| A. R. Teel, "Toward larger domains of attraction for local nonlinear control schemes," In Proceedings of the European Control Conference, 1991. |
....Due to its non linearity, the ball and beam problem has been addressed quite often in the control systems literature. The most common demonstration is that of tracking a sinusoidally moving set point. These results for our system are included for comparison with the published results of [Cas90, Tee91, HSK92, HR92] who use similar ball and beam dynamics. The sinusoidal set point which we will employ is s(t) 0:375 sin(2 t T ) where T is the period of oscillation. Thus this sinusoid moves between s 1 and s 3 of the previous experiment. Again, we start the output matrix at all zeros ....
....by the uncompressed and compressed rules and how this difference might affect control performance. 10.2. 2 Connection to Control Theory There are a number of papers citing similar performance on the sinusoid tracking problem with the same simulated ball and beam system we have presented [Cas90, Tee91, HSK92, HR92] It would be interesting to determine if the learning system has discovered a strategy similar to one of those suggested by these authors. 10.2.3 Dependent Rule Inference Scheme The fact that there is any difference at all between the performance of the compressed and uncompressed ....
A. R. Teel, "Toward larger domains of attraction for local nonlinear control schemes," In Proceedings of the European Control Conference, 1991.
....nut to crack. Early progress was made by the nonlinear regulator approach of Isidori Byrnes [Isidori and Byrnes, 1990] which extended to the nonlinear case results of the Francis Wonham regulator. Some drawbacks of this approach were the assumption of an exo system and small domains of attraction [Teel, 1991]. A major advance in a general framework for tracking for nonminimum phase systems was made in a collection of papers by Devasia, Paden and Chen [Devasia et al. 1996] Devasia and Paden, 1994] in which they provide a non causal exact tracking compensator for nonlinear (possibly multi input ....
A. Teel. Toward larger domains of attraction for local nonlinear control schemes. In European Control Conference, pages 638--642, 1991.
....and cannot be directly related to a stable exo system. In addition, this technique requires solving a partial differential equation which may be impossible to do in closed form. Finally, Jacobian linearization is used for stabilization, which may lead to vanishingly small domains of attraction [6]. A different approach to the problem involves determining a set of outputs that make the system flat [7] These are outputs that can be used to reconstruct the trajectory of the entire state, the inputs and their derivatives. In [8] this technique was successfully applied to the model of a ....
A. Teel, "Toward larger domains of attraction for local nonlinear control schemes," in European Control Conference, pp. 638--642, 1991.
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