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Lecture 3��MPC Formulation, Constraint Handling, and Control Horizons

Instructor: Ercan Atam

Institute for Data Science & Artificial Intelligence

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Course: DSAI 586- Data-Driven Model Predictive Control

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List of contents for this lecture

  • Mathematical representation of MPC
  • Terms used in MPC
  • Constraint handling in MPC
  • MPC formulation with soft/hard constraints
  • MPC with a control horizon / input blocking
  • An alternative way to formulate MPC for LTI systems

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Mathematical Representation of MPC

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Terms used in MPC (1)

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Terms used in MPC (2)

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Terms used in MPC (3)

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Terms used in MPC (4)

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Constraint Handling in MPC

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Input constraints (1)

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Input constraints (2)

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State constraints

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Output constraints

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Hard versus soft constraints

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MPC formulation with soft/hard constraints (1)

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MPC formulation with soft/hard constraints (2)

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MPC formulation with soft/hard constraints (3)

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MPC formulation with soft/hard constraints (4)

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MPC with a control horizon (1)

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MPC with a control horizon (2)

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MPC with input blocks

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Example - Input blocking

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Remarks on control horizon/control input blocking

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An alternative way to formulate MPC for LTI systems (1)

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An alternative way to formulate MPC for LTI systems (2)

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An alternative way to formulate MPC for LTI systems (3)

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An alternative way to formulate MPC for LTI systems (4)

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An alternative way to formulate MPC for LTI systems (5)

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An alternative way to formulate MPC for LTI systems (6)

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An alternative way to formulate MPC for LTI systems (7)

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An alternative way to formulate MPC for LTI systems (8)

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An alternative way to formulate MPC for LTI systems (9)

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An alternative way to formulate MPC for LTI systems (10)

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An alternative way to formulate MPC for LTI systems (11)

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An alternative way to formulate MPC for LTI systems (12)

(1)

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An alternative way to formulate MPC for LTI systems (13)

(2)

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An alternative way to formulate MPC for LTI systems (14)

(1)

(2)

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An alternative way to formulate MPC for LTI systems (15)

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An alternative way to formulate MPC for LTI systems (16)

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An alternative way to formulate MPC for LTI systems (17)

(3)

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An alternative way to formulate MPC for LTI systems (18)

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Summary – MPC for reference tracking control problem

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References �(utilized for preparation of lecture notes or MATLAB code)

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  • “Model Predictive Control System Design and Implementation Using MATLAB”, Liuping Wang, Springer 2009.

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