How do you deal with the computational complexity and scalability of MPC for large-scale systems?

1 Problem formulation

The first step in dealing with the complexity and scalability of MPC is to formulate the optimization problem in a suitable way. This involves defining the objective function, the state-space model, the prediction horizon, the control inputs, and the constraints of the system. Depending on the nature and size of the system, you may need to make some simplifying assumptions, use linear or nonlinear models, discretize the time or space domain, or apply some transformations or approximations to reduce the dimensionality or nonlinearity of the problem. The choice of the problem formulation can have a significant impact on the computational cost and accuracy of the MPC solution.

2 Solution methods

The second step is to choose an appropriate method to solve the optimization problem at each time step. There are various methods available, such as gradient-based methods, interior-point methods, sequential quadratic programming, or direct transcription. Some methods are more suitable for linear or convex problems, while others can handle nonlinear or nonconvex problems. Some methods are faster or more reliable than others, but may also require more memory or iterations. The choice of the solution method depends on the trade-off between speed, accuracy, robustness, and memory requirements of the MPC problem.

3 Distributed and decentralized MPC

The third step is to consider the possibility of using distributed or decentralized MPC, especially for large-scale systems that consist of multiple interconnected subsystems or agents. Distributed MPC involves coordinating the local MPC controllers of each subsystem or agent through a communication network, while decentralized MPC involves designing independent MPC controllers for each subsystem or agent without any communication or coordination. Both approaches can reduce the computational burden and enhance the scalability of MPC, but they also introduce some challenges, such as ensuring stability, feasibility, and performance of the overall system, or dealing with communication delays, failures, or uncertainties.

4 Online and offline MPC

The fourth step is to decide whether to use online or offline MPC, depending on the availability and quality of the data and the model of the system. Online MPC involves solving the optimization problem at each time step using the current measurements and predictions of the system, while offline MPC involves pre-computing and storing the optimal control inputs for different scenarios or states of the system, and then applying them online according to the measurements. Online MPC can adapt to changing conditions and uncertainties, but it requires more computational resources and time. Offline MPC can save computation time and ensure feasibility, but it requires more storage space and may not capture all possible scenarios or uncertainties.

5 Adaptive and learning MPC

The fifth step is to consider the use of adaptive or learning MPC, especially for systems that have uncertain or varying parameters, dynamics, or constraints. Adaptive MPC involves updating the model or the parameters of the system online using the measurements and the estimation techniques, such as recursive least squares, extended Kalman filter, or particle filter. Learning MPC involves using data-driven methods, such as artificial neural networks, reinforcement learning, or Bayesian optimization, to learn the model or the optimal control inputs of the system online or offline. Both approaches can improve the accuracy and robustness of MPC, but they also require more data and computational power, and may introduce some errors or biases.

6 Hardware and software MPC

The sixth step is to choose the appropriate hardware and software platforms to implement and execute the MPC algorithm. This involves selecting the sensors, actuators, processors, memory devices, communication devices, and software tools that can support the MPC requirements and specifications. Depending on the system size, complexity, and constraints, you may need to use dedicated or embedded hardware, such as field-programmable gate arrays (FPGAs), microcontrollers, or digital signal processors (DSPs), or general-purpose hardware, such as personal computers (PCs), servers, or cloud computing. You may also need to use specialized or customized software, such as MATLAB, Simulink, CPLEX, or YALMIP, or general-purpose software, such as Python, C++, or Java. The choice of the hardware and software platforms depends on the trade-off between performance, flexibility, reliability, and cost of the MPC implementation.