Embedded Online Optimization for Model Predictive Control at Megahertz Rates (1303.1090v1)

Abstract: Faster, cheaper, and more power efficient optimization solvers than those currently offered by general-purpose solutions are required for extending the use of model predictive control (MPC) to resource-constrained embedded platforms. We propose several custom computational architectures for different first-order optimization methods that can handle linear-quadratic MPC problems with input, input-rate, and soft state constraints. We provide analysis ensuring the reliable operation of the resulting controller under reduced precision fixed-point arithmetic. Implementation of the proposed architectures in FPGAs shows that satisfactory control performance at a sample rate beyond 1 MHz is achievable even on low-end devices, opening up new possibilities for the application of MPC on embedded systems.

• The paper develops tailored computational architectures using Nesterov’s fast gradient and ADMM methods to solve constrained linear-quadratic MPC problems.
• It ensures robust control performance through thorough error analysis and fixed-point arithmetic, maintaining bounded numerical stability.
• It demonstrates practical viability with FPGA implementations achieving over 1 MHz sampling rates, enabling fast, real-time control on low-power devices.

Embedded Online Optimization for Model Predictive Control at Megahertz Rates

The research paper presents an advanced paper on the acceleration of Model Predictive Control (MPC) algorithms by employing embedded online optimization techniques suitable for resource-constrained platforms. This exploration is particularly focused on first-order optimization methods implemented on Field Programmable Gate Arrays (FPGAs) to demonstrate significant computational improvements.

Overview of Contributions

The primary contributions of the paper include:

1. Custom Computational Architectures: The authors developed parameterized architectures tailored for different first-order optimization methods. These methods can efficiently solve linear-quadratic MPC problems with constraints. The methods explored include Nesterov’s fast gradient method for input-constrained problems and the Alternating Direction Method of Multipliers (ADMM) for state-constrained problems.
2. Fixed-Point Arithmetic Implementation: The paper provides a detailed analysis to ensure MPC controllers' reliable operation using reduced precision fixed-point arithmetic. This technical implementation is crucial for the adoption of these techniques on low-cost, low-power devices where floating-point arithmetic is not available or is limited by cost and power consumption.
3. Performance Analysis and Proofs: The paper rigorously presents an error analysis yielding theoretical bounds on numerical stability under fixed-point arithmetic. This includes mathematical derivations ensuring that any error from fixed-point arithmetic remains bounded during iterations, thus not compromising the performance of the controller.
4. Practical Implementations: The paper delivers a comprehensive set of guidelines and a design tool for synthesizing these custom controllers on FPGAs. These implementations demonstrate achievable sampling rates beyond 1 MHz, even on low-end devices, thus showing significant potential for real-time applications.

Implications and Results

Numerically, the paper reports MPC sampling rates exceeding 1 MHz, which represents a substantial leap over previous implementations. This efficiency facilitates the application of MPC in systems with stringent timing constraints, thus broadening MPC's applicability in fast dynamic systems.

Moreover, the findings suggest that efficient online MPC solutions are feasible for larger problem instances that would traditionally be unsolvable on embedded platforms due to computational and memory limitations. This can potentially revolutionize how control tasks are executed in embedded systems, providing them with real-time decision-making capabilities previously reserved for high-power desktop solutions.

Theoretical and Practical Impact

Theoretically, the paper extends the knowledge on embedded control systems, particularly demonstrating the feasibility of using fixed-point arithmetic to achieve significant reductions in computational latency. Practically, the research can inspire the reengineering of processes in industries relying on fast and efficient real-time control such as robotics, automotive control systems, and telecommunications.

In terms of future developments, the research sets a groundwork for further exploring fixed-point implementations of other complex algorithms in the control domain. As the computational power of embedded systems continues to increase, these techniques can lead to even faster implementations and wider applications beyond the field discussed in the paper.

Overall, this paper provides substantial insights into the marriage of advanced optimization techniques with embedded control systems, marking a step forward toward real-time, efficient, and low-power control systems on a chip. The explicit demonstration of implementing such techniques on low-end FPGAs demonstrates practical viability and opens avenues for broader application in adaptive and predictive control scenarios.