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access icon free Computationally efficient model predictive control for a class of linear parameter-varying systems

© The Institution of Engineering and Technology
Received 02/10/2017, Accepted 01/03/2018, Revised 26/01/2018, Published 06/03/2018

The use of linear parameter varying (LPV) prediction models has been proven to be an effective solution to develop model predictive control (MPC) algorithms for linear and non-linear systems. However, the computational effort is a crucial issue for LPV-MPC, which has severely limited its application especially in embedded control. Indeed, for dynamical systems of dimension commonly found in embedded applications, the time needed to form the quadratic programming (QP) problem at each time step, can be substantially higher than the average time to solve it, making the approach infeasible in many control boards. This study presents an algorithm that drastically reduces this computational complexity for a particular class of LPV systems. They show that when the input matrix is right-invertible, the rebuild phase of the QP problem can be accelerated by means of a coordinate transformation which approximates the original formulation. Then they introduce a variant of the algorithm, able to further reduce this time, at the cost of a slightly increased sub-optimality. The presented results on vehicle dynamics and electrical motor control confirm the effectiveness of the two novel methods, especially in those applications where computational load is a key indicator for success.

Inspec keywords: time-varying systems; machine control; quadratic programming; predictive control; electric motors; computational complexity; linear systems; vehicle dynamics; control system synthesis

Other keywords: model predictive control algorithms; crucial issue; effective solution; control boards; linear parameter-varying systems; QP problem; embedded applications; embedded control; vehicle dynamics; computationally efficient model predictive control; average time; computational load; LPV prediction models; computational complexity; LPV-MPC; LPV systems; computational effort; electrical motor control; quadratic programming problem

Subjects: Time-varying control systems; Optimisation techniques; Linear control systems; Control system analysis and synthesis methods; d.c. machines; Optimal control; a.c. machines; Control of electric power systems

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