Implicit dual adaptive control for systems with functional uncertainties

Abstract The paper proposes an implicit type of dual control for a class of nonlinear stochastic systems subject to functional uncertainty. The unknown functions of the system are modelled by multi-layered perceptron neural networks where the unknown parameters are found in real-time. The control design is based on the Bellman optimisation recursion where the length of the recursion is shortened to two stages to reduce computational burdens and to ensure dual features between estimation and control aims. The inherent obstacle of determining the expectation is tackled by employing a technique based on the stochastic integration rule. The design is then accomplished using an iterative procedure, which is summarised by algorithms. Numerical simulations and a Monte Carlo analysis show that the proposed approach may compete with existing solutions based solely on the explicit type of dual control and removes their drawback of tuning additional design parameters.