  Changing conditions or environments can cause system dynamics to vary over
time. To ensure optimal control performance, controllers should adapt to these
changes. When the underlying cause and time of change is unknown, we need to
rely on online data for this adaptation. In this paper, we will use
time-varying Bayesian optimization (TVBO) to tune controllers online in
changing environments using appropriate prior knowledge on the control
objective and its changes. Two properties are characteristic of many online
controller tuning problems: First, they exhibit incremental and lasting changes
in the objective due to changes to the system dynamics, e.g., through wear and
tear. Second, the optimization problem is convex in the tuning parameters.
Current TVBO methods do not explicitly account for these properties, resulting
in poor tuning performance and many unstable controllers through
over-exploration of the parameter space. We propose a novel TVBO forgetting
strategy using Uncertainty-Injection (UI), which incorporates the assumption of
incremental and lasting changes. The control objective is modeled as a
spatio-temporal Gaussian process (GP) with UI through a Wiener process in the
temporal domain. Further, we explicitly model the convexity assumptions in the
spatial dimension through GP models with linear inequality constraints. In
numerical experiments, we show that our model outperforms the state-of-the-art
method in TVBO, exhibiting reduced regret and fewer unstable parameter
configurations.
