The problem of trajectory tracking for a class of differentially driven wheeled mobile robots (WMRs) under partial loss of the effectiveness of the actuated wheels is investigated in this paper. Such actuator faults may cause the loss of strong controllability of the WMR, such that the conventional fault-tolerant control strategies unworkable. In this paper, a new mixed-gain adaption scheme is devised, which is adopted to adapt the gain of a decoupling prescribed performance controller to adaptively compensate for the loss of the effectiveness of the actuators. Different from the existing gain adaption technique which depends on both the barrier functions and their partial derivatives, ours involves only the barrier functions. This yields a lower magnitude of the resulting control signals. Our controller accomplishes trajectory tracking of the WMR with the prescribed rate and accuracy even in the faulty case, and the control design relies on neither the information of the WMR dynamics and the actuator faults nor the tools for function approximation, parameter identification, and fault detection or estimation. The comparative simulation results justify the theoretical findings.

On the power supply side, renewable energy (RE) is an important substitute to traditional energy, the effective utilization of which has become one of the major challenges in risk-constrained power system operations. This paper proposes a risk-based power dispatching strategy considering the demand response (DR) and RE utilization in the stochastic optimal scheduling of parallel manufacturing process (PMP) in industrial manufacturing enterprises (IME). First, the specific production behavior model of PMP is formulated to characterize the flexibility of power demand. Then, a two-step strategic model is proposed to comprehensively quantify multiple factors in the optimal scheduling of DR in PMP loads considering risk-based power system dispatch, thermal generators, wind power integration. Case studies are based on the modified IEEE 24-bus power system, which verify the effectiveness of the proposed strategy in optimally coordinating IME assets with generation resources for promoting the RE utilization, as well as the impacts of power transmission risk on decision performance.