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Model Predictive Control Algorithms

Model Predictive Control optimizes control actions by solving constrained optimization problems over a prediction horizon.

Model Predictive Control (MPC) is an advanced control strategy that uses a mathematical model

of the system to predict future behavior and optimize control actions over a finite prediction horizon. Unlike traditional control methods, MPC explicitly handles constraints on inputs, outputs, and states while optimizing a performance objective.

MPC has become the standard control method in process industries and is increasingly used in automotive, aerospace, and robotics applications. Its ability to handle multivariable systems, constraints, and nonlinear dynamics makes it particularly powerful for complex control problems where traditional methods fall short.

Overview

Key Characteristics:

  • Predictive Control

    Uses system model to predict future behavior and optimize control actions

  • Constraint Handling

    Explicitly handles constraints on inputs, outputs, and states

  • Receding Horizon

    Optimizes over finite horizon and implements only the first control action

  • Multivariable Control

    Naturally handles systems with multiple inputs and outputs

Common Applications:

  • chemical plants

  • oil refineries

  • power plants

  • pulp and paper

  • engine control

  • vehicle dynamics

  • hybrid vehicles

  • autonomous driving

  • flight control

  • spacecraft guidance

  • unmanned aerial vehicles

  • manipulator control

  • mobile robot navigation

  • humanoid robots

  • smart grids

  • renewable energy

  • battery management

  • microgrids

Key Concepts

  • Prediction Horizon

    Time window over which future behavior is predicted

  • Control Horizon

    Time window over which control actions are optimized

  • Receding Horizon

    Strategy of implementing only the first control action and shifting horizon

  • Constraints

    Limitations on system inputs, outputs, and states

  • Cost Function

    Mathematical expression of control objectives to be minimized

  • State Estimation

    Process of estimating current system state from measurements

  • Disturbance Rejection

    Ability to maintain performance despite external disturbances

  • Stability

    Ensuring closed-loop system remains stable under MPC control

Complexity Analysis

Complexity Overview

Time: O(N³) to O(N⁶) Space: O(N²) to O(N⁴)

Complexity depends on prediction horizon N, system dimensions, and optimization method used

Linear vs Nonlinear MPC

Linear MPC:

  • Uses linear system models
  • Quadratic cost functions
  • Convex optimization problems
  • Fast computation, guaranteed convergence
  • Limited to linear system dynamics

Nonlinear MPC:

  • Uses nonlinear system models
  • General cost functions
  • Non-convex optimization problems
  • More computationally intensive
  • Handles complex nonlinear dynamics

MPC Constraint Categories

  1. Input Constraints: Limits on control actions (actuator limits)
  2. State Constraints: Limits on system states (safety limits)
  3. Output Constraints: Limits on system outputs (performance limits)
  4. Rate Constraints: Limits on rate of change of inputs or states
  5. Soft vs Hard Constraints: Violatable vs strictly enforced constraints

Practical MPC Implementation

Computational Requirements: - Real-time optimization within sampling period - Efficient numerical methods (QP, SQP, interior-point) - Warm-starting for faster convergence

Robustness and Stability: - Terminal constraints for stability - Robust MPC for uncertainty handling - Feasibility and recursive feasibility

Tuning Parameters: - Prediction and control horizons - Weighting matrices in cost function - Constraint softening parameters

Comparison Table

Algorithm Status Time Complexity Space Complexity Difficulty Applications
Distributed MPC 📋 Planned O(N × n³) O(N × n²) Medium Smart Grids, Transportation Systems
Economic MPC 📋 Planned O(N³) O(N²) Medium Process Industries, Energy Systems
Robust MPC 📋 Planned O(N⁴) O(N³) Medium Aerospace Systems, Automotive Systems
Linear MPC 📋 Planned O(N³) O(N²) Medium Industrial Process Control, Automotive Systems
Nonlinear MPC 📋 Planned O(N⁶) O(N⁴) Medium Chemical Process Control, Robotics and Mechatronics
Model Predictive Control 📋 Planned O(N³) O(N²) Medium Process Industries, Automotive Systems
Learning MPC 📋 Planned O(N³ + M) O(N² + M) Medium Robotics and Mechatronics, Automotive Systems

Algorithms in This Family

  • Distributed MPC - Model Predictive Control for large-scale systems using distributed optimization and coordination between multiple local controllers to achieve global objectives.

  • Economic MPC - Model Predictive Control that optimizes economic objectives rather than tracking performance, focusing on profit maximization and cost minimization in process industries.

  • Robust MPC - Model Predictive Control that handles model uncertainty and disturbances through robust optimization techniques to ensure constraint satisfaction and stability.

  • Linear MPC - Model Predictive Control for linear time-invariant systems formulated as a Quadratic Programming problem with efficient real-time solution.

  • Nonlinear MPC - Model Predictive Control for nonlinear systems using Sequential Quadratic Programming to handle complex dynamics and constraints.

  • Model Predictive Control - Advanced control strategy that uses system models to predict future behavior and optimize control actions over a finite horizon while handling constraints.

  • Learning MPC - Model Predictive Control that learns system dynamics and improves performance through data-driven approaches, combining machine learning with predictive control.

Implementation Status

  • Complete

    0/7 algorithms (0%)

  • Planned

    7/7 algorithms (100%)

  • Control: MPC is a specialized control method within the broader control family

  • Optimization: MPC relies heavily on optimization algorithms for solving control problems

  • System-Identification: System models required for MPC are obtained through system identification

  • State-Estimation: State estimation is often integrated with MPC for practical implementation

References

No References

No references available for this algorithm family.

Tags

Model Predictive Control Advanced control algorithms using predictive models

Control Theory Algorithms for system control and feedback

Optimization Algorithms that find optimal solutions to problems

Algorithms General algorithmic concepts and implementations