Cautious hierarchical switching control of stochastic linear systems

Abstract

Standard switching control methods are based on the certainty equivalence philosophy in that, at each switching time, the supervisor selects the candidate controller that is better tuned to the currently estimated process model. If the estimated model does not appropriately describe the process, this procedure may result in the selection of a controller that is not appropriate for the actual process.In this paper, we propose a supervisory switching logic that takes into account the uncertainty on the process description when performing the controller selection. Specifically, a probability measure describing the likelihood of the different models is computed on-line based on the collected data and, at each switching time, the supervisor selects the candidate controller that, according to this probability measure, performs the best on the average. If the candidate controller set is hierarchically structured, the supervisor automatically selects the controller that appropriately compromises robustness and performance, given the actual level of uncertainty on the process description. The use of randomized algorithms makes the supervisor implementation computationally tractable.

Scaling of gain bounds for switched adaptive control with large uncertainties

“…Since we have shown that the availability of too many controllers right after initialization can lead to high gains, this behaviour is suppressed by limiting the number of available controllers over time. We observe that a similar procedure has been investigated in a stochastic context in [1], but with a rather different motivation. In particular we choose to relate the availability of controllers at time k ∈ N to the size of the observed signal T k w 2 .…”

Robust trajectory tracking for a reversing tractor trailer

“…Of course, more sophisticated switching strategies are available [see, e.g., Campi, Hespanha, and Prandini (2004) and Morse (2003a, 2003b)], but the hysteresis concept has proven to be sufficient in practice in this instance. However, this strategy assumes that the trajectory has been planned as a smooth path with a relatively low maximum curvature and, consequently, the desired hitch angle ψ is always small.…”

Hierarchical switching for active disturbance attenuation with fine controller tuning

“…In fact, in the adaptive stabilization problem, it is supposed that the a priori information on the plant is not sufficient to design a stabilizing controller. Hence, the main goal is that of modifying on line the control law (either by continuous adaptation or switching [20][21][22][23][24][25][26][27][28][29]), so as to ensure stabilization. On the other hand, in the ADA problem, it is supposed that the a priori information on the plant is sufficient to design a stabilizing controller, by resorting for instance to standard (robust) control techniques.…”