This paper addresses the control design problem for fuzzy vehicular platoon system consisting of one leading vehicle and N following vehicles. Due to external disturbances, the uncertainty exists in the platoon system and is usually nonlinear and possibly fast time-varying. In order to deal with the uncertainty, fuzzy theory is employed to describe the platoon system, thereby the so-called fuzzy vehicular platoon system. Based on the fuzzy property of the uncertainty, a type of adaptive law is proposed. Since the original state of the system is one-side bounded when collision avoidance is taken into account, a state transformation is made, by which a new global state is obtained. Then, the swarm intelligence is embedded into the platoon system via a function which mimics the swarm behavior. For the control design, we focus on adaptiveness and optimization. A switching-type adaptive robust control is proposed. The control is not IF-THEN rule-based. We further explore the problem of control parameter optimization. A performance index consisting of transient control cost and average control cost is proposed. Aiming at minimizing the performance index, the optimal problem is formulated. The solution to the optimal problem (i.e., optimal control parameter) exists and is unique. The control with optimal parameter is called optimal control, which guarantees the platoon system both deterministic performance (uniform boundedness, uniform ultimate boundedness and collision avoidance) and fuzzy performance.

The tracking performance of mobile robot is often affected by uncertainties from the deviation of initial conditions, external disturbances and varying loads, etc. An Udwadia-Kalaba based adaptive robust control is proposed for the trajectory tracking of an omnidirectional mobile robot in the presence of uncertainties. The proposed control includes nominal control part based on Udwadia-Kalaba theory and adaptive robust control part. The desired trajectory is considered as a virtual servo constraint applied to the robot system and converted into the second order standard form. So that the analytical form of constraint force could be obtained via Udwadia-Kalaba Fundamental Equation (UKFE). The system will precisely obey the given constraint (i.e., the desired trajectory) under the obtained constraint force in ideal cases. No auxiliary variables are required and it is effective whether the constraints are holonomic or nonholonomic. The designed adaptive law is in leakage type and the adaptive parameters are adjusted according to the performance of the system in order to compensate for the effect caused by uncertainty in the system. No extra information of uncertainty is needed except for the existence of uncertainty bound. Comparing with PID control, it can be found that the proposed control has better performance and can realize higher precision trajectory tracking control.

A fuzzy approach to the optimal control design for a kind of uncertain flexible joint manipulator is proposed. The system contains mismatched uncertainty which is described by fuzzy set theory and is assumed to be bounded. By implanting a fictitious control and transforming the system with new state variables, an adaptive robust controller is designed to guarantee the uniform boundedness and uniform ultimate boundedness of the transformed system. The proposed control is only based on the existence of the uncertainty bound and is not if–then heuristic rules‐based. Furthermore, the performance of the original system is also proven theoretically. By applying D ‐operation, the optimal design problem associated with the control can then be solved by minimising a constrained performance index. The performance index, which is based on the fuzzy information, includes average fuzzy system performance and control effort. The resulting control design is systematic and is able to assure the deterministic performance as well as the fuzzy performance. An illustrative example is given to demonstrate the authors' conclusions.

We consider an articial swarm mechanical system consisting of multiple agents. The agents are composed of mechanical components. The ideal kinematic performance includes mutual attractions and repulsions. This kinematic performance is embedded into the dynamics by being treated as a constraint. The Udwadia-Kalaba theory is then used to generate the required servo constraint force to assure the constraint is met for the nominal system. The system also includes uncertainty. The uncertainty in the swarm mechanical system is time-varying, whose value falls within a prescribed fuzzy set. For the robust control design, a creative β-measure based approach is introduced. The robust control guarantees uniform boundedness and uniform ultimate boundedness regardless of the actual value of the uncertainty. For the optimal choice of a control design parameter, a fuzzy-theoretic performance index is introduced. The resulting optimization problem is proven to be tractable, with the global solution to be existent and unique. Furthermore, the analytic expression of this solution is obtained. As a result, the optimal design problem is completely solved. To further demonstrate its effectiveness,we compare the performances of the swarm mechanical system under the robust control and Linear-Quadratic Regulator (LQR) control through simulation results with an illustrative example