Fast model predictive control for linear periodic systems with state and control constraints

Nguyen, Hoaï-Nam; Bourdais, Romain; Gutman, Per‐Olof

doi:10.1002/rnc.3760

Cited by 10 publications

(16 citation statements)

References 35 publications

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“…Here A ∈ R n×n and B n × m are the system matrices, it is assumed that the pair (A,B) is stabilizable; and the trajectories of (8) are required to be constrained in a convex nonempty polytope set centered at the origin. Under the assumptions for and , the polytope  and Definitions 1 and 2, the problem to deal with, can be stated as: to design a robust state feedback control strategy for the system (8) such that the closed-loop trajectories…”

Section: Problem Statementmentioning

confidence: 99%

“…Lemma 1. Let y ∈ R n be the measured value of the system output (8) in a given time instant t = T k ≥ 0, this is y = y(T k ), let…”

Section: Control Designmentioning

confidence: 99%

“…is feasible for a matrix Y ∈ R mxn , some symmetric matrices P 0 , G, H ∈ R nxn . Then, for the closed-loop system (8) with the control input u = Ky with K = YQ( * ), it is true that 1. The convex hull (Q( * )) is an invariant set for the system trajectories.…”

Section: Control Designmentioning

confidence: 99%

“…then,̂∞ = (Q( * ) −1P 0 Q( * ) −1 ) is the minimal attractive set for the closed-loop system (8) with the minimizing control input given by u =Ky, withK =ŶQ( * ).…”

Section: Control Designmentioning

confidence: 99%

“…5 Several control design methods have been applied to address the problem of stabilizing systems with state constraints. [6][7][8][9] Some of these methods include the model predictive control (MPC) approach, which offers an alternative to deal with constraints in the state and the input of discretized linear systems, 7,8 neural networks, 10,11 and fuzzy controllers. 12,13 The study proposed by Li et al 12 extends the control design results in the case of time delay in the control function.…”

Section: Introductionmentioning

confidence: 99%

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Robust control for state constrained systems based on composite barrier Lyapunov functions

Llorente-Vidrio

Mera

Salgado

et al. 2020

Intl J Robust & Nonlinear

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This study aims to design a robust state feedback controller for uncertain and perturbed linear systems with state constraints described by a polytope. This novel design incorporates the use of a composite barrier Lyapunov function (CBLF) and the convex hull of a set of ellipsoids inscribed in the given polytopic constraint set. The CBLF is used to ensure that this convex hull is an invariant set for the perturbed system states. Then, an optimization scheme is implemented to maximize the size of this invariant set to use it as a safe set. This is a set of initial conditions ensuring that the system solutions conform to the constraints for any subsequent time instant. Additionally, a minimal ultimate bound for the states is calculated to ensure asymptotic convergence to a region as close to the origin as possible. This region is characterized by a second convex hull of ellipsoids using the well-known attractive ellipsoid method and the CBLF. Numerical simulations illustrate and compare the obtained results against a similar approach, considering the classical quadratic Lyapunov function, instead of the CBLF.

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Section: Problem Statementmentioning

confidence: 99%

“…Lemma 1. Let y ∈ R n be the measured value of the system output (8) in a given time instant t = T k ≥ 0, this is y = y(T k ), let…”

Section: Control Designmentioning

confidence: 99%

Section: Control Designmentioning

confidence: 99%

“…then,̂∞ = (Q( * ) −1P 0 Q( * ) −1 ) is the minimal attractive set for the closed-loop system (8) with the minimizing control input given by u =Ky, withK =ŶQ( * ).…”

Section: Control Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust control for state constrained systems based on composite barrier Lyapunov functions

Llorente-Vidrio

Mera

Salgado

et al. 2020

Intl J Robust & Nonlinear

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show abstract

Adaptive neural network command filtered backstepping control of pure‐feedback systems in presence of full state constraints

Zhou

Zong

2019

Adaptive Control & Signal

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Summary An adaptive neural network (NN) command filtered backstepping control is proposed for the pure‐feedback system subjected to time‐varying output/stated constraints. By introducing a one‐to‐one nonlinear mapping, the obstacle caused by full stated constraints is conquered. The adaptive control law is constructed by command filtered backstepping technology and radial basis function NNs, where only one learning parameter needs to be updated online. The stability analysis via nonlinear small‐gain theorem shows that all the signals in closed‐loop system are semiglobal uniformly ultimately bounded. The simulation examples demonstrate the effectiveness of the proposed control scheme.

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Application of terminal region enlargement approach for discrete time quasi infinite horizon nonlinear model predictive control

Gupta,

Rajhans

2024

Adaptive Control & Signal

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SummaryEnsuring nominal asymptotic stability of the nonlinear model predictive control (NMPC) controller is not trivial. Stabilizing ingredients such as terminal penalty term and Terminal Region (TR) are crucial in establishing the asymptotic stability. Approaches available in the literature provide limited degrees of freedom for the characterization of the TR for the discrete time quasi infinite horizon NMPC formulation. Current work presents alternate approaches namely arbitrary controller based approach and linear quadratic regulator (LQR) based approach, which provide larger degrees of freedom for enlarging the TR. Both the approaches are scalable to system of any dimension. Approach from the literature provides a scalar whereas proposed approaches provide two additive matrices as tuning parameters for shaping of the TR. Proposed approaches involve solving modified Lyapunov equations to compute terminal penalty term, followed by explicit characterization of the TR. Efficacy of the proposed approaches is demonstrated using benchmark two state system. TR obtained using the arbitrary controller based approach and LQR based approach are approximately 10.4723 and 9.5055 times larger by area measure when compared to the largest TR obtained using the approach from the literature. As a result, there is significant reduction in the prediction horizon length while retaining the feasibility of the controller.

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Fast model predictive control for linear periodic systems with state and control constraints

Cited by 10 publications

References 35 publications

Robust control for state constrained systems based on composite barrier Lyapunov functions

Robust control for state constrained systems based on composite barrier Lyapunov functions

Adaptive neural network command filtered backstepping control of pure‐feedback systems in presence of full state constraints

Application of terminal region enlargement approach for discrete time quasi infinite horizon nonlinear model predictive control

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