Quantization in Control Systems and Forward Error Analysis of Iterative Numerical Algorithms

The use of control theory to study iterative algorithms, which can be considered as dynamical systems, opens many opportunities to find new tools for analysis of algorithms. In this paper we show that results from the study of quantization effects in control systems can be used to find systematic ways for forward error analysis of iterative algorithms. The proposed schemes are applied to the classical iterative methods for solving a system of linear equations. The obtained bounds are compared with bounds given in the numerical analysis literature

A Warm-start Interior-point Method for Predictive Control

In predictive control, a quadratic program (QP) needs to be solved at each sampling instant. We present a new warm-start strategy to solve a QP with an interior-point method whose data is slightly perturbed from the previous QP. In this strategy, an initial guess of the unknown variables in the perturbed problem is determined from the computed solution of the previous problem. We demonstrate the effectiveness of our warm-start strategy to a number of online benchmark problems. Numerical results indicate that the proposed technique depends upon the size of perturbation and it leads to a reduction of 30–74% in floating point operations compared to a cold-start interior-point method

Computer Architectures to Close the Loop in Real-time Optimization

© 2015 IEEE.Many modern control, automation, signal processing and machine learning applications rely on solving a sequence of optimization problems, which are updated with measurements of a real system that evolves in time. The solutions of each of these optimization problems are then used to make decisions, which may be followed by changing some parameters of the physical system, thereby resulting in a feedback loop between the computing and the physical system. Real-time optimization is not the same as fast optimization, due to the fact that the computation is affected by an uncertain system that evolves in time. The suitability of a design should therefore not be judged from the optimality of a single optimization problem, but based on the evolution of the entire cyber-physical system. The algorithms and hardware used for solving a single optimization problem in the office might therefore be far from ideal when solving a sequence of real-time optimization problems. Instead of there being a single, optimal design, one has to trade-off a number of objectives, including performance, robustness, energy usage, size and cost. We therefore provide here a tutorial introduction to some of the questions and implementation issues that arise in real-time optimization applications. We will concentrate on some of the decisions that have to be made when designing the computing architecture and algorithm and argue that the choice of one informs the other

Energy-aware MPC co-design for DC-DC converters

In this paper, we propose an integrated controller design methodology for the implementation of an energy-aware explicit model predictive control (MPC) algorithms, illustrat- ing the method on a DC-DC converter model. The power consumption of control algorithms is becoming increasingly important for low-power embedded systems, especially where complex digital control techniques, like MPC, are used. For DC-DC converters, digital control provides better regulation, but also higher energy consumption compared to standard analog methods. To overcome the limitation in energy efficiency, instead of addressing the problem by implementing sub-optimal MPC schemes, the closed-loop performance and the control algorithm power consumption are minimized in a joint cost function, allowing us to keep the controller power efficiency closer to an analog approach while maintaining closed-loop op- timality. A case study for an implementation in reconfigurable hardware shows how a designer can optimally trade closed-loop performance with hardware implementation performance

Robust explicit MPC design under finite precision arithmetic

We propose a design methodology for explicit Model Predictive Control (MPC) that guarantees hard constraint satisfaction in the presence of finite precision arithmetic errors. The implementation of complex digital control techniques, like MPC, is becoming increasingly adopted in embedded systems, where reduced precision computation techniques are embraced to achieve fast execution and low power consumption. However, in a low precision implementation, constraint satisfaction is not guaranteed if infinite precision is assumed during the algorithm design. To enforce constraint satisfaction under numerical errors, we use forward error analysis to compute an error bound on the output of the embedded controller. We treat this error as a state disturbance and use this to inform the design of a constraint-tightening robust controller. Benchmarks with a classical control problem, namely an inverted pendulum, show how it is possible to guarantee, by design, constraint satisfaction for embedded systems featuring low precision, fixed-point computations