Optimal Adaptive Control of Linear-Quadratic-Gaussian Systems Academic Article uri icon


  • The problem of adaptively controlling an unknown linear-Gaussian system with a standard quadratic cost criterion, including a control cost, is considered. By means of a counterexample, it is shown that a commonly mentioned adaptive control scheme can lead to severe problems. To overcome this, a new adaptive control law, based on biasing the usual least-squares parameter estimation criterion with a term favoring parameters associated with lower optimal costs, is introduced. A salient feature of this adaptive control scheme is its imperviousness to the closed-loop identification problem. Properties such as closed-loop system identification, convergence of the adaptive control law to an optimal control law, overall stability of the controlled system and optimality with respect to the long-term average cost of the adaptive controller are proved.

published proceedings

  • SIAM Journal on Control and Optimization

author list (cited authors)

  • Kumar, P. R.

citation count

  • 62

complete list of authors

  • Kumar, PR

publication date

  • March 1983