Economic MPC

Economic MPC

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

Family: Model Predictive Control Status: 📋 Planned

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Overview

Economic MPC extends the predictive control framework to optimize economic objectives rather than traditional tracking performance. Unlike standard MPC, which focuses on minimizing tracking errors and control effort, Economic MPC directly optimizes economic metrics such as profit, cost, energy consumption, or resource utilization.

This approach is particularly valuable in process industries where economic performance is the primary concern. Economic MPC can handle complex economic objectives, market conditions, and operational constraints while maintaining system stability and safety. The key challenge is to balance economic optimization with system stability and constraint satisfaction.

Mathematical Formulation

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Key Properties

Economic Optimization

min Σ L_econ(x,u,d)

Direct optimization of economic objectives

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Market Integration

L_econ = f(prices, costs, demand)

Incorporates market conditions and forecasts

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Multi-objective

L_econ = α₁L₁ + α₂L₂ + ...

Can combine multiple economic objectives

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Key Properties

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• Economic Focus

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  Optimizes economic objectives rather than tracking performance

• Market Integration

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  Incorporates market prices, demand forecasts, and economic conditions

• Multi-objective Optimization

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  Can handle multiple conflicting economic objectives

• Stability Considerations

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  Must ensure system stability while optimizing economics

• Constraint Handling

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  Maintains operational and safety constraints

Implementation Approaches

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Basic Economic MPC Controller

Standard Economic MPC implementation with economic stage cost

Complexity:

• Time: O(N³)
• Space: O(N²)

Advantages

• Direct optimization of economic objectives

• Incorporates market conditions and forecasts

• Handles multiple economic objectives

• Maintains operational constraints

Disadvantages

• May not guarantee stability without additional terms

• Requires accurate economic models

• Complex tuning of economic parameters

• May be sensitive to market fluctuations

Complete Implementation

The full implementation with error handling, comprehensive testing, and additional variants is available in the source code:

• Main implementation with economic optimization: src/algokit/mpc/economic_mpc.py

• Comprehensive test suite including economic performance tests: tests/unit/mpc/test_economic_mpc.py

Complexity Analysis

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Time & Space Complexity Comparison

Approach	Time Complexity	Space Complexity	Notes
Basic Economic MPC	O(N³)	O(N²)	Complexity depends on prediction horizon N and system dimensions

Performance Considerations

• Economic optimization requires real-time solution

• Computational complexity scales with prediction horizon

• Memory requirements scale with system dimensions

Use Cases & Applications

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Application Categories

Process Industries

• Chemical Plants: Profit maximization in reactor control

• Oil Refineries: Energy optimization in distillation columns

• Power Plants: Economic dispatch and load following

• Manufacturing: Production optimization with market demand

Energy Systems

• Smart Grids: Economic optimization of power generation and distribution

• Renewable Energy: Profit maximization with market prices

• Battery Management: Economic optimization of charging and discharging

• Microgrids: Economic operation of distributed energy resources

Automotive Systems

• Hybrid Vehicles: Fuel economy optimization

• Electric Vehicles: Energy cost minimization

• Fleet Management: Route optimization for cost reduction

• Autonomous Vehicles: Energy-efficient path planning

Supply Chain Management

• Inventory Control: Cost minimization with demand forecasting

• Production Planning: Profit maximization with capacity constraints

• Logistics: Transportation cost optimization

• Resource Allocation: Optimal resource utilization

Financial Systems

• Portfolio Management: Risk-adjusted return optimization

• Trading Systems: Profit maximization with risk constraints

• Insurance: Premium optimization with risk assessment

• Banking: Loan portfolio optimization

Educational Value

• Control Theory: Economic optimization in control systems

• Optimization: Multi-objective optimization and economic modeling

• System Analysis: Economic performance metrics and trade-offs

• Real-time Systems: Implementation of economic optimization algorithms

References & Further Reading

:material-book: Core Textbooks

:material-book:

Model Predictive Control: Theory, Computation, and Design

2017 • Nob Hill Publishing • ISBN 978-0-9759377-0-9

:material-amazon: Buy on Amazon

:material-book:

Model Predictive Control: Classical, Robust and Stochastic

2017 • Springer • ISBN 978-3-319-42053-9

:material-amazon: Buy on Amazon

:material-library: Economic MPC Theory

:material-book:

Optimizing process economic performance using model predictive control

2009 • Nonlinear Model Predictive Control • Pages 119-138

:material-book:

Economic model predictive control with time-varying objective function for nonlinear process systems

2014 • AIChE Journal • Volume 60, pages 507-519

:material-web: Online Resources

:material-link:

Economic MPC

Wikipedia article on MPC

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Process Optimization

Control Engineering article on economic MPC

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Market-based Control

MATLAB Economic MPC documentation

:material-code-tags: Implementation & Practice

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GAMS

General Algebraic Modeling System for optimization

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Pyomo

Python-based optimization modeling language

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CVXPY

Python-embedded modeling language for convex optimization

Interactive Learning

Try implementing the different approaches yourself! This progression will give you deep insight into the algorithm's principles and applications.

Pro Tip: Start with the simplest implementation and gradually work your way up to more complex variants.

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Navigation

Related Algorithms in Model Predictive Control:

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

• 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.