Set-valued state estimation of nonlinear discrete-time systems with nonlinear invariants based on constrained zonotopes

Rego, Brenner S.; Scott, Joseph K.; Raimondo, Davide M.; Raffo, Guilherme V.

doi:10.1016/j.automatica.2021.109638

Cited by 25 publications

(10 citation statements)

References 42 publications

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“…with Z w defined as in the statement of the corollary (this CZ can be obtained analogously to Remark 4 in Rego et al (2021)), which proves the corollary.…”

Section: Nonlinear Systems With Linear Output Equationsupporting

confidence: 63%

“…As in the linear case (8), the objective is to enclose the trajectories of (13) as accurately as possible by a set Ẑk ⊂ R n+n p for any k ≥ 0. This is accomplished by extending the method proposed in Rego et al (2021) to a joint state and parameter estimation framework to allow the refinement of the parameter enclosure P over time, as well as to preserve the couplings between states and parameters. The proposed predictionupdate scheme is given by…”

Section: Nonlinear Systems With Linear Output Equationmentioning

confidence: 99%

“…As in the previous case, the scheme is initialized with Z0 X0 × P in the joint update step. We first extend the prediction method described by Proposition 1 in Rego et al (2021) to consider both states and model parameters in a more general framework. This result will be necessary for the nonlinear joint state and parameter estimation method developed in this section.…”

Section: Nonlinear Systems With Linear Output Equationmentioning

confidence: 99%

“…Choose any (x, p, w) ∈ X × P × W. Let r (x, p), γ r (γ x , γ p ), R X×P. Lemma 1 in Rego et al (2021) (with α f, x r, γ x γ r , and X R) ensures that there exists a real matrix Ĵ ∈ J such that f(x, u, p, w) = f(γ x , u, γ p , w) + Ĵ(z − γ z ), with z = (x, p). By Theorem 1 and the choice of Z w , it follows that f(x, u, p, w) ∈ Z w ⊕ (J, Z − γ z ), as desired.…”

Section: Nonlinear Systems With Linear Output Equationmentioning

confidence: 99%

“…The work presented in this note proposes a method for setbased joint state and parameter estimation of discrete-time systems. The strategy extends the algorithms based on constrained zonotopes (CZs) proposed in Scott et al (2016) and Rego et al (2021), to include parameter estimation in a unified framework for the first time. In contrast to interval-based methods 1 , this framework implemented using CZs allows the estimated enclosures to propagate existing dependencies between states and model parameters.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Joint state and parameter estimation based on constrained zonotopes

Rego¹,

Locatelli²,

Raimondo³

et al. 2022

Preprint

Self Cite

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This note presents a new method for set-based joint state and parameter estimation of discrete-time systems using constrained zonotopes. This is done by extending previous set-based state estimation methods to include parameter identification in a unified framework. Unlike in interval-based methods, the existing dependencies between states and model parameters are maintained from one time step to the next, thus providing a more accurate estimation scheme. In addition, the enclosure of states and parameters is refined using measurements through generalized intersections, which are properly captured by constrained zonotopes. The advantages of the new approach are highlighted in two numerical examples.

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“…with Z w defined as in the statement of the corollary (this CZ can be obtained analogously to Remark 4 in Rego et al (2021)), which proves the corollary.…”

Section: Nonlinear Systems With Linear Output Equationsupporting

confidence: 63%

Section: Nonlinear Systems With Linear Output Equationmentioning

confidence: 99%

Section: Nonlinear Systems With Linear Output Equationmentioning

confidence: 99%

Section: Nonlinear Systems With Linear Output Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Joint state and parameter estimation based on constrained zonotopes

Rego¹,

Locatelli²,

Raimondo³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Set-Membership Filtering for 2-D Systems with State Constraints Under the FlexRay Protocol

Liang

2023

Lecture Notes in Networks and Systems

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Reducing the wrapping effect of set computation via Delaunay triangulation for guaranteed state estimation of nonlinear discrete-time systems

Wan,

Jaulin

2024

Computing

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Set computation methods have been widely used to compute reachable sets, design invariant sets and estimate system state for dynamic systems. The wrapping effect of such set computation methods plays an essential role in the accuracy of their solutions. This paper studies the wrapping effect of existing interval, zonotopic and polytopic set computation methods and proposes novel approaches to reduce the wrapping effect for these set computation methods based on the task of computing the dynamic evolution of a nonlinear uncertain discrete-time system with a set as the initial state. The proposed novel approaches include the partition of a polytopic set via Delaunay triangulation and also the representation of a polytopic set by the union of small zonotopes for the following set propagation. The proposed novel approaches with the reduced wrapping effect has been further applied to state estimation of a nonlinear uncertain discrete-time system with improved accuracy. Similar to bisection for interval and zonotopic sets, Delaunay triangulation has been introduced as a set partition tool for polytopic sets, which has opened new research directions in terms of novel set partition, set representation and set propagation for reducing the wrapping effect of set computation.

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Set-valued state estimation of nonlinear discrete-time systems with nonlinear invariants based on constrained zonotopes

Cited by 25 publications

References 42 publications

Joint state and parameter estimation based on constrained zonotopes

Joint state and parameter estimation based on constrained zonotopes

Set-Membership Filtering for 2-D Systems with State Constraints Under the FlexRay Protocol

Reducing the wrapping effect of set computation via Delaunay triangulation for guaranteed state estimation of nonlinear discrete-time systems

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