A Dissipativity Formulation for Stability Analysis of Nonlinear and Parameter Dependent MPC

Cisneros, Pablo S. G.; Werner, Herbert

doi:10.23919/acc.2018.8431417

Cited by 12 publications

(20 citation statements)

References 17 publications

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“…This is, the state evolution X k always lies inside the RPI set X f . Definition 8 (D/G scalings 29 ). Let Θ = diag{𝜌 1 (k)I size{𝜌 1 } , … , 𝜌 n p (k)I size{𝜌 n p } }, with 𝜌 j ∈ R. Accordingly, the set of D/G-Scalings is defined as follows:…”

Section: Definition 6 (Recursive Feasibilitymentioning

confidence: 99%

A fast dissipative robust nonlinear model predictive control procedure via quasi‐linear parameter varying embedding and parameter extrapolation

Morato

Normey-Rico

Sename

2021

Intl J Robust & Nonlinear

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In this article, a robust model predictive control (MPC) procedure for quasi-linear parameter varying (qLPV) systems is proposed. The novelty resides in considering a recursive extrapolation algorithm to estimate the values of the scheduling parameters along the prediction horizon N p , which fastens the sluggish performances achieved with the robust qLPV MPCs from the literature.The bounds on the estimation errors of the scheduling parameters through N p are taken into account by the robust MPC, which solves an online min-max problem: first, a constrained convex program is resolved in order to determine the worst-case bound on the cost function and, subsequently, a second constrained quadratic program is solved to minimize this worst-case cost function with respect to a control sequence vector. Since the bounds on the estimation error for the scheduling parameters are usually much smaller than the bounds on the actual scheduling parameter, the conservativeness of the solution is quite reduced. Recursive feasibility and stability of the proposed algorithm are demonstrated with dissipativity arguments given in the form of a linear matrix inequality remedy, which determines the zone of attraction for which input-to-state stability is ensured. The nonlinear temperature regulation problem of a flat solar collector is considered as a case study. Using a realistic simulation benchmark, the proposed technique is compared to other robust min-max LPV MPC algorithms from the literature, proving itself efficient while achieving good performances. K E Y W O R D Sdissipativity, linear parameter varying systems, quadratic programming, robust model predictive control, solar collectors INTRODUCTIONModel predictive control (MPC) is one of the most widespread control techniques, with many industrial applications. 1 Its implementation is relatively simple, requiring the solution of an online optimization problem, written in terms of a prediction model and operational constraints. MPC is a sliding-horizon paradigm, which means that the algorithm Abbreviations: LPV, linear parameter varying; LTI, linear time-invariant; MPC, model predictive control.

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Section: Definition 6 (Recursive Feasibilitymentioning

confidence: 99%

A fast dissipative robust nonlinear model predictive control procedure via quasi‐linear parameter varying embedding and parameter extrapolation

Morato

Normey-Rico

Sename

2021

Intl J Robust & Nonlinear

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“…A vantagem da síntese através da versão LFT do sistema é que o Teorema 1 é reformulado de forma independente dos parâmetros. Neste caso, o procedimento de síntese não mais requererá a verificação em uma sequência infinita de pontos ao longo do espectro de (ρ, δρ), mas apenas múltiplas instâncias das desigualdades do Teorema, definidas em termos de A , B , etc, tal como em (Cisneros and Werner, 2018;Veenman and Scherer, 2014). Nota 5.…”

Section: Configura ç ãO Do Mpcunclassified

“…A estrutura proposta é flexível e não requer o uso de ingredientes terminais, uma vez que o canal de realimentação LPV assegura estabilidade entrada-estado e apenas alguns critérios de dissipatividade da função custo do MPC devem ser verificados, tal como em (Cisneros and Werner, 2018). A síntese offline é linear nas variáveis de decisão, ao passo que a parte online consiste na solução de um único Programa Quadrático (QP) por período de amostragem.…”

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Síntese Estruturada para Controladores Preditivos LPV

Morato

Normey-Rico²,

Sename

2021

Procedings Do XV Simpósio Brasileiro De Automação Inteligente

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We present a novel framework for the design of dissipative Model Predictive Control (MPC) schemes for Linear Parameter Varying (LPV) systems. The synthesis directly considers both time-and frequency-domain specifications, as well as optimal performance costs. The novelty is the retraction of parameter-dependency from the optimisation problem, enable by a stabilising LPV feedback. Moreover, the framework suppresses the use of terminal ingredients, since the LPV feedback ensures input-to-state stability by design. The method is compared to a standard min/max MPC, exhibiting good performances with reduced computational load. Resumo: Apresentamos uma estrutura para o projeto de Controle Preditivo baseado em Modelo (MPC) para sistemas Lineares a Parâmetros Variantes (LPV). O método considera diretamente especificações no domínio do tempo e da frequência, bem como custos de desempenho quadráticos. A novidade é o desacoplamento da dependência dos parâmetros de agendamento do problema de otimização, viabilizada por uma realimentação estabilizante LPV. Além disso, a estrutura elimina os ingredientes terminais, uma vez que a realimentação LPV garante estabilidade entrada-estado por construção. O método proposto é comparada com um MPC robusto (min/max), garantindo bom desempenho com carga computacional reduzida.

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“…A robust output MPC design based on dissipativity for unstructured uncertainties has been proposed in [9]. More recently, IQCs in conjunction with dissipativity have been used for multi-model MPC [10] and later for LPV based MPC [11]. To overcome the extensive conservatism in MPC stability analysis, the existence of Zames-Falb (ZF) multipliers, originally proposed in [12], was shown in [13], for time-invariant linear constraints.…”

Section: Introductionmentioning

confidence: 99%

Robust Stability of Barrier-Based Model Predictive Control

Petsagkourakis

Heath

Carrasco

et al. 2021

IEEE Trans. Automat. Contr.

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Conditions for robust input-output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs). The IQCs can be used to determine sufficient conditions for global closed-loop stability. In particular conditions for robust stability can be obtained in the presence of unstructured model uncertainty. IQCs with both static and dynamic multipliers are developed and appropriate convex searches for the multipliers are presented. The effectiveness of the robust stability analysis is demonstrated through an illustrative numerical example.

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A Dissipativity Formulation for Stability Analysis of Nonlinear and Parameter Dependent MPC

Cited by 12 publications

References 17 publications

A fast dissipative robust nonlinear model predictive control procedure via quasi‐linear parameter varying embedding and parameter extrapolation

A fast dissipative robust nonlinear model predictive control procedure via quasi‐linear parameter varying embedding and parameter extrapolation

Síntese Estruturada para Controladores Preditivos LPV

Robust Stability of Barrier-Based Model Predictive Control

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