Prescribed performance nonholonomic trajectory-tracking control of uncertain mechanical systems: a transformation-free approach

Conventional uncertain mechanical systems tracking control design guaranteeing prescribed performance is generally based on state transformations that bring high computational complexity, and cannot deal with nonholonomic reference trajectory. This paper proposes a transformation-free approach for robust tracking control design of uncertain mechanical systems to simultaneously achieve the following goals: (1) rendering the system to approximately track nonholonomic reference trajectory; (2) guaranteeing prescribed transient and steady-state tracking performance (PTSSP); (3) countering (possibly fast) time-variant and bounded uncertainty. Firstly, we synthesize control structure with designed parameters that renders the tracking error uniform boundedness and uniform ultimate boundedness. Secondly, we propose selection rules for designed control parameters by the meticulous analysis of error-based Lyapunov function and uncertainty bound to satisfy required prescribed performance. The design approach is transformation-free, approximation-free and does not invoke any auxiliary variables, hence is low-complexity and more easy-to-use comparing with the popular transformation-based prescribed performance control. Furthermore, to the best of our knowledge, it is the first that guarantees PTSSP in nonholonomic trajectory-tracking control of uncertain mechanical systems.