Guaranteed State and Parameter Estimation for Nonlinear Continuous-Time Systems with Bounded-Error Measurements

Lin, Youdong; Stadtherr, Mark A.

doi:10.1021/ie0707725

Cited by 32 publications

(34 citation statements)

References 21 publications

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“…Numerical examples demonstrate that this approach provides a very effective way to determine tight enclosures of all possible solutions to parametric ODEs. The method presented, as implemented in VSPODE, is now being used in a number of practical applications, including simulation of bioreactors with parametric uncertainties [13], model-based fault diagnosis [14], deterministic global optimization for fitting time series data [10] and for optimal control [12], and state and parameter estimation for nonlinear, continuoustime systems [11]. Information about the availability of the VSPODE code can be obtained by contacting the authors.…”

Section: Discussionmentioning

confidence: 99%

Validated solutions of initial value problems for parametric ODEs

Lin

Stadtherr

2007

Applied Numerical Mathematics

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169

195

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In initial value problems for ODEs with interval-valued parameters and/or initial values, it is desirable in many applications to be able to determine a validated enclosure of all possible solutions to the ODE system. Much work has been done for the case in which initial values are given by intervals, and there are available software packages that deal with this case. However, less work has been done on the case in which parameters are given by intervals. We describe here a new method for obtaining validated solutions of initial value problems for ODEs with interval-valued parameters. The method also accounts for interval-valued initial values. The effectiveness of the method is demonstrated using several numerical examples involving parametric uncertainties.

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Section: Discussionmentioning

confidence: 99%

Validated solutions of initial value problems for parametric ODEs

Lin

Stadtherr

2007

Applied Numerical Mathematics

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169

195

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“…We then fixed the Taylor model order at q = 3 and considered different ITS truncation orders κ, with results shown in Table 10, again for p ≤ 4. The ranges of the κ and q values used covers values that we have found useful in various other applications 33,34,55,56,63 involving VSPODE. For each value of p, the ǫ-global optimum found is the same, within the ǫ tolerance, for all the combinations of κ and q values.…”

Section: Example 3: Parallel Reactions In An Isothermal Semi-batch Rementioning

confidence: 99%

“…43,44,54 It is widely used in various forms in connection with interval methods. It has been shown previously how efficient constraint propagation schemes, based on hull consistency and using Taylor models, can be developed for inequality constraints, 32 bound constraints, 55 and equality constraints. 56 In the method described below, we use the procedure given by Lin and Stadtherr 32 for constraint propagation with Taylor models on an inequality constraint c(x) ≤ 0, with x ∈ X.…”

Section: Constraint Propagation With Taylor Modelsmentioning

confidence: 99%

Rigorous Global Optimization for Dynamic Systems Subject to Inequality Path Constraints

Zhao

Stadtherr

2011

Ind. Eng. Chem. Res.

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A new approach is described for the rigorous global optimization of dynamic systems subject to inequality path constraints (IPCs). This method employs the sequential (control parameterization) approach and is based on techniques developed for the verified solution of parametric systems of ordinary differential equations. These techniques provide rigorous interval bounds on the state variables, and thus on the path constraints and objective function in the dynamic optimization problem. These techniques also provide explicit analytic representations (Taylor models) of these bounds in terms of the decision variables in the optimization problem. This facilitates the use of constraint propagation techniques that can greatly reduce the domain to be searched for the global optimum. Since IPCs are often related to safety concerns, we adopt a conservative, innerapproximation approach to constraint satisfaction. Through this approach, the search for the global optimum is restricted to a space in which continuous satisfaction of the IPCs is rigorously guaranteed, and an ǫ-global optimum within this space is determined. Examples are presented that demonstrate the potential and computational performance of this approach.

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“…The first issue was addressed recently, e.g., in Lin and Stadtherr [2007b] and Paulen et al [2013], by applying novel bounding techniques for parametric dynamic systems based on Taylor model arithmetic or ellipsoidal calculus. Large improvements of the rate of convergence of the set-inversion algorithm could be obtained this way.…”

Section: Introductionmentioning

confidence: 99%

Optimization-based Domain Reduction in Guaranteed Parameter Estimation of Nonlinear Dynamic Systems

Paulen

Villanueva

Chachuat

2013

IFAC Proceedings Volumes

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This paper is concerned with guaranteed parameter estimation in nonlinear dynamic systems in a context of bounded measurement error. The problem consists of finding-or approximating as closely as possible-the set of all possible parameter values such that the predicted outputs match the corresponding measurements within prescribed error bounds. An exhaustive search procedure is applied, whereby the parameter set is successively partitioned into smaller boxes and exclusion tests are performed to eliminate some of these boxes, until a prespecified threshold on the approximation level is met. In order to enhance the convergence of this procedure, we investigate the use of optimization-based domain reduction techniques for tightening the parameter boxes before partitioning. We construct such bound-reduction problems as linear programs from the polyhedral relaxation of Taylor models of the predicted outputs. When applied to a simple case study, the proposed approach is found to reduce the computational burden significantly, both in terms of CPU time and number of iterations.

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Guaranteed State and Parameter Estimation for Nonlinear Continuous-Time Systems with Bounded-Error Measurements

Cited by 32 publications

References 21 publications

Validated solutions of initial value problems for parametric ODEs

Validated solutions of initial value problems for parametric ODEs

Rigorous Global Optimization for Dynamic Systems Subject to Inequality Path Constraints

Optimization-based Domain Reduction in Guaranteed Parameter Estimation of Nonlinear Dynamic Systems

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