Interval Techniques for Design of Optimal and Robust Control Strategies

Rauh, Andreas; Minisini, Johanna; Hofer, Eberhard P.

doi:10.1109/scan.2006.27

Cited by 8 publications

(7 citation statements)

References 14 publications

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“…The computational efficiency of this approach will be demonstrated through application to benchmark problems, including optimal control problems. In the context of optimal control, a global minimization algorithm based on different validated ODE solvers has recently been presented by Rauh et al18…”

Section: Introductionmentioning

confidence: 99%

Deterministic global optimization of nonlinear dynamic systems

Lin

Stadtherr

2007

AIChE Journal

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A new approach is described for the deterministic global optimization of dynamic systems, including optimal control problems. The method is based on interval analysis and Taylor models and employs a type of sequential approach. A key feature of the method is the use of a new validated solver for parametric ODEs, which is used to produce guaranteed bounds on the solutions of dynamic systems with interval-valued parameters. This is combined with a new technique for domain reduction based on the use of Taylor models in an efficient constraint propagation scheme. The result is that an -global optimum can be found with both mathematical and computational certainty.Computational studies on benchmark problems are presented showing that this new approach provides significant improvements in computational efficiency, well over an order of magnitude in most cases, relative to other recently described methods.

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Section: Introductionmentioning

confidence: 99%

Deterministic global optimization of nonlinear dynamic systems

Lin

Stadtherr

2007

AIChE Journal

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“…The integrand f 0 x(t), p(t), u(t), t quantifies both deviations of the current states from the desired trajectories of the state variables and the required control effort u(t). A general framework for interval arithmetic structure and parameter optimization for dynamic systems with both nominal and uncertain parameters was presented Rauh et al, 2007d). Using the definition of optimality for uncertain systems introduced therein, a control strategy is optimal if it leads to the smallest upper bound of the performance index for all possible p ∈ [p].…”

Section: Integration In An Interval Arithmetic Framework For the Desimentioning

confidence: 99%

“…Combinations with optimality criteria and the definition of bounds for the admissible range of control inputs which lead to further constraints on both the parameters of controllers with a predefined structure and to constraints on the controller structure itself are usually not considered. First approaches leading in this direction were proposed in (Rauh and Hofer, 2005;Rauh et al, 2007d;. In these articles, interval arithmetic procedures for the design of controllers for linear as well as nonlinear dynamical systems with uncertainties were developed.…”

mentioning

confidence: 99%

Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with Uncertainties

Rauh

Minisini

Hofer

2009

International Journal of Applied Mathematics and Computer Science

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Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.

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“…Finally, VALENCIA-IVP is a promising approach for improvement of enclosure quality and reduction of computing time in interval arithmetic procedures for dynamical optimization. A general framework for the design of robust and optimal control strategies using validated IVP solvers has been presented in [3]. In this optimization procedure, guaranteed enclosures of the state variables and the cost function are computed.…”

Section: Application Of Valencia-ivp To Dae Systems and Dynamical Optmentioning

confidence: 99%

Extensions of ValEncIA‐IVP for reduction of overestimation, for simulation of differential algebraic systems, and for dynamical optimization

Rauh

Auer

Minisini

et al. 2007

Proc Appl Math and Mech

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1BasicTypeofStateEnclosuresforVALENCIA-IVPVALENCIA-IVPiscapableofcalculatingguaranteedintervalenclosuresofallreachablestatesofdynamicalsystemsdescribedbyODEs,seehttp://www.valencia-ivp.com.Itisassumedthatthestatevector x (t ) ∈ R n ofasetof ODEs ˙x (t ) = f (x ( t ) , t ) consistsoftheactualsystemstatesandalluncertain(possiblytime-varying)parameters.LetaninitialvalueproblemIVPbedefinedfor ˙x (t ) = f (x ( t ) , t ),wheretheinitialstateisboundedbyanintervalboxarecomputedbyafixed-pointiterationaccordingto Ṙ ( κ + 1) (t ) = − ˙x app (t ) + f x app (t ) + R (κ ) (t ) , t = : r R ( κ ) (t ) , t .(Inthisiteration,theintervalbounds [R (t )] aredeterminedbyvalidatedintegrationofthecorrespondingtimederivatives [1,2].

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Interval Techniques for Design of Optimal and Robust Control Strategies

Cited by 8 publications

References 14 publications

Deterministic global optimization of nonlinear dynamic systems

Deterministic global optimization of nonlinear dynamic systems

Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with Uncertainties

Extensions of ValEncIA‐IVP for reduction of overestimation, for simulation of differential algebraic systems, and for dynamical optimization

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