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Optimal Event-triggered Control under Costly Observations

Digital control design is commonly constrained to time-triggered control systems with equidistant sampling intervals. The emergence of more and more complex and distributed systems urges the development of advanced triggering schemes that utilize computational and communication resources efficiently. This paper considers a linear stochastic continuous-time setting, where the design objective is to find an event-triggered controller that optimally meets the trade-off between control performance and resource utilization. This is reflected by imposing a cost penalty on updating the controller by current observations that is added to a quadratic control cost. It is shown that the underlying optimization problem results in an event-triggered controller, where the controller is updated, when the estimation error of the controller exceeds a apriori determined threshold. The controller design is related to linear quadratic Gaussian regulation and to optimal stopping time problems. Contrary to the initial problem, these can be solved by standard methods of stochastic optimal control. Numerical examples underline the effectiveness compared to optimal time-triggered controllers.