Optimal adaptive design of the prescribed-structure controllers

For the continuous linear control plants with parametric uncertainty, a new approach to the $\mathrm H_2$-design of multivariable controllers of the prescribed structure was suggested. For the desired reference model of the control system of full and low order, the property of adaptability of such control systems was defined, and the criteria for adaptability in terms of matrices and adaptability gramians were formulated. The structural properties of the matrices and adaptability gramians were analyzed, and their relation to the matrices and the gramians of controllability and observability were established. A new approach to the parametric controller optimization with the use of adaptability gramians was proposed. The integral estimates of the degree of deviation of the performance indices of the stationary continuous control systems with a prescribed-structure controller and the parametric uncertainty of the interval-type plant from the performance indices of the desired reference model of full and low order were obtained.