Abstract Online tuning of particle accelerators is a complex optimisation problem that continues to require manual intervention by experienced human operators. Autonomous tuning is a rapidly ...expanding field of research, where learning-based methods like Bayesian optimisation (BO) hold great promise in improving plant performance and reducing tuning times. At the same time, reinforcement learning (RL) is a capable method of learning intelligent controllers, and recent work shows that RL can also be used to train domain-specialised optimisers in so-called reinforcement learning-trained optimisation (RLO). In parallel efforts, both algorithms have found successful adoption in particle accelerator tuning. Here we present a comparative case study, assessing the performance of both algorithms while providing a nuanced analysis of the merits and the practical challenges involved in deploying them to real-world facilities. Our results will help practitioners choose a suitable learning-based tuning algorithm for their tuning tasks, accelerating the adoption of autonomous tuning algorithms, ultimately improving the availability of particle accelerators and pushing their operational limits.
We propose a distributed model predictive control scheme for linear time-invariant constrained systems that admit a separable structure. To exploit the merits of distributed computation algorithms, ...the terminal cost and invariant terminal set of the optimal control problem need to respect the coupling structure of the system. Existing methods to address this issue typically separate the synthesis of terminal controllers and costs from the one of terminal sets, and do not explicitly consider the effect of the current and predicted system states on this synthesis process. These limitations can adversely affect performance due to small or even empty terminal sets. Here, we present a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the same optimization problem. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the terminal cost and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several numerical examples.
This paper considers the convergence speed of multi-agent systems with discrete-time double-integrator dynamics. The communication topology is assumed to be fixed and undirected. The speed of ...convergence of the associated average consensus protocol is analyzed, and the problem of maximizing the convergence speed over the free parameters in the consensus protocol is considered. A closed-form solution to this problem is proposed assuming that the ratios of weights of communication links are fixed. Furthermore it is shown that when the weight ratios are considered as decision variables, a global optimum of the convergence speed can be obtained by solving an LMI problem. Simulation results are provided that demonstrate the effectiveness of the proposed approach.
This paper considers the optimization of the convergence speed of consensus under given damping constraints for multi-agent systems with discrete-time double-integrator dynamics with fixed ...interconnection topology. This work summarizes and details existing results in the case of undirected topologies and extends them to directed ones. The interconnection topology is assumed to be connected or to contain a rooted-out branching, respectively. Depending on the minimum required damping, for undirected interconnection topologies in most cases analytic solutions are provided. The structure of these solutions is independent of the size of the network and only depends on the largest and second smallest eigenvalue of the corresponding Laplacian. For the remaining cases without analytic solutions provided, a combined bisection grid search is presented that solves the constrained optimization problem efficiently. This algorithm can also be applied to directed interconnection topologies and, as for the undirected case, converges to the single optimum. Simulation results are provided that demonstrate the effectiveness of the proposed approach.
Various efforts have been devoted to developing stabilizing distributed model predictive control (MPC) schemes for tracking piecewise constant references. In these schemes, terminal sets are usually ...computed offline and used in the MPC online phase to guarantee recursive feasibility and asymptotic stability. Maximal invariant terminal sets do not necessarily respect the distributed structure of the network, hindering the distributed implementation of the controller. On the other hand, ellipsoidal terminal sets respect the distributed structure, but may lead to conservative schemes. In this article, a novel distributed MPC scheme is proposed for reference tracking of networked dynamical systems, where the terminal ingredients are reconfigured online depending on the closed-loop states to alleviate the aforementioned issues. The resulting nonconvex infinite-dimensional problem is approximated using a quadratic program. The proposed scheme is tested in simulation, where the proposed MPC problem is solved using distributed optimization.
We present an approximate method for solving nonlinear control problems over long time horizons, in which the full nonlinear model is preserved over an initial part of the horizon, while the ...remainder of the horizon is modeled using a linear relaxation. As this approximate problem may still be too large to solve directly, we present a Benders decomposition-based solution algorithm that iterates between solving the nonlinear and linear parts of the horizon. This extends the dual dynamic programming approach commonly employed for optimization of linearized hydro power systems. We prove that the proposed algorithm converges after a finite number of iterations, even when the nonlinear initial stage problems are solved inexactly. We also bound the suboptimality of the split-horizon method with respect to the original nonlinear problem, in terms of the properties of a map between the linear and nonlinear state-input trajectories. We then apply this method to a case study concerning a multiple reservoir hydro system, approximating the nonlinear head effects in the second stage using McCormick envelopes. We demonstrate that near-optimal solutions can be obtained in a shrinking horizon setting when the full nonlinear model is used for only a short initial section of the horizon. For this example, the approach is shown to be more practical than both conventional dynamic programming and a multi-cell McCormick envelope approximation from the literature.
This paper considers distributed control of a class of interconnected systems, namely decomposable linear parameter-varying (LPV) systems, which include multi-agent systems with LPV agent models and ...switching communication topology as a special case. Sufficient conditions for stability are established for uncertain time-invariant as well as for time-varying interconnection topologies in a known set. Recent work on distributed state feedback controller synthesis is extended to robust output feedback controller synthesis. Here robustness refers to variations in the topology as well as the LPV dynamics of the subsystems.
This article presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are ...interconnected over a directed graph are considered. Techniques from robust and gain-scheduled controller synthesis are employed, in particular, the full-block S-procedure, to deal with the decentralized system part in a nominal condition and with the interconnection part in a multiplier condition. Under some structural assumptions, we can decompose the synthesis conditions into conditions that are the size of the individual subsystems. To solve these decomposed synthesis conditions that are coupled only over neighboring subsystems, we propose a distributed method based on the alternating direction method of multipliers. It only requires nearest-neighbor communication and no central coordination is needed. Then, a new classification of systems is introduced that consists of groups of homogeneous subsystems with different interconnection types. This classification includes heterogeneous systems as the most general and homogeneous systems as the most specific case. Based on this classification, we show how the interconnected system model and the decomposed synthesis conditions can be formulated in a more compact way. The computational scalability of the presented methods with respect to a growing number of subsystems and interconnections is analyzed, and the results are demonstrated in numerical examples.
In this paper, we consider the problem of controller tuning for an operating unit in a building energy system. The illustrative example used here is a real heat pump located in the NEST building at ...Empa, Dubendorf, Zurich, with its outflow temperature controlled by a PI-controller. The plant is in use and accordingly, intervening in its normal operation is not allowed. Moreover, the model of plant is not available or it can be changed due to aging or possible modification. Accordingly, it is desired to utilize a tuning method which is model-free, operates online, does not intervene with the normal operation of the plant and use only the available historical measurement data. Additionally, it is required to guarantee the safety of the plant during the tuning procedure. In this regard, we formulate the controller tuning problem as a black-box optimization and adopt a safe Bayesian optimization approach for controller parameters tuning. In order to assess numerically the performances of the scheme, first we model the plant as a nonlinear ARX model in form of a feedforward neural network. Subsequently, we train the neural network using the available historical measurement data. Finally, the obtained model is used as an oracle in the controller tuning procedure in order to numerically verify the effectivity of the proposed approach.
Superconducting cavities are responsible for beam acceleration in superconducting linear accelerators. Challenging cavity control specifications are necessary to reduce radio frequency (RF) costs and ...to maximize the availability of the accelerator. Cavity detuning and bandwidth are two critical parameters to monitor when operating particle accelerators. Cavity detuning is strongly related to the power required to generate the desired accelerating gradient. Cavity bandwidth is related to the cavity RF losses. A sudden increase in bandwidth can indicate the presence of a quench or multipacting event. Therefore, calculating these parameters in real time in the low-level RF (LLRF) system is highly desirable. A real-time estimation of the bandwidth allows for a faster response of the machine protection system in the case of quench events, whereas the estimation of cavity detuning can be used to drive piezoelectric tuner-based resonance control algorithms. In this article, a new field programmable gate array (FPGA)-based estimation component is presented. Such a component is designed to be used either in continuous wave (CW) or pulsed operation mode with loaded quality factors between <inline-formula> <tex-math notation="LaTeX">10^{6} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">10^{8} </tex-math></inline-formula>. Results of this component with free-electron LASer in Hamburg (FLASH), European X-ray free electron laser (EuXFEL), cryo module test bench (CMTB), and electron linac for beams with high brilliance and low emittance (ELBE) are presented.
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