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# lec16 - MIT OpenCourseWare http/ocw.mit.edu 16.323...

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MIT OpenCourseWare http://ocw.mit.edu 16.323 Principles of Optimal Control Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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16.323 Lecture 16 Model Predictive Control Allgower, F., and A. Zheng, Nonlinear Model Predictive Control, Springer-Verlag, 2000. Camacho, E., and C. Bordons, Model Predictive Control, Springer-Verlag, 1999. Kouvaritakis, B., and M. Cannon, Non-Linear Predictive Control: Theory & Practice, IEE Publishing, 2001. Maciejowski, J., Predictive Control with Constraints, Pearson Education POD, 2002. Rossiter, J. A., Model-Based Predictive Control: A Practical Approach, CRC Press, 2003.
Spr 2008 16.323 16–1 MPC Planning in Lecture 8 was effectively “open-loop” Designed the control input sequence u ( t ) using an assumed model and set of constraints. Issue is that with modeling error and/or disturbances, these inputs will not necessarily generate the desired system response. Need a “closed-loop” strategy to compensate for these errors. Approach called Model Predictive Control Also known as receding horizon control Basic strategy: At time k , use knowledge of the system model to design an input sequence u ( k | k ) , u ( k + 1 | k ) , u ( k + 2 | k ) , u ( k + 3 | k ) , . . . , u ( k + N | k ) over a finite horizon N from the current state x ( k ) Implement a fraction of that input sequence, usually just first step. Repeat for time k + 1 at state x ( k + 1) June 18, 2008 Reference "Optimal" future outputs "Optimal" future inputs Future outputs, no control Future inputs, no control Old outputs Old inputs Past Present Future Time MPC: basic idea (from Bo Wahlberg) Figure by MIT OpenCourseWare.

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Spr 2008 16.323 16–2 Note that the control algorithm is based on numerically solving an optimization problem at each step Typically a constrained optimization Main advantage of MPC: Explicitly accounts for system constraints. Doesn’t just design a controller to keep the system away from them. Can easily handle nonlinear and time-varying plant dynamics, since the controller is explicitly a function of the model that can be mod- ified in real-time (and plan time) Many commercial applications that date back to the early 1970’s, see http://www.che.utexas.edu/ ~ qin/cpcv/cpcv14.html Much of this work was in process control - very nonlinear dynamics, but not particularly fast. As computer speed has increased, there has been renewed interest in applying this approach to applications with faster time-scale: trajec- tory design for aerospace systems.
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