Adaptive control for jump parameter systems via nonlinear filtering

The authors first present an error analysis for the process of estimates generated by the Wonham filter when it is used for the estimation of the jump-Markov parameters of a linear stochastic system and further give bounds on certain functions of these estimates. Then, a stochastic Lyapunov analysis establishes that a certainty equivalence adaptive LQG (linear-quadratic-Guassian) feedback control law using the estimates generated by the nonlinear filter stabilizes the Markov jump parameter linear system in the mean square average sense. The conditions for this result are that certain products of the parameter process jump rate and the solution of the control Riccati equation and its second derivatives should be less than certain given bounds. An example is given where the controlled linear system has state dimension two