Adaptive Control of a Constrained First Order Sliding Mode for Visual Formation Convergence Applications

Most existing solutions that guarantee finite-time convergence of a constrained first-order sliding mode either assume that the structure of the perturbation is known apriori, or the perturbation and its derivative are bounded by unknown constants. Moreover, convergence is usually guaranteed only in a small domain of attraction of the predefined constrained region through discontinuous control action. In contrast with these approaches, the sliding mode is assumed to be subject to perturbations with a state-dependent structure in this study, and two adaptive integral control strategies are proposed that guarantee finite-time convergence of this perturbed sliding mode from any initial condition within the predefined constrained region. First, an invertible nonlinear map is used to transform the constrained system into a constraint-free system, and an adaptive integral control strategy is used to guarantee finite-time convergence of the resulting sliding mode to a uniform ultimate bound using continuous and bounded control action. Subsequently, an alternative barrier-function based adaptive control policy is synthesized that ensures sliding mode convergence in a prescribed time to a prescribed bound that is independent of the magnitude of the perturbation term. Experimental studies of vision-based leader-follower formation control are used to validate and demonstrate superior performance of the proposed schemes compared to leading alternative designs.