Data-driven NODE based multirate sampled data state feedback control

In control systems, multirate sampled data systems are widely used because they improve system performance and adaptability, especially when systems deal with both continuous and discrete signals or entirely asynchronous sampling signals. This paper addresses the challenges of system stability and optimization in these multirate systems, specifically for a certain class of nonlinear systems. Existing controllers, though capable in certain contexts, tend to be overly complex and often lack guidance on appropriate sampling interval selection for these intricate systems. Our approach takes into account both system stability and practical considerations, providing a criterion for selecting multiple sample periods that guarantees system stability, as well as an optimal choice of parameters by Neural Ordinary Differential Equation (NODE) for the linear practical controller that maximizes performance according to a predefined performance index. With the construction of a set of linear stabilizers that are implemented using multirate sampled data, the stability and controller design at three different sampling levels are studied. To demonstrate the effectiveness of our proposed strategy, the simulations and real world application of a single-link robot system are presented.