Abstract
Model predictive control (MPC) is a multi-objective control technique that can handle system constraints. However, the performance of an MPC controller highly relies on a proper prioritization weight for each objective, which highlights the need for a precise weight tuning technique. In this paper, we propose an analytical tuning technique by matching the MPC controller performance with the performance of a linear quadratic regulator (LQR) controller. The proposed methodology derives the transformation of a LQR weighting matrix with a fixed weighting factor using a discrete algebraic Riccati equation (DARE) and designs an MPC controller using the idea of a discrete time linear quadratic tracking problem (LQT) in the presence of constraints. The proposed methodology ensures optimal performance between unconstrained MPC and LQR controllers and provides a sub-optimal solution while the constraints are active during transient operations. The resulting MPC behaves as the discrete time LQR by selecting an appropriate weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. In this paper, the effectiveness of the proposed technique is investigated in the application of a novel vehicle collision avoidance system that is designed in the form of linear inequality constraints within MPC. The simulation results confirm the potency of the proposed MPC control technique in performing a safe, feasible and collision-free path while respecting the inputs, states and collision avoidance constraints.
Highlights
A simulation environment is used to investigate the ability of the proposed trajectory planning architecture to perform a collision avoidance manoeuvre
We have presented an Model predictive control (MPC)-based collision avoidance framework by means of an analytical tuning methodology
The main contribution of this paper lies in the derivation of the transformation of a discrete time linear quadratic regulator (LQR) weighting matrix Q to generate the MPC weighting matrix
Summary
MPC has been recognised as one of the most powerful multi-objective optimal control techniques for a wide range of applications with its ability to formulate the system constraints as a finite-horizon constrained optimisation problem. The complexity increases with an increase in the number of control objectives [4]. The necessity of developing a precise tuning procedure for MPC weights has arisen. This has been investigated by previous research works using different techniques [5,6]. [6] presented a solution for selecting weights in order to match the MPC as an LQR-based linear controller
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have