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Model Predictive Control (MPC) is a computationally demanding control technique that allows dealing with multiple-input and multiple-output systems, while handling constraints in a systematic way. The necessity of solving an optimization problem at every sampling instant often (i) limits the application scope to slow dynamical systems and/or (ii) results in expensive computational hardware implementations. Traditional MPC design is based on manual tuning of software and computational hardware design parameters, which leads to suboptimal implementations. This paper proposes a framework for automating the MPC software and computational hardware co-design, while achieving the optimal trade-off between computational resource usage and controller performance. The proposed approach is based on using a multiobjective optimization algorithm, namely BiMADS. Two test studies are considered: Central Processing Unit (CPU) and Field-Programmable Gate Array (FPGA) implementations of fast gradient-based MPC. Numerical experiments show that optimization-based design outperforms Latin Hypercube Sampling (LHS), a statistical sampling-based design exploration technique.

Abstract-In order to achieve the best possible performance of a model predictive controller (MPC) for a given set of resources, the software algorithm and computational platform have to be designed simultaneously. Moreover, in practical applications the controller design problem has a multi-objective nature: performance is traded off against computational hardware resource usage, namely time, energy and space. This paper proposes formulating an MPC design problem as a multiobjective optimization (MOO) problem in order to explore the design trade-offs in a systematic way.Since the design objectives in the resulting MOO problem are expensive to evaluate, i.e. evaluation requires time consuming simulations, most of the classical and evolutionary MOO algorithms cannot be employed for this class of design problems. For this reason a practical MOO algorithm that can deal with expensive-to-evaluate functions is presented. The algorithm is based on Kriging and the hypervolume criterion that was recently proposed in the expensive optimization literature. A numerical example for a fast gradient-based controller design shows that the proposed approach can efficiently explore optimal performance-resource trade-offs. I. PERFORMANCE VS. TIME, ENERGY AND SPACEModel predictive control (MPC) has already proven to be an efficient and reliable solution for a wide-range of applications, most of which are characterized by relatively slow dynamics. The necessity of solving an optimization problem at each sampling instance has traditionally been the main bottleneck that prevented more significant expansion of MPC, especially in relation to fast dynamic plants. Recent developments in communication technologies and hardware processing systems have sped up online optimization solvers and hence increased the potential application scope of MPC.Most MPC and underlying optimization algorithms are designed at a high level of abstraction without regard to the intended hardware platform. This decoupled approach usually leads to inefficient utilization of available resources [1]. In contrast, the co-design approach implies simultaneous design of both software and hardware components in order to achieve the best possible performance for a given set of available resources. However, improvement of the closed-loop performance cannot be considered as the only design objective. In practice, there is a trade-off between *The work leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Unions Seventh Framework Programme (FP7/2007(FP7/ -2013 e.kerrigan@imperial.ac.uk performance and computational hardware resource usage. Resources that are required to perform computations include time, energy and space, which are also the functions of the MPC algorithm and hardware platform. Instead of looking for one optimal design (which often does not exist due to conflicts between objectives) engineers might make a decision based on the whole series of Pareto optimal designs, i.e. designs that cannot be improved ...

Abstract-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.

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