Truncated program lines

Although line searches are typically easier to program, trust region methods may be effective when the procedure for determining the search direction p is not necessarily one of descent. This may be the case for methods that use finite-difference approximations to the Hessian in the procedure for specifying p (discussed in later sections). As we shall see later, in BFGS quasi-Newton or truncated Newton methods line searches may be preferable because descent directions are guaranteed. 

In this paper we present a Model Reduction technique incorporated with multi-parametric programming and control, namely Balanced Truncation (T3T). The use of Balanced Truncation eliminates a number of states of dynamic linear systems, while a bound on the maximum error obtained for the output vector can be established. This then allows for the derivation of (approximate) linear parametric controllers, which can be tested and validated (against the original high-fidelity model) off-line. These theoretical developments are presented next. 

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