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Title Numerical Methods for Model Predictive Control
Author Yang, Jing
Supervisor Jørgensen, John Bagterp (Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2008
Abstract This thesis presents two numerical methods for the solutions of the unconstrained optimal control problem in model predictive control (MPC). The two methods are Control Vector Parameterization (CVP) and Dynamic Programming (DP). This thesis also presents a structured Interior-Point method for the solution of the constrained optimal control problem arising from CVP. CVP formulates the unconstrained optimal control problem as a dense QP problem by eliminating the states. In DP, the unconstrained optimal control problem is formulated as an extended optimal control problem. The extended optimal control problem is solved by DP. The constrained optimal control problem is formulated into an inequality constrained QP. Based on Mehrotra’s predictor- corrector method, the QP is solved by the Interior-Point method. Each method discussed in this thesis is implemented in Matlab. The Matlab simulations verify the theoretical analysis of the computational time for the different methods. Based on the simulation results, we reach the following conclusion: The computational time for CVP is cubic in both the predictive horizon and the number of inputs. The computational time for DP is linear in the predictive horizon, cubic in both the number of inputs and states. The complexity is the same in terms of solving the constrained or unconstrained optimal control problem by CVP. Combining the effects of the predictive horizon, the number of inputs and the number of states, CVP is efficient for optimal control problems with relative short predictive horizons, while DP is efficient for optimal control problems with relative long predictive horizons. The investigations of the different methods in this thesis may help others choose the efficient method to solve different optimal control problems. In addition, the MPC toolbox developed in this thesis will be useful for forecasting and comparing the results between the CVP method and the DP method.
Series IMM-M.Sc.-2008-02
Fulltext
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Admin Creation date: 2008-03-03    Update date: 2008-07-15    Source: dtu    ID: 211456    Original MXD