A new approach to the control design for fuzzy dynamical systems is proposed. For a fuzzy dynamical system, the uncertainty lies within a fuzzy set. The desirable system performance is twofold: one deterministic and one fuzzy. While the deterministic performance assures the bottom line, the fuzzy performance enhances the cost consideration. Under this setting, a class of robust controls is proposed. The control is deterministic and is not if-then rules-based. An optimal design problem associated with the control is then formulated as a constrained optimization problem. We show that the problem can be solved and the solution exists and is unique. The closed-form solution and cost are explicitly shown. The resulting control is able to guarantee the prescribed deterministic performance and minimize the average fuzzy performance.

In this paper, we propose a fuzzy approach for optimal robust control design of an automotive electronic throttle (ET) system. Compared with the conventional ET control systems, we establish the fuzzy dynamical model of the ET system with parameter uncertainties, nonlinearities, and external disturbances, which may be nonlinear, (possibly fast) time varying. These uncertainties are assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. A robust control that is deterministic and is not the usual if-then rules-based control is presented to guarantee the controlled system to achieve the deterministic performance: uniform boundedness and uniform ultimate boundedness. Furthermore, a fuzzy-based system performance index including average fuzzy system performance and control cost is proposed based on the fuzzy information. The optimal design problem associated with the control can then be solved by minimizing the fuzzy-based performance index. With this optimal robust control, the performance of the fuzzy ET system is both deterministically guaranteed and fuzzily optimized.

This paper proposes a novel robust control design for mechanical systems based on constraint following and multivariable optimization. The state of the concerned system is affected by (possibly fast) time-varying and bounded uncertainty. The objective is to drive the system to obey a set of prescribed constraints. A β-measure is defined to gauge the constraint following error; based on which, a robust control scheme, which invokes design parameters, is proposed. For the seeking of optimal design parameters, a multivariable constrained optimization problem is formulated. The problem is successfully solved: with the ${existence,\ uniqueness}$ , and ${analytical\ expression (i.e.,\ closed\ form)}$ of the optimal design parameters demonstrated. With the optimal parameters, the proposed robust control can render dual performance: guaranteed and optimal. As the guaranteed performance, the β-measure is assured to be uniform boundedness and uniform ultimate boundedness. As the optimal performance, the performance index is globally minimized.

We consider the control design problem for a class of constrained uncertain systems in this paper. The uncertainty in the system, including unknown system parameters and external disturbance, is nonlinear and time-varying. The bound of the uncertainty is described via a fuzzy set. The states of the system are constrained to be bounded. We propose a one-to-one state transformation to convert the bounded state constrained system into the unconstrained system. A new robust control scheme is then proposed for the transformed system, which is in deterministic form and not fuzzy if-then rule-based. By fuzzy description of the uncertainty bound, the optimal design of the control gain is proposed, which minimizes a fuzzy performance index associated with both the fuzzy system performance and the control effort. The analytic solution to the optimization problem is demonstrated to always exist and be unique. The resulting control can guarantee uniform boundedness and uniform ultimate boundedness of the uncertain system, while minimizing the fuzzy-based performance index. In addition, the state constraint can be always guaranteed.

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.