Suboptimal adaptive tracking control for FIR systems with binary-valued observations

In this paper, we investigate and analyze the suboptimal adaptive control for finite impulse response (FIR) systems with binary-valued observations. As the parameters of FIR systems are unknown and the measurable observations can only provide limited information, we propose and analyze a two-segment design method of an adaptive control law. First, we divide the system running time axis into many sections; each of these sections is divided into two segments. During the short segment, we design the system inputs for estimating parameters. Thus, we employ the empirical-measure-based technique for designing the identification algorithm. Second, we introduce a tracking control law to track a given target based on the system parameter estimates obtained in the short segment. We achieve this using the certainty equivalent principle in the long segment. As the length of short segments tends to infinity, we observe that the parameter estimation algorithm is consistent. However, when the length of segments tends to infinity, we find that the adaptive tracking control law is asymptotically suboptimal. Finally, we demonstrate the efficiency of the two-segment design method using the simulation results.