Transformations for linear parameter varying systems

Szabó, Zoltán; Bokor, József

doi:10.1016/j.ifacol.2018.11.163

Cited by 3 publications

(6 citation statements)

References 25 publications

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“…The scheduling parameters are bounded and known (their current values ρ(k) can be measured online or estimated) -note that their future behaviour is generally not known. Theoretical analysis of LPV system properties, such as stability, observability, controllability, often falls into the framework of linear timevarying systems or of nonlinear systems, which usually presents more difficulty compared to the classical LTI framework (Blanchini & Miani, 2003;Bokor & Balas, 2005;Szabó & Bokor, 2018).…”

Section: Linear Parameter Varying Systemsmentioning

confidence: 99%

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: Linear Parameter Varying Systemsmentioning

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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“…In this terminal cost, is a constant matrix of adequate sizes taken according to LMI (24) and ensuring ISS property and recursive feasibility (explained in the sequel). is also strictly positive definite with rank{ } = .…”

Section: Terminal Costmentioning

confidence: 99%

“…(74). It is direct to verify that if LMI holds, since is a scalar and LMI (24) implies the regional decrease of , Axiom A3 is valid. Therefore, is computed such that (24) and (75) hold, being also full-rank and positive definite by definition.…”

Section: Proposition 3 Recursive Feasibilitymentioning

confidence: 99%

“…• Step (3): Solve LMIs (24) and (75), verifying that inequality (25) holds for the Lipschitz constant Γ. Compute the terminal set according to and Theorem 1;…”

Section: Loopmentioning

confidence: 99%

“…Theoretical analysis of LPV system properties, such as stability, observability, controllability, often falls into the framework of linear time-varying systems or of nonlinear systems, which usually presents more difficulty compared to the classical LTI case 23,24. …”

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confidence: 99%

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An input‐to‐state stable model predictive control framework for Lipschitz nonlinear parameter varying systems

Morato

Normey-Rico

Sename

2020

Intl J Robust & Nonlinear

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This paper develops a state-feedback Model Predictive Control (MPC) framework for Nonlinear Parameter Varying (NLPV) systems with explicit Lipschitz nonlinearities along the input trajectory. Considering a guess for the evolution of the scheduling parameters along the prediction horizon, the proposed optimization procedure for the MPC design includes a terminal stage cost, a contracting terminal region constraint and nominal predictions scheduled with respect to this guess. The terminal region is taken so that it is monotonically decreasing to a predetermined set, which guarantees recursive feasibility of the algorithm with respect to a bound on the admissible uncertainties (introduced from the scheduling parameter guess). The terminal set is a scheduled robust control invariant set for Lipschitz nonlinear systems, computed through some proposed LMIs. The inclusion of the terminal ingredient also serves to demonstrate Input-to-State Quadratic Stability. This paper ends with a successful numerical simulation example of the technique applied to the control of a Semi-Active automotive suspension system equipped with Electro-Rheological dampers.

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Remarks on the geometry of the feedback loop

Szabó

Bokor

2019

2019 18th European Control Conference (ECC)

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Youla parametrization of stabilizing controllers is a fundamental result of control theory. It provides a theoretical and practical tool that renders LFT loops into model matching framework. Based on the geometric techniques introduced in our previous work we have provided a controller blending rule that defines a controller semigroup structure based only on the knowledge of the plant and a single stabilizing controller and we have introduced a novel, geometry based parametrization. In this paper we investigate the possibility to construct stabilizing fractions of the given stabilizing controller relative to the blending rule. We also extend our geometry based framework to the LFT loops. Our main goal is to show that every controller which stabilizes the interior loop also stabilizes the LFT loop. Contrary to the expectations, this problem is far from being trivial.

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Transformations for linear parameter varying systems

Cited by 3 publications

References 25 publications

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

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

An input‐to‐state stable model predictive control framework for Lipschitz nonlinear parameter varying systems

Remarks on the geometry of the feedback loop

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