How to find a changing relation between continuous variables?
Besides doing initial EDA and plotting dependent vs independent variables, it would seem prudent to try to first identify the "maintenance" points. According to your description of the problem, we can expect to see a decline in output o punctuated by single spike-step indicating improved performance. In other words you should in general see a negative slope interspersed with very high positive slope. We see a similar type of spike behavior in EEG signal, where the "blips" or "spikes" correspond to unwanted artifacts (e.g., eye blinks). These can be identified relatively easily by running a sliding window over the data and looking for big changes in slope. The time segments marked in green below are identified as artifacts by monitoring for changes in slope. You can look into EEGlab and ERPlab -- which are Matlab based -- to find out more about this approach.



For feature engineering, because of the input-to-response lag, you will want to initially include variable lags. For example, for variable a_left and a corresponding change in output o, you would want to add as features a_left_1, a_left_2, ... a_left_n, where each feature refers to the input value at some lagged time prior to the observed change in behavior.