  In this paper, a time-varying distributed convex optimization problem is
studied for continuous-time multi-agent systems. Control algorithms are
designed for the cases of single-integrator and double-integrator dynamics. Two
discontinuous algorithms based on the signum function are proposed to solve the
problem in each case. Then in the case of double-integrator dynamics, two
continuous algorithms based on, respectively, a time-varying and a fixed
boundary layer are proposed as continuous approximations of the signum
function. Also, to account for inter-agent collision for physical agents, a
distributed convex optimization problem with swarm tracking behavior is
introduced for both single-integrator and double-integrator dynamics.
