Near-Optimal Strategies for Nonlinear and Uncertain Networked Control Systems

We consider problems where a controller communicates with a general nonlinear plant via a network, and must optimize a performance index. The system is modeled in discrete time and may be affected by a class of stochastic uncertainties that can take finitely many values. Admissible inputs are constrained to belong to a finite set. Exploiting some optimistic planning algorithms from the artificial intelligence field, we propose two control strategies that take into account the communication constraints induced by the use of the network. Both strategies send in a single packet long-horizon solutions, such as sequences of inputs. Our analysis characterizes the relationship between computation, near-optimality, and transmission intervals. In particular, the first strategy imposes at each transmission a desired near-optimality, which we show is related to an imposed transmission period; for this setting, we analyze the required computation. The second strategy has a fixed computation budget, and within this constraint it adapts the next transmission instant to the last state measurement, leading to a self-triggered policy. For this case, we guarantee long transmission intervals. Examples and simulation experiments are provided throughout the paper.