From Model Reduction to Efficient Predictive Control with Guarantees
Martin Löhning
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Martin Löhning, From Model Reduction to Efficient Predictive Control with Guarantees (2022), Logos Verlag, Berlin, ISBN: 9783832584764
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Description / Abstract
High-dimensional dynamic models frequently occur in many
practical problems. Using these models is often computationally
intractable. For instance, analysis via repeated simulations or
control design. In this book, several algorithms relying on model
reduction are proposed to deal with the high-dimensionality of
these models.
The main contribution is a novel model predictive control
scheme, which uses reduced models for linear time-invariant
systems. An intermediate result is a generalized bound for the
error between the high-dimensional and the reduced model,
while simulating the reduced model. This error bounding system
is included in the model predictive control scheme in order to
guarantee 1) asymptotic stability, 2) satisfaction of hard input
and state constraints, 3) a bound for the cost functional value,
and 4) minimization of the infinite horizon cost functional for the
high-dimensional model. For discrete-time models, it is shown
that the optimization problem of the model predictive control
scheme can be reformulated as a second-order cone program.
The applicability of the proposed methods is demonstrated by
means of a nonisothermal tubular chemical reactor.
A further contribution is a model reduction procedure, which
approximates the input-output map of continuous-time nonlinear
ordinary differential equations. This method allows to
preserve the location and local exponential stability of multiple
steady states.
practical problems. Using these models is often computationally
intractable. For instance, analysis via repeated simulations or
control design. In this book, several algorithms relying on model
reduction are proposed to deal with the high-dimensionality of
these models.
The main contribution is a novel model predictive control
scheme, which uses reduced models for linear time-invariant
systems. An intermediate result is a generalized bound for the
error between the high-dimensional and the reduced model,
while simulating the reduced model. This error bounding system
is included in the model predictive control scheme in order to
guarantee 1) asymptotic stability, 2) satisfaction of hard input
and state constraints, 3) a bound for the cost functional value,
and 4) minimization of the infinite horizon cost functional for the
high-dimensional model. For discrete-time models, it is shown
that the optimization problem of the model predictive control
scheme can be reformulated as a second-order cone program.
The applicability of the proposed methods is demonstrated by
means of a nonisothermal tubular chemical reactor.
A further contribution is a model reduction procedure, which
approximates the input-output map of continuous-time nonlinear
ordinary differential equations. This method allows to
preserve the location and local exponential stability of multiple
steady states.
Table of content
- BEGINN
- Acknowledgments
- Table of Contents
- List of Figures
- List of Tables
- List of Abbreviations
- List of Symbols
- Abstract
- Deutsche Kurzfassung
- Introduction
- Motivation
- Overview of the Research Area
- Contributions of the Thesis
- Design Workflow of the Proposed Model Predictive Control Scheme
- Outline of the Thesis
- Background
- Model Reduction
- A-Posteriori Bounds for the Model Reduction Error
- Model Predictive Control
- Nonisothermal Tubular Chemical Reactor
- Trajectory-Based Model Reduction for Nonlinear Systems
- Problem Statement
- Procedure of Trajectory-Based Model Reduction
- Preserving Stability in Trajectory-Based Model Reduction
- Comparison with Approaches Relying Only on Simulated Trajectories
- Summary
- A-Posteriori Bound for the Model Reduction Error
- Problem Statement
- Preprocessing of the Plant
- A Bound for the Norm of the Matrix Exponential
- Asymptotically Stable Error Bounding System
- Example: Tubular Reactor
- Summary
- MPC Using Reduced Models for Continuous-Time Systems
- Problem Statement
- Preprocessing and Model Reduction
- Guaranteeing Constraint Satisfaction
- MPC Scheme Using the Reduced Model and Error Bound
- Eliminating the Model Reduction Error in the Cost Functional
- Guaranteeing Asymptotic Stability
- Relation to Existing Approaches
- Example: Tubular Reactor
- Summary
- MPC Using Reduced Models for Discrete-Time Systems
- Problem Statement
- MPC Scheme Using the Reduced Model and Error Bound
- Equivalence of the Optimization Problem to a Second-Order Cone Problem
- Example: Tubular Reactor
- Summary
- Conclusions
- Summary
- Outlook
- Linearization and Spatial Discretization of the Tubular Reactor
- Model of the MAPK Cascade
- Application of the MPC Schemes to a Two-Dimensional System
- Problem Setup
- Design of the Model Predictive Controllers
- Time Response
- Asymptotic Stability
- Performance
- Region of Attraction
- Bibliography