Observer‐based consensus tracking control for a class of nonstrict‐feedback nonlinear multi‐agent systems with prescribed performance and input quantization

Abstract

This article investigates the consensus tracking problem with predefined transient and steady performance requirements for a class of nonstrict-feedback nonlinear multi-agent systems (MASs) with input quantization under a directed graph. Based on prescribed performance error transformation methods and command filtered backstepping techniques, a novel observer-based adaptive control protocol is proposed, where neural observers are designed to estimate unmeasurable states and radial basis function neural networks are constructed to compensate command filter errors. The proposed protocol can be applied to a more general class of nonlinear MASs with nonstrict-feedback nonlinear dynamics and unmeasurable states information. It is strictly proved that all signals in the whole MAS are semi-globally uniformly ultimately bounded and both the transient and steady performances of the consensus tracking errors satisfy prescribed performance requirements. Finally, three numerical examples are presented to validate the effectiveness of the proposed protocol.

Observer‐based adaptive emotional command‐filtered backstepping for cooperative control of input‐saturated uncertain strict‐feedback multi‐agent systems

“…Theorem 1. Consider uncertain non-linear multi-agent system (1) under the proposed design for virtual and actual control signals (20) to (23), emotional observer (10), command filter (19), compensating signals (28) to (31), and adaptation laws (25) to ( 27), where x(0) ∈ Ω d and [V T i, j (0), W T i, j (0), b i, j (0)] T ∈ Ω w , the cooperative output tracking error and the observer error converge to small regions around zero, and all the closed-loop signals are cooperatively semi-globally uniformly ultimately bounded.…”

“…This is in contrast to the previous emotional controllers [28, 32] in which the emotional system is modelled as a part of the mammalian brain in isolation. We take inspiration from the emotional contagion in human society to share RBENNs’ approximations of other models among followers, hence reducing design complexity. This is in contrast to the CFBC‐based controller [15], which uses another learning system to model the dynamics of other agents. An emotional neural network, which has a different structure and adaptation laws than conventional neural networks and fuzzy systems considered in [14–20], is used to design an adaptive observer and manage mismatched uncertainties in MAS. The inherent competitive nature of the emotional models helps cope faster with changing dynamics and hence better face uncertainties. We propose to combine an emotional learning system with the backstepping technique for the cooperative output‐feedback control of MAS that are subject to mismatched uncertainties and input saturation, and are only able to access the outputs of their neighbours.…”

“…However, some states may not be a physical quantity to measure in the real world, or their measurement may not be affordable. The combination of CFBC/DSC and adaptive neural/fuzzy observer is the subject of the study in [14][15][16][17][18][19][20]. In [14], the authors present a neural observer-based consensus control for MAS with external disturbances and input delay.…”

“…For containment control of non-strict-feedback MAS, the authors in [19] offer a finite-time output-feedback neural controller. Also, in [20], neural networks are used both to approximate unknown dynamics and to compensate the error of command filters in output-feedback consensus control of MAS subjected to input quantization and prescribed performance.…”

“…This is in contrast to the CFBC-based controller [15], which uses another learning system to model the dynamics of other agents. • An emotional neural network, which has a different structure and adaptation laws than conventional neural networks and fuzzy systems considered in [14][15][16][17][18][19][20], is used to design an adaptive observer and manage mismatched uncertainties in MAS. The inherent competitive nature of the emotional models helps cope faster with changing dynamics and hence better face uncertainties.…”