Identification-Approximation Approach of Adaptive Control of the MIMO Object Output

The problem of controlling the output of a multidimensional object under conditions of the current uncertainty of the parameters of the object and the action of external uncontrolled disturbance is considered. A solution to the problem is proposed based on the use of an identification-approximation approach, also called as an approach using "simplified” adaptability conditions. It is based on the use of an algorithm for the current parametric identification of the object model, an implicit reference model and approximation of the dynamics of the object. The latter is performed at two levels: a structural approximation, which assumes the use of a sufficiently simple model in the structure of the customizable model in the identification algorithm, as well as a parametric approximation, which assumes the " description” of the model by current parameter estimates that do not coincide with their exact values. In this case, the criterion for the accuracy of approximation for the control synthesis problem is the convergence of the identification discrepancy with some fairly simple requirements for parameter estimates during control. This provision can be interpreted as a refinement of the well-known "certainty equivalence principle,” which requires asymptotically accurate estimation of unknown parameters. An additional advantage is the speed of adaptability and the non-need for a constantly exciting regressor ("richness” of the input signal). The conditions for suboptimality of the control law are also determined. These requirements are simple enough for practical applicability. An example of computer simulation in the Matlab environment is given.