Dual MPC for FIR Systems: Information Anticipation

Abstract

Dual model predictive control (dmpo) optimally combines plant excitation and control based on current and predicted parameter estimation errors. Exact solution of dual control problems with constraints is in general computationally prohibitive. Our deterministic equivalent of the stochastic optimal control problem enables convergence toward optimality for a specific class of finite-horizon problems. The cost function shows that the optimal controls are functions of the current and future parameter-estimate error covariances. Our proposed objective-function reformulation provides the optimal combination of caution, probing, and nominal control. We show that the nonconvex optimization problem can be solved as a quadratic program with bilinear constraints. This type of problem can be efficiently solved with existing algorithms based on branch and bound with McCormick-type estimators. We demonstrate the application of DMPC to a singe-input single-output (siso) finite impulse response (fir) system. In the simulation example the parameter estimates converge quickly, and accurate and precise estimates are obtained even though the excitation vanishes.