Convex relaxation techniques for set-membership identification of LPV systems

Set-membership identification of single-input single-output linear parameter varying models is considered in the paper under the assumption that both the output and the scheduling parameter measurements are affected by bounded noise. First, we show that the problem of computing the parameter uncertainty intervals requires the solutions to a number of nonconvex optimization problems. Then, on the basis of the analysis of the regressor structure, we present some ad hoc convex relaxation schemes to compute parameter bounds by means of semidefinite optimization. Advantages of the new techniques with respect to previously published results are discussed both theoretically and by means of simulations. Index Terms—Bounded error identification, Linear Param- eter Varying, LMI relaxation, Parameters bounds.

...One possible solution to overcome such a problem is to relax the identification problems (12) to convex optimization problems in order to numerically compute lower bounds of θ j as well as upper bounds of θj. It can be shown (see [18]) that (12) are semialgebraic optimization problems with an inherent structured sparsity...
...Proofs of Results 1 and 2 can be found in [18]...
...Proof of Property 1 is based on the fact the set D s is an outer approximation of both D r and D c . Technical details can be found in [18]...
...Besides, when the relative measurement error on both the output wt and on the scheduling variable λt is smaller than 100%, also the sign of yt − ηt and zt − εt, appearing the definition of D c and D r respectively, is known. See [18] for technical details...
...In particular, the number of optimization variables p is O(N (nθ + na) 2δ ), while the size of the LMI describing D pd,δ i is O(N (nθ + na) δ ). See [18] for technical...
...The proof of Properties P4.1 and P4.2 (see [18] for details) follows from properties of monotone converge of sparse LMI-relaxation techniques...

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Convex relaxation techniques for set-membership identification of LPV systems,V. Cerone,D. Piga,D. Regruto

Citation Context (1)

V. Cerone, et al. Convex relaxation techniques for set-membership identification of LPV ...

References (16)

Identification of linear parametrically varying systems (Citations: 20)

Identification of Linear Parameter-Varying Systems Using Nonlinear Programming (Citations: 53)

Identification of linear parameter varying models (Citations: 68)

Subspace identification of multivariable linear parameter-varying systems (Citations: 59)

Subspace identification of MIMO LPV systems using a periodic scheduling sequence (Citations: 37)

Citations (1)

Convex relaxation techniques for set-membership identification of LPV systems (Citations: 1)


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