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.