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.

In order to better understand the dynamic behavior and decrease the muzzle vibration of marching tank, a mechanical–electrical–hydraulic integrated dynamic model of marching tank was established based on a novel dynamic co-simulation method. The hydraulic system model was modeled in Amesim and the dynamic model of marching tank was established in RecurDyn based on multi-body system theory, vehicle terramechanics, and gun launch dynamics. The control system model was modeled in MATLAB/Simulink. Therein, the adaptive robust control algorithm was introduced to design the vertical stabilizer controller and the simulation program of the designed controller was developed by C language. The simulation results show that the muzzle vibration of marching tank can be controlled effectively by the ARC method. Furthermore, the muzzle error compensation signal was added in the designed controller to weaken the detrimental effect of the barrel flexibility on muzzle vibration. This work provides an approach to investigate the dynamic behavior of marching tank considering effects among the mechanical, hydraulic, and control subsystems.