Min-max piecewise constant optimal control for multi-model linear systems
For control engineers dealing with uncertain linear systems with a finite number of models, this provides a theoretical framework and algorithm for min-max optimal control.
This paper solves a finite-horizon linear-quadratic optimal control problem for uncertain systems with piecewise constant controls, where system parameters belong to a finite set. A min-max approach is used, and the optimal control is derived via a multi-model Lagrange multiplier method, expressed through a discrete-time Riccati equation and an optimization over a simplex. A numerical algorithm is proposed and tested by simulation.
The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set (i.e., there exist only finitely many possible models for the plant). Uncertainty is dealt with using a min-max approach (i.e., we seek the best control for the worst possible plant). The optimal control is derived using a multi-model version of Lagrange's multipliers method, which specifies the control in terms of a discrete-time Riccati equation and an optimization problem over a simplex. A numerical algorithm for computing the optimal control is proposed and tested by simulation.