Flatness-based constrained optimal control of reaction-diffusion systems

Andrej, Julian; Meurer, Thomas

doi:10.23919/acc.2018.8431201

Cited by 7 publications

(3 citation statements)

References 20 publications

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“…Here the penalty parameter is chosen such that the initial acceleration and final deceleration are not penalized, i.e., c 1 (t < 10 s ∨ t > 110 s) = 0 and c 1 (10 s ≤ t ≤ 110 s) = 10. The results of a cross-evaluation of the energy and distance measure, given by the integral over ( 5) and (15) with c 1 (t) = 0, ∀t, are given in Table III. While the path lengths differ only slightly, the difference in actuator energy cost is significant.…”

Section: Simulation Resultsmentioning

confidence: 99%

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Optimal Trajectory Planning and Model Predictive Control of Underactuated Marine Surface Vessels using a Flatness-Based Approach

Lutz

Meurer

2021

2021 American Control Conference (ACC)

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This paper demonstrates a refined approach to solving dynamic optimization problems for underactuated marine surface vessels. To this end the differential flatness of a mathematical model assuming full actuation is exploited to derive an efficient representation of a finite dimensional nonlinear programming problem, which in turn is constrained to apply to the underactuated case. It is illustrated how the properties of the flat output can be employed for the generation of an initial guess to be used in the optimization algorithm in the presence of static and dynamic obstacles. As an example energy optimal point to point trajectory planning for a nonlinear 3 degrees of freedom dynamic model of an underactuated surface vessel is undertaken. Input constraints, both in rate and magnitude as well as state constraints due to convex and non-convex obstacles in the area of operation are considered and simulation results for a challenging scenario are reported. Furthermore, an extension to a trajectory tracking controller using model predictive control is made where the benefits of the flatness based direct method allow to introduce nonuniform sample times that help to realize long prediction horizons while maintaining short term accuracy and real time capability. This is also verified in simulation where additional disturbances in the form of environmental disturbances, dynamic obstacles and parameter mismatch are introduced.

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Section: Simulation Resultsmentioning

confidence: 99%

“…In those works an ansatz with basis functions for the highest derivative of the flat output is made, whereas [12] uses a piecewise constant function for this purpose. This is also used in the context of distributed parameter systems, e.g, by [15].…”

Section: Introductionmentioning

confidence: 99%

Optimal Trajectory Planning and Model Predictive Control of Underactuated Marine Surface Vessels using a Flatness-Based Approach

Lutz

Meurer

2021

2021 American Control Conference (ACC)

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“…Alternatively, a transformation approach exists to bypass points of a singularity [43]. In addition to differential flatness of ODE systems, flatness-based methods are also being used for discrete-time systems and partial differential equations (PDEs); see [44][45][46], and references within. Application scenarios based on differential flatness cover predominantly (electro)mechanical problems, but also process technologies like heat exchangers [47], crystallizers [48] or (bio)reactors [45,49], lithium-ion batteries [50], and more.…”

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confidence: 99%

Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Schulze

Schenkendorf

2020

Processes

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Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty.

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Motion Planning for PDEs

Meurer

2019

Encyclopedia of Systems and Control

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Flatness-based constrained optimal control of reaction-diffusion systems

Cited by 7 publications

References 20 publications

Optimal Trajectory Planning and Model Predictive Control of Underactuated Marine Surface Vessels using a Flatness-Based Approach

Optimal Trajectory Planning and Model Predictive Control of Underactuated Marine Surface Vessels using a Flatness-Based Approach

Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Motion Planning for PDEs

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