. Where [10] solves a sequence of LTV MPC problems at each time instant, the tube-based method that this paper proposes solves a single LP or QP which is, however, more complex than the problems solved in [10].…”

Section: Introductionmentioning

confidence: 99%

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Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes

Hanema

Tóth

Lazăr

2021

IET Control Theory & Appl

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This paper proposes a model predictive control (MPC) approach for non-linear systems where the non-linear dynamics are embedded inside a linear parameter-varying (LPV) representation. The non-linear MPC problem is therefore replaced by an LPV MPC problem, without using linearization. Compared to general non-linear MPC, advantages of this approach are that it allows for the tractable construction of a terminal set and cost, and that only a single convex program must be solved online. The key idea that enables proving recursive feasibility and stability, is to restrict the state evolution of the non-linear system to a time-varying sequence of state constraint sets. Because in LPV embeddings, there exists a relationship between the scheduling and state variables, these state constraints are used to construct a corresponding future scheduling tube. Compared to non-time-varying state constraints, tighter bounds on the future scheduling trajectories are obtained. Computing a scheduling tube in this setting requires applying a non-linear function to the sequence of constraint sets. Outer approximations of this non-linear projection-based scheduling tube can be found, e.g., via interval analysis. The computational properties of the approach are demonstrated on numerical examples.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes

Hanema

Tóth

Lazăr

2021

IET Control Theory & Appl

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“…In this scenario, terminal state constraints would not lead to a reasonable implementation as far away set points (even without obstacles) would need a long horizon, even though dynamically there is no difference from the case in which the set point is close. This issue can be handled by exploiting the velocity algorithm, which establishes stability by using terminal constraints on the velocity vector alone, thereby increasing the size of the feasible set.…”

Section: Discussionmentioning

confidence: 99%

“…Stability is enforced by the offline solution of two LMI problems to obtain the terminal ingredients. The approach was later extended to consider parameter dependent terminal ingredients which can drastically reduce conservatism brought by the stability requirement . However, the offline optimization problem was given by a bilinear matrix inequality (BMI) problem, which is nonconvex and generally hard to solve, an algorithm akin to D ‐ K iteration from μ‐theory was disclosed.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear model predictive control for models in quasi‐linear parameter varying form

Cisneros

Werner

2020

Intl J Robust & Nonlinear

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This article presents a nonlinear model predictive control (NMPC) approach based on quasi-linear parameter varying (quasi-LPV) representations of the model and constraints. Stability of the proposed algorithm is ensured by the offline solution of an optimization problem with linear matrix inequality constraints in conjunction with an online terminal state constraint. Furthermore, an iterative approach is presented with which the NMPC optimization problem can be handled by solving a series of Quadratic Programs at each time step, this being highly computationally efficient. A practical and simple way of obtaining quasi-LPV representations of the system using velocity-based linearization is presented in two examples. K E Y W O R D S efficient algorithms, linear matrix inequality, nonlinear model predictive control, quasi-linear parameter varying systems 1 Int J Robust Nonlinear Control. 2020;30:3945-3959.wileyonlinelibrary.com/journal/rnc

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“…Such method was extended and further formalized in (Cisneros & Werner, 2017a), where the reference tracking problem was embedded to the NP formulation. In (Cisneros & Werner, 2017b), parameterdependent stability conditions for these algorithms were presented. Finally, an alternative stabilizing tubebased formulation of such algorithm was seen in (Hanema et al, 2017b).…”

Section: Nonlinear Programming Methodsmentioning

confidence: 99%

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

Morato

Normey‐Rico

Sename

2020

Annual Reviews in Control

127

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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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Parameter-dependent stability conditions for quasi-LPV Model Predictive Control

Cited by 13 publications

References 7 publications

Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes

Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes

Nonlinear model predictive control for models in quasi‐linear parameter varying form

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

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