Exponential Convergence of A Learning Scheme for Unknown Linear Systems

In this paper the issue of convergence rate is introduced for a learning control scheme we have developed and applied for tracking of unknown linear systems. A sufficient condition under which the output trajectory converges exponentially fast is obtained using the controllability grammian of controllable linear systems. Under the same condition it is also shown that the learning control input converges exponentially with the same rate as the rate of output convergence. A numerical example with computer simulation results is presented to show the feasibility of the scheme.