A decentralized adaptive control architecture for large-scale active-passive modular systems

Adaptive control of unactuated dynamical systems through interconnections: Stability and performance guarantees

“…While we do not consider the actuated and unactuated system uncertainties to be time varying in the theoretical development of this article, we include this final condition on the restricted potential function such that our results can be readily extended for the practical case, in which the uncertainties are time varying. Second, as considered in References , a candidate restricted potential function that satisfies all the conditions stated in Definition has the form . Finally, as discussed in Reference , Definition is a generalized definition of the restricted potential function (Barrier Lyapunov function) used in References .…”

“…The proposed control is applied to stabilize the overall interconnected system in the presence of unknown physical interconnections as well as uncertainties in both the actuated and unactuated dynamics. The performance guarantees are enforced using a set-theoretic model reference adaptive control approach * such that the respective system error trajectories of the actuated and unactuated dynamics are restricted to stay inside user-defined *Note that a set-theoretic adaptive control architecture is utilized in the prior work of the authors; [35][36][37][38][39] however, they are not applicable as-they-are to the problem considered in this article (see Section 2). compact sets.…”

“…This is also considered to be important in other works, in which an ideal reference model has been modified. 57,69 For this purpose, we definex r (t) ≜ x r (t) − x id r (t) as the error between the reference model given by (23) and the ideal reference (38). Next, note that…”

“…Theorem 2. Consider the reference model for the actuated dynamics given by (18), the reference model for the unactuated dynamics given by (23), and the ideal reference model given by (38) subject to the control signal given by (20) and the update laws (21) and (22). Under Assumption 1, the upper bound for ‖x r (t)‖ 2 is given by…”

“…Proof. Consider the reference model error dynamics obtained from the reference model (23) and the ideal reference model (38) subject to the control signal (20) given bẏx…”