Distributed estimation and control of multiple nonholonomic mobile agents with external disturbances

Adaptive event‐based finite‐time consensus of nonholonomic multi‐agent systems subject to unknown disturbances

“…Output: Feasible adaptation parameters a i , A i ; Upper bounds m * i , M * i ; Switching time T * . Update sliding-mode variable S i2 based on (3); Update adaptation law Mi based on rules (8), (9); Update states x i2 , x i3 according to dynamics (20), choose control parameters 𝜇 , 𝜇 2 satisfying inequality (18); Update state x i1 according to dynamics ̇xi1 = 𝛿 + d i1 ; Determine whether the controller u i2 is updated according to the triggering function (19); if there exists an instant t 1 satisfying S i2 (t − 1 ) ≠ 0 and S i2 (t) = 0, ∀t ≥ t 1 then Record T 1 = t 1 ; print Feasible adaptation parameter A i = Mi (T 1 ) and upper bound (1−d∕2) with W(t) satisfying (26); print Switching time T * = T 1 + T 2 ; When t > T * , update state x i1 according to (16); Update sliding-mode manifold S i1 based on (2); Determine whether the controller u i1 is updated according to the triggering function (40); if there exists an instant t 2 satisfying S i1 (t −…”

“…Theorem 4. For the nonholonomic MASs (1) with Assumption 1, all the system states can reach consensus in finite time under the event-based control protocols ( 10)-( 12) with the triggering functions defined in (19) and (40), where the relevant parameters meet Theorems 1 and 2. In addition, the system does not exhibit Zeno behavior.…”

“…In the work, 14 a chattering-free ISMC scheme was designed to ensure the global finite-time tracking consensus of robotic systems with parametric uncertainties. For the chain-form nonholonomic MASs with disturbances, it has been a hot spot [16][17][18][19] due to extensive pracatical applications. For instance, controllers based on ISMC were constructed in Reference 19 to ensure the states to track the state of the reference signal in finite time.…”

“…For the chain‐form nonholonomic MASs with disturbances, it has been a hot spot 16‐19 due to extensive pracatical applications. For instance, controllers based on ISMC were constructed in Reference 19 to ensure the states to track the state of the reference signal in finite time. However, all these controllers are constructed under the assumption that the upper bounds of the disturbances are precisely known.…”

Formation control of nonholonomic wheeled mobile robots using adaptive distributed fractional order fast terminal sliding mode control

“…Where the primary objective of using consensus protocol is to synchronize the motion of robots to reach a common position or velocity in order to establish a certain geometric shape. Different control strategies have been used alongside with consensus protocol to address the formation control problem, these include Model predictive control [14], Backstepping techniques [15,16], Sliding mode control [17][18][19] and other control schemes [20,21].…”