Minimum Reaching Time Multivariable Super-Twisting Control Design*

This paper aims to address and solve a minimum time control design problem in the framework of the Multivariable Super-Twisting Algorithm. The solution of this optimal control problem is particularly important because one of the most useful characteristics of STA is the finite time convergence towards the equilibrium point, which naturally increases the interest in reaching it in a minimum elapsed time evolving from any initial condition. As usual, in this class of optimal control problems, an upper bound on an appropriate weighted norm of the control gain is imposed. It is shown that the control design problem to be solved is convex and can be expressed by LMIs provided that a scalar variable is fixed, a situation that is well resolved by a line search procedure, achieving global optimality. An illustrative example borrowed from the literature is solved and discussed.