Eckhard, D.
2012.
Ferramentas para melhoria da convergência dos métodos de identificação por erro de predição. , Porto Alegre: Universidade Federal do Rio Grande do Sul
AbstractThe Prediction Error Method is related to a non-convex optimization problem. It is usual to apply iterative algorithms to solve this optimization problem. However, iterative algorithms can get stuck at a local minimum of the cost function or converge to the border of the searching space. An analysis of the cost function and sufficient conditions to ensure the convergence of the iterative algorithms to the global minimum are presented in this work. It is observed that this conditions depend on the spectrum of the input signal used in the experiment. This work presents tools to improve the convergence of the algorithms to the global minimum, which are based on the manipulation of the input spectrum.
Campestrini, L, Eckhard D, Konrad O, Bazanella AS.
2012.
Identificação não-linear de um biorreator através da minimização do erro de predição. XIX Congresso Brasileiro de Automática. :3066–3072., Campina Grande: SBA
AbstractThis work presents a non-linear identification of a bioreactor through the minimization of the prediction error, where the output data are the measurements of the methane gas generated by the process, during 37 days. Since the chosen model is non-linear, an iterative method is used to obtain the model parameters. This method depends on the cost function?s gradient, whose calculus is implemented recursively, since it does not have a closed form. The algorithm used in the minimization of the cost function is a combination of two methods: the gradient method and the Newton-Raphson method. The model obtained is validated with output data from the process and it reproduces the behavior of the bioreactor with good precision.
Eckhard, D, Hjalmarsson H, Rojas C, Gevers M.
2012.
Mean-Squared Error Experiment Design for Linear Regression Models. 16th {IFAC} Symposium on System Identification. :1629–1634., Brussels: IFAC
AbstractThis work solves an experiment design problem for a linear regression problem using a reduced order model. The quality of the model is assessed using a mean square error measure that depends linearly on the parameters. The designed input signal ensures a predefined quality of the model while minimizing the input energy.
Campestrini, L, Eckhard D, Bazanella AS, Gevers M.
2012.
Model Reference Control Design by Prediction Error Identification. 16th {IFAC} Symposium on System Identification. :1478–1483., Brussels: IFAC
AbstractThis paper studies a one-shot (non-iterative) data-based method for Model Reference (MR) control design. It shows that the optimal controller can be obtained as the solution of a Prediction Error (PE) identification problem that directly estimates the controller parameters through a reparametrization of the input-output model. The standard tools of PE Identification can thus be used to analyze the statistical properties (bias and variance) of the estimated controller. It also shows that, for MR control design, direct and indirect data-based methods are essentially equivalent.
Eckhard, D, Bazanella AS, Rojas C, Hjalmarsson H.
2012.
On the Convergence of the Prediction Error Method to Its Global Minimum. 16th {IFAC} Symposium on System Identification. :698–703., Brussels: IFAC
AbstractThe Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The existence of local minima, and hence the difficulty in solving the optimization, depends mainly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. It is therefore possible to avoid the existence of local minima by properly choosing the spectrum of the input; in this paper we show how to perform this choice. We present sufficient conditions for the convergence of PEM to the global minimum and from these conditions we derive two approaches to avoid the existence of nonglobal minima. We present the application of one of these two approaches to a case study where standard identification toolboxes tend to get trapped in nonglobal minima.
Eckhard, D, Bazanella AS.
2012.
Optimizing the convergence of data-based controller tuning. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering. 226:563–574., Number 4
AbstractData-based control design methods most often consist of iterative adjustment of the controller?s parameters towards the parameter values which minimize an Formula performance criterion. Typically, batches of input-output data collected from the system are used to feed directly a gradient descent optimization algorithm ? no process model is used. Two topics are important regarding this algorithm: the convergence rate and the convergence to the global minimum. This paper discusses these issues and provides a method for choosing the step size to ensure convergence with high convergence rate, as well as a test to verify at each step whether or not the algorithm is converging to the global minimum.
Eckhard, D, Bazanella AS.
2012.
Robust convergence of the steepest descent method for data-based control. International Journal of Systems Science. 43:1969–1975., Number 10
AbstractIterative data-based controller tuning consists of iterative adjustment of the controller parameters towards the parameter values which minimise an {H2} performance criterion. The convergence to the global minimum of the performance criterion depends on the initial controller parameters and on the step size of each iteration. This article presents convergence properties of iterative algorithms when they are affected by disturbances.