The optimal design problem of adaptive robust control for fuzzy mechanical systems with uncertainty is investigated in this paper. The uncertainty that may be nonlinear and (possibly fast) time-varying is assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. Based on the Udwadia and Kalaba's approach, an adaptive robust controller, which is deterministic and is not the usual if-then rules-based is proposed to render the system to follow a class of prespecified constraints approximately. The adaptive law is of leakage type that can adjust the magnitude of the adaptive parameter based on the nonlinear performance-dependent gain. The resulting controlled system is uniformly bounded and uniformly ultimately bounded, which is proved via the Lyapunov minimax approach. Furthermore, we propose a novel concept: fuzzy confidence to measure the expectation value of a fuzzy number. Then, a fuzzy-based system performance index that includes the expectation value of the uniform ultimate boundedness (the average fuzzy performance) and the control cost is formulated. The optimal design problem associated with the control can then be solved by minimizing the performance index. As a result, the performance of the fuzzy mechanical system is both deterministically guaranteed and fuzzily optimized under this control.

In order to improve the control performance of the Cyber-Physical Systems (CPSs), an integrated modelling-control-design trio framework is established in this paper. In the modelling part, CPS has two components, cyber component and physical component, so the system may be subject to (possibly fast) time-varying cyber interference and (possibly fast) time-varying physical uncertainty. A dynamic model encompassing these two phases of the CPS is established. In the control part, a novel control design is proposed based on the dynamic model. The problem of constraint-following for CPS operating under cyber interference and physical uncertainty is considered. In the design part, the choice of control parameters is investigated. This procedure consists of two stages. The first stage is to design a control scheme based on feasible control design parameters, so that it can guarantee the performance in the case of both cyber interference and physical uncertainty. The second stage is to seek the optimal design among the feasible control design parameters, which is resolved by an intelligent multi-agent game-theoretic approach. We invoke both Nash game and Stackelberg strategy to choose the optimal parameters. Interestingly, the optimal parameters obtained from different game settings are the same. This shows the conception of optimality we established spans in a broader context. The robustness and superiority of the system performance are demonstrated in the intelligent transportation system.

The dynamic modeling and trajectory tracking control of a mobile robot is handled by a hierarchical constraint approach in this study. When the wheeled mobile robot with complex generalized coordinates has structural constraints and motion constraints, the number of constraints is large and the properties of them are different. Therefore, it is difficult to get the dynamic model and trajectory tracking control force of the wheeled mobile robot at the same time. To solve the aforementioned problem, a creative hierarchical constraint approach based on the Udwadia–Kalaba theory is proposed. In this approach, constraints are classified into two levels, structural constraints are the first level and motion constraints are the second level. In the second level constraint, arbitrary initial conditions may cause the trajectory to diverge. Thus, we propose the asymptotic convergence criterion to deal with it. Then, the analytical dynamic equation and trajectory tracking control force of the wheeled mobile robot can be obtained simultaneously. To verify the effectiveness and accuracy of this methodology, a numerical simulation of a three-wheeled mobile robot is carried out.