Zonotope-based set-membership estimation for Multi-Output uncertain systems

Le, Vu Tuan Hieu; Stoica, Cristina; Álamo, T.; Camacho, Eduardo F.; Dumur, Didier

doi:10.1109/isic.2013.6658619

Cited by 28 publications

(28 citation statements)

References 20 publications

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“…Hence, according to [9], it can be generally obtained by λ = HH T C C T HH T C+σ 2 in order to minimize the segments of the zonotope.…”

Section: Direct Imagementioning

confidence: 99%

“…On the other hand, the set-membership state estimation is the other approach for estimating the system state including the measured output and bounded noises [9], [10]. Furthermore, there are several geometrical structures in the literature to compute the set of states in both approaches, e.g., polytopes [11], [12], ellipsoids [13], [14], [15], [16] and zonotopes [17], [18], [9], [19].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, there are several geometrical structures in the literature to compute the set of states in both approaches, e.g., polytopes [11], [12], ellipsoids [13], [14], [15], [16] and zonotopes [17], [18], [9], [19]. Typically, the set approximation is used to reduce the complexity of computing the uncertain state.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparison of set-membership and interval observer approaches for state estimation of uncertain systems

Pourasghar¹,

Puig²,

Ocampo‐Martínez³

2016

2016 European Control Conference (ECC)

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Abstract-This paper presents the analysis and comparison of interval-observer-based and set-membership approaches for the state estimation of linear uncertain systems. In both approaches noise and disturbances are assumed to be unknown but bounded. In this paper, both approaches are compared when implemented using zonotopes. Mathematical expressions of both approaches are compared and conditions under which they provide the same state estimation are derived. At the end, an example based on a two-tanks system is used to test the obtained conditions.

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“…Hence, according to [9], it can be generally obtained by λ = HH T C C T HH T C+σ 2 in order to minimize the segments of the zonotope.…”

Section: Direct Imagementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comparison of set-membership and interval observer approaches for state estimation of uncertain systems

Pourasghar¹,

Puig²,

Ocampo‐Martínez³

2016

2016 European Control Conference (ECC)

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show abstract

“…However, since process disturbances and measurement noises are taken into account, it is impossible to have the real states. Instead, only state estimations can be used to update the MPC controller to generate control actions (see (9)). Due to state estimation errors, the MPC controller cannot always guarantee constraint satisfaction.…”

Section: Constraint Satisfactionmentioning

confidence: 99%

Set‐valued observer‐based active fault‐tolerant model predictive control

Puig

Ocampo‐Martínez

et al. 2016

Optim Control Appl Methods

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This paper proposes an integrated actuator and sensor active fault-tolerant model predictive control (FTMPC) scheme. In this scheme, fault detection (FD) is implemented by using a set-valued observer, fault isolation (FI) is done by set manipulations and faulttolerant control (FTC) is carried out through the design of a robust model predictive control (MPC) law. In this paper, a set-valued observer is used to passively complete the FD task while FI is actively performed by making use of the constraint-handling capability of robust MPC. The set-valued observer is chosen to implement fault detection and isolation (FDI) due to its simple mathematical structure that is not affected by the type of faults such as sensor, actuator and system-structural faults. This means that only one set-valued observer is needed to monitor all considered actuator and sensor statuses (health and fault) and to carry out the FDI task instead of using a bank of observers (each observer matching a health/fault status). Furthermore, in the proposed scheme, the advantage of robust MPC is that it can effectively deal with system constraints, disturbances and noises and allow to implement an active FI strategy, which can improve FI sensitivity when compared with the passive FI methods. Finally, a case study based on the well-known two-tank system is used to illustrate the effectiveness of the proposed FTMPC scheme.

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“…Based on this method, a zonotope containing x i,j,i k d can be constructed by considering (31) composed of q inequalities (i.e., strips). Besides, the method proposed by Le et al (2013) can also be used to construct a zonotopic set containingx i,j,i k d . This method can compute a zonotopic approximation of the intersection of a zonotope and a polytope.…”

Section: Fault Isolation Approachmentioning

confidence: 99%

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

Puig

Ocampo‐Martínez

et al. 2014

53rd IEEE Conference on Decision and Control

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In this paper, a fault-tolerant control (FTC) scheme is proposed for actuator faults, which is built upon tube-based model predictive control (MPC) as well as set-based fault detection and isolation (FDI). In the class of MPC techniques, tubebased MPC can effectively deal with system constraints and uncertainties with relatively low computational complexity compared with other robust MPC techniques such as min-max MPC. Set-based FDI, generally considering the worst case of uncertainties, can robustly detect and isolate actuator faults. In the proposed FTC scheme, fault detection (FD) is passive by using invariant sets, while fault isolation (FI) is active by means of MPC and tubes. The active FI method proposed in this paper is implemented by making use of the constraint-handling ability of MPC to manipulate the bounds of inputs. After the system has been detected to become faulty, the input-constraint set of the MPC controller is adjusted to actively excite the system for achieving FI guarantees on-line, where an active FI-oriented input set is designed off-line. In this way, the system can be excited in order to obtain more extra system-operating information for FI than passive FI approaches. Overall, the objective of this paper is to propose an actuator MPC scheme with as little as possible of FI conservatism and computational complexity by combining tube-based MPC and set theory within the framework of MPC, respectively. Finally, a case study is used to show the effectiveness of the proposed FTC scheme.

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Zonotope-based set-membership estimation for Multi-Output uncertain systems

Cited by 28 publications

References 20 publications

Comparison of set-membership and interval observer approaches for state estimation of uncertain systems

Comparison of set-membership and interval observer approaches for state estimation of uncertain systems

Set‐valued observer‐based active fault‐tolerant model predictive control

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

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