760 research outputs found
Simulation Error Minimization-Based Identification of Polynomial Input-Output Recursive Models
No full textPolynomial input–output recursive models are widely used in nonlinear model identification for their flexibility and representation capabilities. Several identification algorithms are available in the literature dealing both with model selection and parameter estimation, based on various criteria. Previous works have shown the limits of the classical prediction error minimization approach, and suggested the use of a simulation error minimization approach for better model selection. The present paper goes a step further by integrating the model selection procedure with a simulation oriented parameter estimation algorithm. Notwithstanding the algorithmic and computational complexity of the proposed method, it is shown that it can achieve significant performance improvements with respect to previously proposed approaches
Virtual Reference Feedback Tuning for linear discrete-time systems with robust stability guarantees based on Set Membership
No full textIn this paper we propose a novel methodology that allows to design, in a
purely data-based fashion and for linear single-input and single-output
systems, both robustly stable and performing control systems for tracking
piecewise constant reference signals. The approach uses both (i) Virtual
Reference Feedback Tuning for enforcing suitable performances and (ii) the Set
Membership framework for providing a-priori robust stability guarantees.
Indeed, an uncertainty set for the system parameters is obtained through Set
Membership identification, where an algorithm based on the scenario approach is
proposed to estimate the inflation parameter in a probabilistic way. Based on
this set, robust stability conditions are enforced as Linear Matrix Inequality
constraints within an optimization problem whose linear cost function relies on
Virtual Reference Feedback Tuning. To show the generality and effectiveness of
our approach, we apply it to two of the most widely used yet simple control
schemes, i.e., where tracking is achieved thanks to (i) a static feedforward
action and (ii) an integrator in closed-loop. The proposed method is not fully
direct due to the Set Membership identification. However, the uncertainty set
is used with the only objective of providing robust stability guarantees for
the closed-loop system and it is not directly used for the performances
optimization, which instead is totally based on data. The effectiveness of the
developed method is demonstrated with reference to two simulation examples. A
comparison with other data-driven methods is also carried out
Convergence properties of an iterative prediction approach to nonlinear SEM parameter estimation
No full textThis work extends to the nonlinear framework some previous results concerning the convergence of simulation error minimization (SEM) methods for parameter estimation based on an iterative predictor estimation with increasing prediction horizon. Conditions for the applicability of the approach to various model classes, including bilinear, Hammerstein, Wiener and LPV models, are also discussed. The effectiveness of the iterative predictor estimation approach is then shown by means of a simulation example
Identification of Polynomial Input/Output Recursive Models with Simulation Error Minimisation Methods
No full textPolynomial input/output (I/O) recursive models are widely used in nonlinear model identification for their flexibility and representation capabilities. Several identification algorithms are available in the literature, which deal with both model selection and parameter estimation. Previous works have shown the limitations of the classical prediction error minimisation approach in this context, especially (but not only) when the disturbance contribution is unknown, and suggested the use of a simulation error minimisation (SEM) approach for a better selection of the I/O model. This article goes a step further by integrating the model selection procedure with a simulation-oriented parameter estimation algorithm. Notwithstanding the algorithmic and computational complexity of the proposed method, it is shown that it can sometimes achieve great performance improvements
with respect to previously proposed approaches. Two different parameter estimation algorithms are suggested, namely a direct SEM optimisation algorithm, and an approximate method based on multi-step prediction iteration, which displays several convenient properties from the computational point of view. Several simulation examples are shown to demonstrate the effectiveness of the suggested SEM approaches
Distributed state estimation for independent linear systems with relative and absolute measurements
No full textSome convergence properties of multi-step prediction error identification criteria
No full textMulti-step prediction error identification methods are preferred over plain one-step ahead prediction error ones in application contexts (e.g., predictive control) where model accuracy is required over a wide horizon. For sufficiently high prediction horizons, their properties can be shown to be conveniently related to those of output error methods, for which several important issues (e.g., uniqueness of estimation, robustness with respect to the noise model) have been characterized in the literature. The convergence properties of such criteria with respect to the prediction horizon are analyzed
An iterative algorithm for simulation error based identification of polynomial input-output models using multi-step prediction
No full textEffective identification of polynomial input–output models for applications requiring long-range prediction or simulation performance relies on both careful model selection and accurate parameter estimation. The simulation error minimisation (SEM) approach has been shown to provide significant advantages in the model selection phase by ruling out candidate models with good short-term prediction capabilities but unsuitable long-term dynamics. However, SEM-based parameter estimation has been generally avoided due to excessive computational effort. This article extends to the nonlinear case a computationally efficient approach for this task, that was previously developed for linear models, based on the iterative estimation of predictors with increasing prediction horizon. Conditions for the applicability of the approach to various model classes are also discussed. Finally, some examples are provided to show the effectiveness and computational convenience of the proposed algorithm for polynomial input–output identification, as well as the improvements achievable by enforcing SEM parameter estimation. A benchmark for nonlinear identification is also analysed, with encouraging results
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