Handling actuator magnitude and rate saturation in uncertain over-actuated systems: a modified projection algorithm approach

Discrete Adaptive Control Allocation

“…Considering (13) and the convergence of (k) to zero, we deduce that θ v (k) converges to a constant value as k → ∞. Finally, (25) and the error dynamics (11) lead to the conclusion that lim k→∞ e(k) = 0.…”

“…Dynamic control allocation methods [1], [22], [23], on the other hand, are based on solving differential equations that model the control allocation goals. These methods can be extended to consider actuator limits [24], [25]. A survey of control allocation methods can be found in [26].…”

A Control Theoretical Adaptive Human Pilot Model: Theory and Experimental Validation

“…Step 5: Use ( 29)-( 31) as adaptive laws along with Kr = Proj(K r ˙ K r ), θ x (t) = K r (t)θ 1 (t), and λ(t) = K r (t)λ 1 (t), where the details of the Proj operator can be found in [40] and [41].…”

“…where d and s are obtained from ( 40) and (41), k is the number of participants, and t α/2 is the upper α/2 point of the t distribution with degree of freedom k − 1 [46]. Using the significance level α = 0.05 and degree of freedom k −1 = 10, obtaining t 0.025 = 2.228 from the t-distribution table, calculating d = −0.0068 and s = 0.038 using ( 40) and ( 41), respectively, and substituting μ 0 = 0 and k = 11, the left-hand side of ( 46) can be calculated as 0.5935, which is less than t α/2 .…”

Time‐varying sliding mode controller for over‐actuated systems with constrained and uncertain actuators in flight control applications

“…1,6,13,28,29,31,45,46 Furthermore, a control allocation approach by Naderi et al, 47 employs model predictive control to handle actuator magnitude constraints. In order to allocate control signals in the presence of uncertainty as well as actuator constraints, an adaptive control allocator for constrained systems has been developed by Tohidi et al 38,40 An adaptive control allocator which exploits a modified projection algorithm to handle magnitude and rate constraints in over-actuated systems is proposed by Tohidi et al 48 Although control allocation methods enable modularity for the overall control system design, as they separate the generation of the control signal and its distribution, control allocation errors can be significant in transients and degrade the performance. In vehicle and flight applications, the goal of the control allocation is to match the commanded (v) and the actual (Bu) control moments ∕ forces, where u designates a vector of actuator positions.…”