This study addresses a predefined performance constraint control scheme by applying the concept of graph theory to a distributed wheeled mobile robot (WMR) system. The kinematic and dynamic models of the WMR systems are considered simultaneously to design a finite‐time sliding mode controller with a novel constraint control term that assures the prescribed performances such as overshoot, rising time, and steady‐state error size, for the consensus and formation errors among the distributed WMR systems. Compared with a conventional prescribed controller, the structure of the proposed constraint controller is more compact and can be conveniently implemented in actual systems. The stability conditions and finite convergence time are discussed using the Lyapunov function with the adaptive law to describe the uncertainty. Numerical simulation results of formation control for the WMR systems support the validity of the proposed control method and demonstrate its potential performance.

This paper proposes a hybrid fuzzy dynamic surface control (DSC) method combined with a super-twisting control (STC) method and a super-twisting nonlinear disturbance observer (STO) for multi-input multi-output (MIMO) nonlinear strict-feedback systems is proposed, in addition to a new partial tracking error constraining method. For the design of the stabilizing controls of the DSC, the virtual tracking errors in recursive procedures were transformed into the design variables of the STC. The uncertainties were estimated by a super-twisting nonlinear disturbance observer, which includes the approximation error between the unknown plant dynamics and fuzzy optimization function, in addition to the external disturbances. Furthermore, the proposed DSC combined with the STC scheme can prevent the complex analysis problem of the filtered output error in conventional DSC schemes. Moreover, a novel convenient tracking error constraining method is also presented. Simulation results revealed that the proposed scheme has an improved tracking error performance and robustness to uncertainty than control systems with a conventional nonlinear disturbance observer and several other DSC schemes.