Surrogate problems for tractable excitation management in stochastic MPC

Stochastic optimal output feedback control, in all but linear situations, involves duality of the control signal. That is, the control serves two countervailing purposes: to regulate the plant state and to enhance its observability. Optimal solutions possess this feature inherently but are computationally intractable to find. Here, we replace the stochastic optimal control problem by surrogate problems with different deterministic cost functions, reflecting the two objectives and balancing between them. The problem is first addressed for nonlinear stochastic Model Predictive Control using an Extended Kalman Filter state estimator. By defining a joint state comprising the plant state and the covariance matrix of the filter, we revisit duality as a requirement for cost detectability of the surrogate value function. That is, the value function needs to reflect both the regulation and estimation objectives in order that the control solution should steer a middle course. This is presented for a deterministic finite-horizon optimal control problem and then extended to Model Predictive Control, where the receding-horizon aspects arise. These ideas are then advanced using mechanism design from game theory to arrive at this surrogacy. These surrogate problems admit simple computations to achieve tractable excitation management.