In this article, we apply a high-order control to a dynamical system with uncertainty. There are two characteristics. First, the uncertain part, which is time-varying but bounded, is described in a fuzzy aspect. Specifically, the uncertainty lies within a fuzzy set and the bound is regarded as a fuzzy number. Second, the systems are uniformly bounded and uniformly ultimately bounded with a deterministic controller based on the Lyapunov theory. To obtain better system performance and lower control input, we apply the noncooperative game theory to optimize the parameters by establishing a Nash game. Then, the D-operation is proposed for the uncertainty related to fuzzy numbers. Finally, we perform the numerical simulations of the steering-by-wire system for verification.

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.

In this article, we propose a high-order robust control for fuzzy dynamical systems. The time varying but bounded uncertainty in this system is described by the fuzzy set theory. The control is deterministic and is not based on scif-then fuzzy rules. By the Lyapunov approach, we prove that the control is able to guarantee uniform boundedness and uniform ultimate boundedness. In addition, the tunable parameters in the high-order control are regarded as two players in a cooperative game. Two cost functions are also proposed based on the two players. These two cost functions are related to system performance and control cost. Then, the optimal design problem is solved by finding the Pareto-optimality parameters. Numerical simulations are performed for verification

A novel class of high-order robust controls is presented for uncertain fuzzy systems in this article. The optimal tunable parameters are also obtained based on the Stackelberg game theory. First, a dynamical system structure is formulated with uncertainty. The uncertain portion in the system is bounded, nonlinear, and time-varying which is within prescribed fuzzy set. Thus, this is a fuzzy system. Then, the proof based on the Lyapunov minimax approach shows that the novel high-order robust controls are able to assure deterministic system performance, which is uniform boundedness and ultimate uniform boundedness. Furthermore, the optimal choice of the tunable parameters in the control is considered. We creatively apply the Stackelberg strategy to solving the optimization problem. Two parameters are regarded as leader and follower in a sequential game, respectively. Based on the Stackelberg game rules, we are able to design different cost functions for different parameters. The cost functions include both performance measures and control cost. Finally, the simulations of an electronic throttle system are presented for demonstration.