  In this paper, a distributed velocity-constrained consensus problem is
studied for discrete-time multi-agent systems, where each agent's velocity is
constrained to lie in a nonconvex set. A distributed constrained control
algorithm is proposed to enable all agents to converge to a common point using
only local information. {The gains of the algorithm for all agents need not to
be the same or predesigned and can be adjusted by each agent itself based on
its own and neighbors' information.}
  It is shown that the algorithm is robust to arbitrarily bounded communication
delays and arbitrarily switching communication graphs provided that the union
of the graphs has directed spanning trees among each certain time interval. The
analysis approach is based on multiple novel model transformations, proper
control parameter selections, boundedness analysis of state-dependent
stochastic matrices, exploitation of the convexity of stochastic matrices, and
the joint connectivity of the communication graphs. Numerical examples are
included to illustrate the theoretical results.
