From Model Reduction to Efficient Predictive Control with Guarantees

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.