Abstract
This work is concerned with Model Predictive Control (MPC) algorithm for vehicle obstacle avoidance. The second objective of the algorithm is on-line minimization of fuel utilization. At first, the rudimentary nonlinear MPC optimization problem is formulated. Next, the constraints related to the predicted process state variables are formulated as soft ones to guarantee computational safety. Furthermore, in order to obtain a computationally simple procedure, the process dynamics and the fuel utilization model are linearized on-line and used for prediction in MPC. It leads to a quadratic programming MPC task, the necessity of nonlinear optimization performed in real-time is eliminated. In order to stress advantages of the discussed computationally uncomplicated MPC method it is compared with the basic scheme with on-line nonlinear optimization in terms of control quality and computational time. Additionally, effectiveness of the MPC algorithm is discussed in presence of modeling errors and measurement noise. Finally, additional constraints imposed on the rate of change of the manipulated variables are considered.
Highlights
Model Predictive Control (MPC) [1], [2] explicitly uses a mathematical model of the controlled process for optimization of the control policy
Because the model of the vehicle defined by Eqs. (6) and the fuel utilization penalty term characterized by Eq (21) are nonlinear functions of the computed in MPC decision variables u(k), the minimized cost-function is a nonlinear function
When other types of constraints imposed on predicted state and/or output variables are necessary, in the MPC scheme with Successive Linearization (MPC-SL) algorithm we have to find their linear approximations by means of general Eqs. (35) and (38), respectively
Summary
Model Predictive Control (MPC) [1], [2] explicitly uses a mathematical model of the controlled process for optimization of the control policy. 3) As the general formulation of the problem defined above requires solution of a nonlinear MPC optimization task at each sampling instant in real-time, the process dynamics and the fuel utilization model are linearized on-line. It makes it possible to transform the main components of the MPC cost-function into a quadratic function of the calculated decision variables. The classical formulation of MPC algorithms with on-line successive model linearization is well known and used in process industry [40], the vehicle obstacle avoidance and fuel usage minimization objectives require complicated form of the MPC cost-function and state constraints, not used in process control applications.
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