Information-based complexity and nonparametric worst-case system identification
Journal of Complexity - Special issue: invited articles dedicated to J. F. Traub on the occasion of his 60th birthday
Worst-case control-relevant identification
Automatica (Journal of IFAC) - Special issue on trends in system identification
Modelling of uncertain systems via linear programming
Automatica (Journal of IFAC)
On approximation of stable linear dynamical systems using Laguerre and Kautz functions
Automatica (Journal of IFAC)
Bounded Power Signal Spaces for Robust Control and Modeling
SIAM Journal on Control and Optimization
Alpha-stable signals and adaptive filtering
IEEE Transactions on Signal Processing
Analytic alpha-stable noise modeling in a Poisson field ofinterferers or scatterers
IEEE Transactions on Signal Processing
On linear models for nonlinear systems
Automatica (Journal of IFAC)
Universal approximation bounds for superpositions of a sigmoidal function
IEEE Transactions on Information Theory
LTI approximation of nonlinear systems via signal distribution theory
Automatica (Journal of IFAC)
Measuring a linear approximation to weakly nonlinear MIMO systems
Automatica (Journal of IFAC)
Least-squares LTI approximation of nonlinear systems and quasistationarity analysis
Automatica (Journal of IFAC)
Linear approximations of nonlinear FIR systems for separable input processes
Automatica (Journal of IFAC)
LTI modelling of NFIR systems: near-linearity and control, LS estimation and linearization
Automatica (Journal of IFAC)
Hi-index | 22.15 |
Optimal squared error and absolute error-based approximation problems for static polynomial models of nonlinear, discrete-time, systems are studied in detail. These problems have many similarities with other linear-in-the-parameters approximation problems, such as with optimal approximation problems for linear time-invariant models of linear and nonlinear systems. Nonprobabilistic signal analysis is used. Close connections between the studied approximation problems and certain classical topics in approximation theory, such as optimal L"2(-1,1) and L"1(-1,1) approximation, are established by analysing conditions under which sample averages of static nonlinear functions of the input converge to appropriate Riemann integrals of the static functions. These results should play a significant role in the analysis of corresponding system identification and model validation problems. Furthermore, these results demonstrate that optimal modelling based on the absolute error can offer advantages over squared error-based modelling. Especially, modelling problems in which some signals possess heavy tails can benefit from absolute value-based signal and error analysis.