Robust optimization of nonlinear dynamic systems with application to a jacketed tubular reactor

Houska, Boris; Logist, Filip; Impe, Jan Van; Diehl, Moritz

doi:10.1016/j.jprocont.2012.03.008

Cited by 65 publications

(60 citation statements)

References 35 publications

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“…This latter approach was recently extended to enable convex and concave bounds in [49] using so-called McCormick-Taylor models [50]. The computation of guaranteed state bounds has also been considered in different contexts, including reachability analysis and robust control [51][52][53]. In principle, such ellipsoidal bounds could be used in global optimal control methods too, although there seems to be no literature on this yet.…”

Section: Output: Lower and Upper Boundsmentioning

confidence: 99%

Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

Houska

Chachuat

2013

J Optim Theory Appl

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This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example.

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Section: Output: Lower and Upper Boundsmentioning

confidence: 99%

Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

Houska

Chachuat

2013

J Optim Theory Appl

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“…A technique for computing ellipsoidal enclosures for the solution set of nonlinear parametric ODEs was recently proposed by [8]. Theorem 3: Consider the parametric ODEs (1), where f :…”

Section: Ellipsoidal-based Boundsmentioning

confidence: 99%

“…In response to this, approximate methods that overestimate the solution set of parametric ordinary differential equations (ODEs), yet provide sufficiently tight bounds, have been developed over the years. These methods differ in the shape of the enclosing sets, for instance interval boxes [3], [4], Taylor models [5]- [7] or ellipsoids [8], and also in the way these sets are propagated through the flow of the ODEs. Interval bounds derived from Taylor models were first used by Lin and Stadtherr [9] in the context of guaranteed parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

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Guaranteed parameter estimation in nonlinear dynamic systems using improved bounding techniques

Paulen

Villanueva²,

Fikar

et al. 2013

2013 European Control Conference (ECC)

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Abstract-This paper is concerned with guaranteed parameter estimation in nonlinear dynamic systems in a context of bounded measurement error. The problem consists of findingor 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. Exclusion tests rely on the ability to bound the solution set of the dynamic system for a given parameter subset and the tightness of these bounds is therefore paramount. Equally important is the time required to compute the bounds, thereby defining a trade-off. It is the objective of this paper to investigate this trade-off by comparing various bounding techniques based on interval arithmetic, Taylor model arithmetic and ellipsoidal calculus. When applied to a simple case study, ellipsoidal and Taylor model approaches are found to reduce the number of iterations significantly compared to interval analysis, yet the overall computational time is only reduced for tight approximation levels due to the computational overhead.

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“…Introduction. Set-valued integration methods for uncertain or parameterdependent dynamic systems find applications in many research areas, including reachability and invariance analysis for control systems, robust optimization and control, set-membership estimation, and global optimization; see, e.g., [5,9,18,19,22,26,36,48,50]. One possible classification for such methods distinguishes continuous-time and discretized approaches.…”

mentioning

confidence: 99%

Sensitivity Analysis of Uncertain Dynamic Systems Using Set-Valued Integration

Perić¹,

Villanueva²,

Chachuat³

2017

SIAM J. Sci. Comput.

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Abstract. We present an extension of set-valued integration to enable efficient sensitivity analysis of parameter-dependent ordinary differential equation (ODE) systems, using both the forward and adjoint methods. The focus is on continuous-time set-valued integration, whereby auxiliary ODE systems are derived whose solutions describe high-order inclusions of the parametric trajectories in the form of polynomial models. The forward and adjoint auxiliary ODE systems treat the parameterization error of the original differential variables as a time-varying uncertainty, and propagate the sensitivity bounds forward and backward in time, respectively. This construction enables building on the sensitivity analysis capabilities of state-of-the-art solvers, such as CVODES in the SUNDIALS suite. Several numerical case studies are presented to assess the performance and accuracy of these set-valued sensitivity integrators.

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Robust optimization of nonlinear dynamic systems with application to a jacketed tubular reactor

Cited by 65 publications

References 35 publications

Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

Guaranteed parameter estimation in nonlinear dynamic systems using improved bounding techniques

Sensitivity Analysis of Uncertain Dynamic Systems Using Set-Valued Integration

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