Joint adaptive plant and measurement control of linear stochastic systems

In this paper, the joint plant and measurement control problem of linear, unknown, discrete time systems excited by white Ganssian noise is considered. The performance criterion is quadratic in the state and is additive in the plant and measurement control. The adaptive control solution is obtained by approximating the dynamic programming equation-the approximation amounts to replacing the optimal adaptive cost-to-go in the dynamic programming equation by the average value of the truly optimum cost-to-go for each admissible model. In our solution, the adaptive plant and measurement control schemes can be separated. The adaptive plant control is given by the product of the weighted integrals with the a posteriori probability of the parameter as weights. The adaptive measurement control scheme is obtained as the solution of a constrained nonlinear, optimization problem for each time; the constraint equations being the error covatiance matrix equations in the Kalman filter. An illustrative example of the optimum timing of measurements is discussed where the joint adaptive control scheme is simulated and its performance is compared with the optimum value of the performance if the system parameters were completely known.