Felipe Pait

Parallel algorithms for adaptive control: Robust stability

A class of parallel algorithms for adaptive control of siso linear systems is described. The systems considered are assumed to belong to one among a finite number of classes of admissible process models, and each class is robustly stabilizable by some linear time-invariant controller. The control used is chosen in real time — from among the outputs of a finite set of linear time-invariant candidate controllers — by a tuner or supervisor, according to observations of suitably defined “identification errors.” The method preserves the robustness properties of the linear control design in an adaptive context. We expect that parallel algorithms of the type discussed here will be useful tools to exploit the compromise between performance of an adaptive control system and the computational power of the hardware in which it is implemented. Another application is to fault-tolerant control.

Global tunability of one-dimensional SISO systems

It is shown by example that with a suitably defined certainty equivalence controller Sigma /sub R/, it is possible to make a closed-loop parameterized system Sigma tunable on its entire parameter space P, even though P may contain points at which the parameterized Sigma /sub D/, upon which Sigma /sub R/s definition is based, is not stabilizable. The implications of this discovery are briefly discussed. >

Matchable-Observable Linear Models and Direct Filter Tuning: An Approach to Multivariable Identification

Identification of linear time-invariant multivariable systems can best be understood as comprising three separate problems: selection of system model structure, filter design, and parameter estimation itself. Approaching the first using matchable-observable models originally developed in the adaptive control literature and the second via direct or derivative-free optimization, effective least-squares algorithms can be used for parameter estimation. The accuracy, robustness and moderate computational demands of the methods proposed are demonstrated via simulations with randomly generated models and applied to identification using real process data. The results obtained are comparable or superior to the best results obtained using standard implementations of the algorithms described in the literature.

Multivariable system identification using an output-injection based parameterization

The challenge of identifying multivariable models from input/output data is a subject of great interest, either in scientific works or in industrial plants. The parameterization of multi-output models is considered to be the most crucial task in a MIMO system identification procedure. In this work, a pioneering multivariable identification method is proposed, implemented and evaluated using a linear simulated plant. It is compared to other traditional MIMO identification methods and its results outperformed the other analyzed methods. It was also tested the situation of over-dimensionality of the estimated models, through the use of Hankel singular values and again the proposed method surpassed the other ones in estimating the correct model order.

A cyclic switching strategy for parameter-adaptive control

The authors introduce a strategy called cyclic switching to deal with the well-known certainty equivalence control synthesis problem which arises because of the existence of points in parameter space where the design model Sigma /sub D/ upon which certainty equivalence synthesis is based loses stabilizability. Unlike most previously suggested methods for handling this problem, the technique proposed can be employed with or without excitation. In particular, for the technique to work it is not necessary for there to be a mechanism for moving tuned parameters away from values at which Sigma /sub D/ loses stabilizability, and no such mechanism is in fact used.<<ETX>>

Matchable-observable linear models for multivariable identification: Structure selection and experimental results

Identification of linear time-invariant multivariable systems can best be understood as comprising three separate problems: selection of system model structure, filter design, and parameter estimation itself. In previous contributions we approached the first using matchable-observable models originally developed in the adaptive control literature, and used direct or derivative-free optimization to design filters. In this paper we show a simple and effective structure-selection method and demonstrate its accuracy, robustness and moderate computational demands using data from an industrial evaporator and experimental results with a twin rotor.

Direct filter tuning and optimization in multivariable identification

Identification of linear time-invariant multivariable systems can best be understood as comprising three separate problems: selection of system model structure, filter design, and parameter estimation itself. A previous contribution approaches the first using matchable-observable models originally developed in the adaptive control literature. This paper uses direct or derivative-free optimization to design filters. The accuracy, robustness and moderate computational demands of the methods is demonstrated via simulations with randomly generated models. The results obtained are comparable or superior to the best results obtained using standard implementations of the algorithms described in the literature.

Linear multivariable identification using observable state space parameterizations

The selection of a suitable parameterization for the plant model, a crucial step in the identification of multivariable systems, has direct impact on the numerical properties of the parameter estimation algorithm. We employ a parameterization, particularly suitable for system identification, which has the following properties: observability, match-point controllability, and matchability. Using it, the number of model parameters is kept to a minimum, no undesired pole-zero cancellations can appear, and the use of nonlinear estimation is not necessary. We relate this parameterization to classical autoregressive model structures, and propose an algorithm for parameter estimation. By means of Monte Carlo simulations it is found that the algorithm is promising: fewer data points and lower signal-to-noise ratio are required to obtain results that are similar or better than those obtained by traditional methods.

Reading Wiener in Rio

This self-consciously somewhat rambling paper revisits the connections between the themes of Wieners cybernetics and the social sciences. They seem to be more fruitful in communications and cognition than in feedback control. The phenomena of bubbles and bursts in adaptive control and in financial economies suggest that adaptation is a crucial concept that might serve to rebridge the gaps formed over decades of independent research. Adaptation often involves optimization. The barycenter method is direct optimization technique which may prove useful in extending those employed in adaptive control. It has wider applicability than the better-studied derivative-based methods, and is roughly equivalent to a type of synthetic gradient method. This being a paper about Norbert Wieners work, it concludes with mathematics. We obtain some useful results concerning the barycenter method in a continuous-time framework, which is perhaps more complex but offers a clearer perspective of the relationships with traditional model-based optimization techniques.

Some properties of the Riemannian distance function and the position vector X, with applications to the construction of Lyapunov functions

The quadratic distance function on a Riemannian manifold can be expressed in terms of the position vector, which in turn can be constructed using geodesic normal coordinates through consideration of the exponential map. The formulas for the derivative of the distance are useful to study Lyapunov stability of dynamical systems, and to build cost functions for optimal control and estimation.