On Tuesday, March 13, 2018 at 11:00 in room no. 641, prof. Martin Mönnigmann from Ruhr-Universität Bochum, Germany, will give a lecture on Regional Predictive Control.

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Speaker: Prof. Martin Mönnigmann, Automatic Control and Systems Theory, Ruhr-Universität Bochum, Germany

Time, date, and place: 11:00, March 13, 2018, room no. 641

Abstract: Model predictive control is a theoretically sound and practically relevant method for the control of complex systems. Ultimately, MPC is all about solving constrained optimization problems. It is usually assumed these problems must be solved numerically. As a result, MPC defines a control law only implicitly, or point-by-point: Solving the optimization problem for the current state x(t_k) (a point in state space) results in an optimal input signal u(x(t_k)) (a point in input space). By periodically repeating the optimization for the evolving state x(t₁), x(t₂), x(t₃), ..., the optimal control law x -> u(x) is sampled, resulting in a sequence of points u(x(t₁)), u(x(t₂)), u(x(t₃)), ...

A lot of effort has been invested into tailoring optimization algorithms for MPC. Instead, the present talk advocates investigating conditions under which the optimal control law x -> u(x) can be characterized. The simple central idea is as follows: The solution to the linear-quadratic MPC problem at a point x(t_k) does not only provide the point u(x(t_k)), but it defines an affine control law u(x)=Kx+b. This affine control law is not the global solution to the MPC problem, but it provides the optimal u(x) on a full-dimensional polytope in state space that contains x(t_k). Consequently, no MPC optimization problem needs to be solved at all, as long as the system stays in the same polytope. A computationally simple event-triggered MPC algorithm can be devised that, roughly speaking, uses the affine control law as long as possible, and triggers computing the next affine control law whenever the current polytope is left. It is not required to determine the piecewise affine control law as a whole, but its affine pieces are calculated on demand. 

We introduce the central idea for linear MPC, discuss its computational aspects and implications for networked MPC, and give an outlook on extensions to nonlinear MPC.