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.

This article proposes an adaptive robust formation control scheme for the connected and autonomous vehicle (CAV) swarm system by utilizing swarm property, diffeomorphism transformation, and constraint following. The control design is processed by starting from a 2-D dynamics model with (possibly fast) time varying but bounded uncertainty. The uncertainty bounds are unknown. For compact formation, the CAV system is treated as an artificial swarm system, for which the ideal swarm performance is taken as a desired constraint. By this, formation control is converted into a problem of constraint following and then a performance measure $\beta $ is defined as the control object to evaluate the constraint following error. For collision avoidance, a diffeomorphism transformation on space measure between two vehicles is creatively performed, by which the space measure is positive restricted. For uncertainty handling, an adaptive robust control scheme is proposed to render the $\beta $ -measure to be uniformly bounded and uniformly ultimately bounded, that is, drive the controlled (CAV) swarm system to follow the desired constraint approximatively. As a result, the system can achieve the ideal swarm performance; thereout, compact formation is realized, regardless of the uncertainty. The main contribution of this article is exploring a 2-D formation control scheme for (CAV) swarm system under the consideration of collision avoidance and time-varying uncertainty.

This article explores an adaptive robust control scheme for satellite formation-containment flying in a way of constraint following. For safe flight and uncertainty suppression, both collision avoidance and uncertainty suppression are addressed. First, for uncertainty suppression, (possibly fast) time-varying but bounded uncertainty is considered, and then an adaptive law is proposed to estimate the comprehensive uncertainty bounds online. Second, the problem of formation-containment control with collision avoidance is converted into another problem of constraint-following control by taking the objectives of collision avoidance, formation, and containment, respectively, as the collision-avoidance constraint, formation constraint, and containment constraint. Third, an η-measure is introduced to gauge the constraint-following error, and then an adaptive robust control is proposed to render the error to be uniformly bounded and uniformly ultimately bounded, regardless of the uncertainty. By this, the satellites can follow the above collision-avoidance constraint, formation constraint, and containment constraint approximately. As a result, satellite formation-containment control emphasis on collision avoidance and uncertainty suppression is achieved.

The uncertain optimization problem for structural dynamic responses of artillery systems is studied from the perspective of uncertainty and system engineering. First, a rigid–flexible coupling dynamic model of artillery at the maximum firing angle is constructed, which can achieve coupling relationships between interior ballistics, launching loads and artillery movement. Secondly, an integration method of optimal Latin hypercube design and regression analysis is used to obtain the polynomial model, followed by sensitivity analysis. Thus, the key parameters affecting the dynamic response are identified. An interval uncertain optimization method for artillery structural dynamic responses considering robustness and interval economy is then proposed, based on nonlinear interval programming and the nested optimization solving strategy, which integrates the back-propagation neural network with the genetic algorithm as the inner optimizer, and uses the non-dominated sorting genetic algorithm-II as the outer optimizer. Finally, an example is presented to demonstrate the validity of the proposed method.