Model predictive control

Function (biology)

Algorithm

Control (management)

Biology

Applied mathematics

Constraint (computer-aided design)

Set (abstract data type)

Computer science

Mathematical optimization

Projection (relational algebra)

Evolutionary biology

Augmented Lagrangian method

Genetics

Iterated function

Sequence (biology)

Mathematics

Mathematical analysis

Artificial intelligence

Geometry

Combinatorics

Programming language

Regular polygon

Convex function

IEEE Control Systems Letters

Recently there has been an increasing interest in primal-dual methods for model predictive control (MPC), which require minimizing the (augmented) Lagrangian at each iteration. We propose a novel first order primal-dual method, termed proportional-integral projected gradient method, for MPC where the underlying finite horizon optimal control problem has both state and input constraints. Instead of minimizing the (augmented) Lagrangian, each iteration of our method only computes a single projection onto the state and input constraint set. Our method ensures that, along a sequence of averaged iterates, both the distance to optimum and the constraint violation converge to zero at a rate of O(1/k) if the objective function is convex, where k is the iteration number. If the objective function is strongly convex, this rate can be improved to O(1/k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) for the distance to optimum and O(1/k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) for the constraint violation. We compare our method against existing methods via a trajectory-planning example with convexified keep-out-zone constraints.

Proportional-Integral Projected Gradient Method for Model Predictive Control