Feedback and time are essential for the optimal control of computing systems

The performance, reliability, cost, size and energy usage of computing systems can be improved by one or more orders of magnitude by the systematic use of modern control and optimization methods. Computing systems rely on the use of feedback algorithms to schedule tasks, data and resources, but the models that are used to design these algorithms are validated using open-loop metrics. By using closed-loop metrics instead, such as the gap metric developed in the control community, it should be possible to develop improved scheduling algorithms and computing systems that have not been over-engineered. Furthermore, scheduling problems are most naturally formulated as constraint satisfaction or mathematical optimization problems, but these are seldom implemented using state of the art numerical methods, nor do they explicitly take into account the fact that the scheduling problem itself takes time to solve. This paper makes the case that recent results in real-time model predictive control, where optimization problems are solved in order to control a process that evolves in time, are likely to form the basis of scheduling algorithms of the future. We therefore outline some of the research problems and opportunities that could arise by explicitly considering feedback and time when designing optimal scheduling algorithms for computing systems

Robustly stable feedback min-max model predictive control

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Optimal Active Control of a Wave Energy Converter

Abstract-This paper investigates optimal active control schemes applied to a point absorber wave energy converter within a receding horizon fashion. A variational formulation of the power maximization problem is adapted to solve the optimal control problem. The optimal control method is shown to be of a bang-bang type for a power take-off mechanism that incorporates both linear dampers and active control elements. We also consider a direct transcription of the optimal control problem as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard NLP solver. Since the system model is bilinear and the cost function is non-convex quadratic, the resulting optimization problem is not a convex quadratic program. Results will be compared with an optimal command latching method to demonstrate the improvement in absorbed power. Time domain simulations are generated under irregular sea conditions

Co-design of Hardware and Algorithms for Real-time Optimization

It is difficult or impossible to separate the performance of an optimization solver from the architecture of the computing system on which the algorithm is implemented. This is particularly true if measurements from a physical system are used to update and solve a sequence of mathematical optimization problems in real-time, such as in control, automation, signal processing and machine learning. In these real-time optimization applications the designer has to trade off computing time, space and energy against each other, while satisfying constraints on the performance and robustness of the resulting cyber-physical system. This paper is an informal introduction to the issues involved when designing the computing hardware and a real-time optimization algorithm at the same time, which can result in systems with efficiencies and performances that are unachievable when designing the sub-systems independently. The co-design process can, in principle, be formulated as a sequence of uncertain and non-smooth optimization problems. In other words, optimizers might be used to design optimizers. Before this can become a reality, new systems theory and numerical methods will have to be developed to solve these co-design problems effectively and reliably

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

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

Sensitivity-based multistep MPC for embedded systems

In model predictive control (MPC), an optimization problem is solved every sampling instant to determine an optimal control for a physical system. We aim to accelerate this procedure for fast systems applications and address the challenge of implementing the resulting MPC scheme on an embedded system with limited computing power. We present the sensitivity-based multistep MPC, a strategy which considerably reduces the computing requirements in terms of floating point operations (FLOPs), compared to a standard MPC formulation, while fulfilling closed- loop performance expectations. We illustrate by applying the method to a DC-DC converter model and show how a designer can optimally trade off closed-loop performance considerations with computing requirements in order to fit the controller into a resource-constrained embedded system