A vector-type finite-time output-constrained control algorithm and its application to a mobile robot

Purpose The purpose of this paper is to investigate a vector-type finite-time control strategy with output constraints for first-order and second-order systems. Under the proposed controller, the system can be stabilized within a finite time and the output of the system is always maintained within the prescribed constraint bounds. Design/methodology/approach First, to prevent constraint violations, a piecewise barrier Lyapunov function (BLF) is formulated, which grows to infinity as its arguments approach prescribed limits. By embedding the BLF as a parameter into the design of finite-time controller, the constraints are ensured not to be violated. However, this resulted in a closed-loop system with coupled states, posing challenges for finite-time stability analysis. To tackle this issue, this paper introduces a vector-type fractional power function by skillfully leveraging the sign function, which constructs a continuous vector-type finite time controller with coupled state-dependent gains. Finally, model-based approaches are used to complete the theoretical analysis. It is demonstrated that the proposed controller effectively enables the system to achieve finite-time state convergence while adhering to output constraints. Findings By using a piecewise BLF and using the vector-type fractional power function, a continuous vector-type finite-time controller with coupled state-dependent gains can be constructed for both first-order and second-order systems. This allows the systems to achieve finite-time stabilization while satisfying output constraints. It is worth mentioning that the developed algorithm can be extended to the trajectory tracking of a mobile robot. Originality/value Compared with existing results, the main contributions presented in this paper are: (i) the proposed control scheme guarantees the closed-loop system converges within a finite time. (ii) The introduction of state-dependent gain penalty term effectively tackles the difficulty in ensuring the satisfaction of output constraints under coupled conditions. (iii) The vector-type fractional power function provides a more flexible and powerful tool for the design and analysis of the closed-loop system.