Firstly, a global finite-time control law of the angular velocity is designed for the first-order system in order to stabilize the angle error of mobile robots.
At the lower layer, local MPC regulators, possibly working at different rates, are designed for the full order models of the subsystems to refine the control action computed at the higher layer.
The higher layer of the control structure is designed with robust Model Predictive Control MPCC) based on a reduced order dynamic model of the overall system and is aimed at optimizing long-term performance, while at the lower layer local regulators acting at a higher frequency are designed for the full order models of the subsystems to refine the control action.
Since (3) is only an approximate model of system (1), can a dynamic output feedback designed for the reduced-order subsystem stabilize the original full-order system?
From Theorem 1, we can conclude that the dynamic output feedback controller designed for the reduced-order subsystem stabilizes the original full-order system (30) for a sufficiently small ε.
The proposed method in this paper guarantees that the proper dynamic output feedback controller designed for the reduced-order subsystem is a stabilizing one for the full-order system.
However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly.
Moreover, general methods of CMGPS are designed for the fractional-order real chaotic drive system and the complex chaotic response system, and for the fractional-order complex chaotic drive system and the real chaotic response system, and for two fractional-order complex chaotic systems, respectively.
Moreover, an effective control protocol is designed for the first-order discrete-time systems with fixed time-delays.
Distributed observers are designed for the second-order follower-agents, under the common assumption that the velocity of the active leader cannot be measured in real time.
