MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. MPC is an optimal control technique in which the calculated control actions minimize a cost function for a constrained dynamical system over a finite, receding horizon. At each time step, an MPC controller receives or estimates the current state of the plant. It then calculates the sequence of control actions that minimize the cost over the horizon by solving a constrained optimization problem that relies on an internal plant model and depends on the current system state. The controller then applies to the plant only the first computed control action, disregarding the following ones. In the following time step, the process repeats.

MPC controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is that it allows the current timeslot to be optimized while keeping future timeslots in account. This is achieved by optimizing a finite time horizon but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from a linear–quadratic regulator (LQR). Also, MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability.

Prerequisite: Control Theory, Numerical Optimization, MATLAB and Simulink


Dr Amirhosein Nikoofard

Dr. Amirhossein Nikoofard

Assistant Professor
Department of Electrical Engineering, Control Systems
Member of APAC research group
K. N. Toosi University of Science and Technology

  • Introduction
    • Introduction to MPC
    • Typical industrial structure
    • MPC algorithms architecture
    • History of MPC
  • Linear Model Predictive Control Design
    • Steady-state optimization
    • Dynamic optimization
    • Quick overview of numerical optimization problems
    • MPC for linear time-invariant discrete-time systems. Implementation in code.
    • Overview of quadratic programming and the active set methods.
  • Linear Model Predictive Control Analysis
    • Asymptotic (exponential) stability analysis
    • Feasibility and Stability
    • Stability and Invariance of MPC
    • Practical Issues
  • Nonlinear Systems
    • Linear parameter-varying, time-varying, and nonlinear MPC
    • Moving horizon estimators
  • Advanced Topics on MPC
    • Explicit MPC
    • Economic MPC
    • Hybrid MPC
    • Robust MPC
    • Distributed MPC
    • Stochastic MPC
    • data-driven MPC
  1. Borrelli, F., Bemporad, A. and Morari, M., Predictive control for linear and hybrid systems. Cambridge University Press, 2017.
  2. Camacho, E. F., & Alba, C. B. (2013). Model predictive control. Springer
  3. Wang, L., 2009. Model predictive control system design and implementation using MATLAB®. Springer.
  4. Huang, S., & Lee, T. H. (2013). Applied predictive control. Springer
  5. Grüne, L., & Pannek, J. (2017). Nonlinear model predictive control.
1About the course, Reference, MPC Introduction, Two Different Perspectives, Constraints in Control, Important Aspects of MPC, Daily-life examples of MPC, Autonomous dNaNo Race Cars, History of MPC, MPC in industry, MPC in Aeronautic industry, MPC in Smart Electricity Grids, MPC research is driven by applications, Benefits of MPC2.66 MBDirect Link
2Keywords, Models of Dynamic Systems, Nonlinear Time-Invarient Continuous-Time State Space Models, LTI Continuous-Time State Space Models, Nonlinear Time-Invarient Discrete-Time State Space Models, LTI Discrete-Time State Space Models, Discrete-Time Model, Discrete-Time Model Stability526 KBDirect Link
3Numerical Optimization Methods, Introduction, Unconstrained Optimization, Constrained Optimization, Modeling languages for optimization problems, Solving optimization problems960 KBDirect Link
4Optimal Control Introduction and Unconstrained Linear Quadratic Control, Optimal Control Introduction, Batch Approach, Recursive Approach, Dynamic Programming Algorithm, Linear Quadratic Optimal Control818 KBDirect Link
5Optimal Control, Receding horizon control, Impact of Horizon Length (Example), Linear Quadratic Optimal Control, Constrained Linear Optimal Control, Constrained Optimal Control: 2-Norm3.8 MBDirect Link
6Basic Ideas of Predictive Control, Receding Horizon Control Notation, MPC Features, Stability and Invariance of MPC, Feasibility and Stability, Extension to Nonlinear MPC7.54 MBDirect Link
7Soft Constraints, Reference Tracking457 KBDirect Link
8MPC Simulink488 KBDirect Link
9Robust MPC, Uncertainty Models, Examples of Common Uncertainty Models, Goals of Robust Constrained Control, Uncertain State Evolution, Robust Constraint Satisfaction, Putting it Together, MPC as a Game, Closed-Loop Predictions, Tube MPC, Tube MPC: System Decomposition, Tube MPC: Error Dynamics, Tube MPC: The Idea, Noisy System Trajectory, Constraint Tightening, Tube-MPC: Problem Formulation, Tube MPC -Example, Tube MPC -Summary, Robust MPC for Uncertain Systems Summary880 KBDirect Link
10Hybrid MPC, Introduction, Hybrid dynamical systems, Technological push for studying hybrid systems, Examples of Hybrid Systems, Key requirements for hybrid models, Piecewise Affine (PWA) Systems, Discrete Hybrid Automaton (DHA), Switched affine system, Event generator, Finite state machine, Transformation of a DHA into linear (in)equalities, Mixed Logical Dynamical (MLD) systems, MLD Hybrid Model Well-Posedness, HYbridSystem Description Language2.8 MBDirect Link
11Hybrid MPC, Optimal Control for Hybrid Systems: General Formulation, Mixed Integer Linear Programming, Mixed Integer Quadratic Programming, Branch & bound method for MIQP, Hybrid Model Predictive Control, MIQP formulation of Hybrid MPC, Hybrid MPC for reference tracking, Closed-loop convergence, Closed-loop convergence proof, MILP formulation of Hybrid MPC, Mixed-Integer Programming solvers, MPC for Hybrid Systems -Complexity, Hybrid MPC of an inverted pendulum, Example in supply chain management, Supply chain management -Dynamics, Supply chain management - HYSDEL code, Supply chain management - Objectives, Supply chain management - Performance index, Supply chain management - Simulation setup, Supply chain management - Simulation results, Hybrid MPC: Summary2.2 MBDirect Link
12Explicit Model Predictive Control, Introduction, Multiparametric Programming, Explicit Linear MPC, Explicit Hybrid MPC, Explicit MPC: Summary1.54 MBDirect Link
13Dynamic State Estimation for Dynamical Systems, Introduction, Stochastic estimators, Stochastic Estimator: The Extended Kalman Filter, DeterminsticEstimators (Observers), Luenberger Observerand Plant Dynamics, Observer-Based Control, State observer for MPC, Extended model for observer design, Kalman filter design, I/O feedthrough1.6 MBDirect Link
14Data-driven MPC, Data-driven direct controller synthesis, Data-driven MPC -An example, Optimal data-driven MPC, Data-driven optimal policy search, Optimal Policy Search Problem, Descent Direction, Optimal Policy Search Algorithm, Special Case: Output Tracking, Learning MPC from data950 KBDirect Link
15dynamics, constraints and cost function, MPC: optimal control problem and assumptions, NMPC: a note on computational aspects, Summery:Choiceof prediction model, Conclusions, MPC research areas and researchers419 KBDirect Link