Matrix Riccati Equations in Control and Systems Theory

Abou-Kandil, Hisham; Freiling, Gerhard; Ionescu, Vlad; Jank, Gerhard

doi:10.1007/978-3-0348-8081-7

Cited by 384 publications

(218 citation statements)

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“…Consider the constrained trajectory tracking problem P1-P2 for system (1). Suppose that for all t ∈ [0, T ] :π(t) ∈ (0, ∞) and E t k +Tp =L t k +Tp,V,π .…”

Section: Lemma 2 (Stabilizing Time-varying Level Sets)mentioning

confidence: 99%

A model predictive control approach to trajectory tracking problems via time-varying level sets of Lyapunov functions

Faulwasser

Findeisen

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-We discuss a model predictive control approach to trajectory tracking problems of constrained nonlinear continuous time systems, where the reference trajectory is a priori known and asymptotically constant. The proposed NMPC scheme is able to explicitly consider input and state constraints while guaranteeing recursive feasibility. To handle the timevarying nature of the tracking problem we advocate the use of time-varying level sets of Lyapunov functions as terminal regions. We prove a necessary and sufficient condition for positive invariance of these sets and show how these sets can be efficiently computed, if a quadratic Lyapunov function is available. As an example we consider a nonlinear CSTR reactor.

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“…Consider the constrained trajectory tracking problem P1-P2 for system (1). Suppose that for all t ∈ [0, T ] :π(t) ∈ (0, ∞) and E t k +Tp =L t k +Tp,V,π .…”

Section: Lemma 2 (Stabilizing Time-varying Level Sets)mentioning

confidence: 99%

A model predictive control approach to trajectory tracking problems via time-varying level sets of Lyapunov functions

Faulwasser

Findeisen

2011

IEEE Conference on Decision and Control and European Control Conference

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“…For more detailed topics on Riccati equations, readers are referred to [9,1]. Here we introduce an important property of Riccati inequality and its LMI version which will be used extensively in the following sections, and in those sections we will discuss how to use this LMI relaxation of Riccati equation to impose structure on the synthesis problem in a convex fashion.…”

Section: Riccati Inequalitymentioning

confidence: 99%

“…In (29), S (1) represents the decentralized case; S (2) represents the localized case where each subsystem Σ i only receives information from its direct preceding and succeeding neighbors; S (3) shows the situation where Σ i receives information from all of its preceding neighbors; S (4) indicates Σ i receives information from all of its succeeding neighbors.…”

Section: Structured H 2 Control Via Riccati Inequalitymentioning

confidence: 99%

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LMI relaxation to Riccati equations in structured control

Paganini

2007

International Journal of Control

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In this paper we discuss structured H2 control methods for large-scale interconnected systems. Based on a relaxation of Riccati equations, we derive some linear matrix inequality (LMI) conditions for suboptimal controllers in which information structure can be imposed. In particular, we derive controllers by solving low-dimensional LMIs, which are decentralized except for the sharing information between neighbors, as determined by the plant interconnection; also we optimize a performance bound for each of the derived controllers.

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“…One of the most known idea is to apply a state-space partition based approach [19] or the min-switching strategy introduced in [20,8] for continuous-time. In this framework, sufficient conditions based on LyapunovMetzler inequalities [21,22] are developed in association with a switched quadratic Lyapunov function [23,24]. As suggested in [25], the intuitive use of a switched quadratic Lyapunov function can be improved by considering a switched Lur'e type Lyapunov function (see [6,18] for its introduction).…”

Section: Introductionmentioning

confidence: 99%

Min-switching local stabilization for discrete-time switching systems with nonlinear modes

Jungers

Gonzaga

Daafouz

2013

Nonlinear Analysis: Hybrid Systems

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This paper deals with the discrete-time switched Lur'e problem in finite domain. The aim is to provide a stabilization inside an estimate of the origin's basin of attraction, large as possible, via a suitable switching rule. The design of this switching rule is based on the min-switching policy and can be induced by sufficient conditions given by Lyapunov-Metzler inequalities. Nevertheless instead of intuitively considering a switched quadratic Lyapunov function for this approach, a suitable switched Lyapunov function including the modal nonlinearities is proposed. The assumptions required to characterize the nonlinearities are only mode-dependent sector conditions, without constraints related to the slope of the nonlinearities. An optimization problem is provided to allow the maximization of the size of the basin of attraction estimate -which may be composed of disconnected sets -under the stabilization conditions. A numerical example illustrate the efficiency of our approach and emphasize the specificities of our tools.

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Matrix Riccati Equations in Control and Systems Theory

Cited by 384 publications

References 0 publications

A model predictive control approach to trajectory tracking problems via time-varying level sets of Lyapunov functions

A model predictive control approach to trajectory tracking problems via time-varying level sets of Lyapunov functions

LMI relaxation to Riccati equations in structured control

Min-switching local stabilization for discrete-time switching systems with nonlinear modes

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