Dual adaptive extremum control of a Hammerstein system

This paper proposes a dual adaptive control methodology for extremum control of stochastic Hammerstein systems that are subject to uncertainty and characterised by a nonlinear second-order polynomial function. The design is based on an explicit-type innovations dual cost function that leads to a control law which balances out the need for caution when using uncertain parameter estimates to effect control actions, with the conflicting need to probe the system input so as to reduce parameter uncertainty. This extremum control problem is more challenging than conventional adaptive systems because the reference input is itself a non-linear function of the unknown system parameters. The controller´s performance is analysed through extensive Monte Carlo simulations and shown to be superior to other types of adaptive control systems that use a certainty equivalence assumption.