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Radiation treatment planning involves optimization over a large number of voxels, many of which carry limited information about the clinical problem. We propose an approach to reduce the large optimization problem by only using a representative subset of informative voxels. This way, we drastically improve planning efficiency while maintaining the plan quality. Within an initial probing step, we pre-solve an easier optimization problem involving a simplified objective from which we derive an importance score per voxel. This importance score is then turned into a sampling distribution, which allows us to subsample a small set of informative voxels using importance sampling. By solving a - now reduced - version of the original optimization problem using this subset, we effectively reduce the problem's size and computational demands while accounting for regions where satisfactory dose deliveries are challenging. In contrast to other stochastic (sub-)sampling methods, our technique only requires a single probing and sampling step to define a reduced optimization problem. This problem can be efficiently solved using established solvers without the need of modifying or adapting them. Empirical experiments on open benchmark data highlight substantially reduced optimization times, up to 50 times faster than the original ones, for intensity-modulated radiation therapy (IMRT), all while upholding plan quality comparable to traditional methods. Our novel approach has the potential to significantly accelerate radiation treatment planning by addressing its inherent computational challenges. We reduce the treatment planning time by reducing the size of the optimization problem rather than modifying and improving the optimization method. Our efforts are thus complementary to many previous developments., Comment: 21 pages, 11 figures

Purpose: The importance of robust proton treatment planning to mitigate the impact of uncertainty is well understood. However, its computational cost grows with the number of uncertainty scenarios, prolonging the treatment planning process. We developed a fast and scalable distributed optimization platform that parallelizes this computation over the scenarios. Methods: We modeled the robust proton treatment planning problem as a weighted least-squares problem. To solve it, we employed an optimization technique called the Alternating Direction Method of Multipliers with Barzilai-Borwein step size (ADMM-BB). We reformulated the problem in such a way as to split the main problem into smaller subproblems, one for each proton therapy uncertainty scenario. The subproblems can be solved in parallel, allowing the computational load to be distributed across multiple processors (e.g., CPU threads/cores). We evaluated ADMM-BB on four head-and-neck proton therapy patients, each with 13 scenarios accounting for 3 mm setup and 3:5% range uncertainties. We then compared the performance of ADMM-BB with projected gradient descent (PGD) applied to the same problem. Results: For each patient, ADMM-BB generated a robust proton treatment plan that satisfied all clinical criteria with comparable or better dosimetric quality than the plan generated by PGD. However, ADMM-BB's total runtime averaged about 6 to 7 times faster. This speedup increased with the number of scenarios. Conclusion: ADMM-BB is a powerful distributed optimization method that leverages parallel processing platforms, such as multi-core CPUs, GPUs, and cloud servers, to accelerate the computationally intensive work of robust proton treatment planning. This results in 1) a shorter treatment planning process and 2) the ability to consider more uncertainty scenarios, which improves plan quality., Comment: 20 pages, 6 figures

Reducing proton treatment time improves patient comfort and decreases the risk of error from intra-fractional motion, but must be balanced against clinical goals and treatment plan quality. We formulated the proton treatment planning problem as a convex optimization problem with a cost function consisting of a dosimetric plan quality term plus a weighted $l_1$ regularization term. We iteratively solved this problem and adaptively updated the regularization weights to promote the sparsity of both the spots and energy layers. The proposed algorithm was tested on four head-and-neck cancer patients, and its performance was compared with existing standard $l_1$ and group $l_2$ regularization methods. We also compared the effectiveness of the three methods ($l_1$, group $l_2$, and reweighted $l_1$) at improving plan delivery efficiency without compromising dosimetric plan quality by constructing each of their Pareto surfaces charting the trade-off between plan delivery and plan quality. The reweighted $l_1$ regularization method reduced the number of spots and energy layers by an average over all patients of 40% and 35%, respectively, with an insignificant cost to dosimetric plan quality. From the Pareto surfaces, it is clear that reweighted $l_1$ provided a better trade-off between plan delivery efficiency and dosimetric plan quality than standard $l_1$ or group $l_2$ regularization, requiring the lowest cost to quality to achieve any given level of delivery efficiency. In summary, reweighted $l_1$ regularization is a powerful method for simultaneously promoting the sparsity of spots and energy layers at a small cost to dosimetric plan quality. This sparsity reduces the time required for spot scanning and energy layer switching, thereby improving the delivery efficiency of proton plans., Comment: 38 pages, 13 figures

We present an optimization-based approach to radiation treatment planning over time. Our approach formulates treatment planning as an optimal control problem with nonlinear patient health dynamics derived from the standard linear-quadratic cell survival model. As the formulation is nonconvex, we propose a method for obtaining an approximate solution by solving a sequence of convex optimization problems. This method is fast, efficient, and robust to model error, adapting readily to changes in the patient's health between treatment sessions. Moreover, we show that it can be combined with the operator splitting method ADMM to produce an algorithm that is highly scalable and can handle large clinical cases. We introduce an open-source Python implementation of our algorithm, AdaRad, and demonstrate its performance on several examples., Comment: 30 pages, 8 figures, 2 tables

Wide Area Cyber-Physical Systems (WA-CPSs) are a class of control systems that integrate low-powered sensors, heterogeneous actuators and computer controllers into large infrastructure that span multi-kilometre distances. Current wireless communication technologies are incapable of meeting the communication requirements of range and bounded delays needed for the control of WA-CPSs. To solve this problem, we use a Control-Communication Co-design approach for WA-CPSs, that we refer to as the $C^3$ approach, to design a novel Low-Power Wide Area (LPWA) MAC protocol called \textit{Ctrl-MAC} and its associated event-triggered controller that can guarantee the closed-loop stability of a WA-CPS. This is the first paper to show that LPWA wireless communication technologies can support the control of WA-CPSs. LPWA technologies are designed to support one-way communication for monitoring and are not appropriate for control. We present this work using an example of a water distribution network application which we evaluate both through a co-simulator (modelling both physical and cyber subsystems) and testbed deployments. Our evaluation demonstrates full control stability, with up to $50$\% better packet delivery ratios and $80$\% less average end-to-end delays when compared to a state of the art LPWA technology. We also evaluate our scheme against an idealised, wired, centralised, control architecture and show that the controller maintains stability and the overshoots remain within bounds., Comment: Accepted for publication at ACM Transactions on Cyber-Physical Systems

Industrial Control Systems (ICS) are evolving with advances in new technology. The addition of wireless sensors and actuators and new control techniques means that engineering practices from communication systems are being integrated into those used for control systems. The two are engineered in very different ways. Neither engineering approach is capable of accounting for the subtle interactions and interdependence that occur when the two are combined. This paper describes our first steps to bridge this gap, and push the boundaries of both computer communication system and control system design. We present The Separator testbed, a Cyber-Physical testbed enabling our search for a suitable way to engineer systems that combine both computer networks and control systems., Comment: 6 pages, 4 figures

We consider the problem of non-smooth convex optimization with linear equality constraints, where the objective function is only accessible through its proximal operator. This problem arises in many different fields such as statistical learning, computational imaging, telecommunications, and optimal control. To solve it, we propose an Anderson accelerated Douglas-Rachford splitting (A2DR) algorithm, which we show either globally converges or provides a certificate of infeasibility/unboundedness under very mild conditions. Applied to a block separable objective, A2DR partially decouples so that its steps may be carried out in parallel, yielding an algorithm that is fast and scalable to multiple processors. We describe an open-source implementation and demonstrate its performance on a wide range of examples., Comment: 27 pages, 8 figures

We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex restriction. This restriction is, by definition, conservative; to mitigate its impact on the clinical objectives, we develop a two-pass planning algorithm that allows each dose-volume constraint to be met exactly on a second pass by the solver if its corresponding restriction is feasible on the first pass. In another variant, we add slack variables to each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints or when the constraints are made infeasible by our restriction. Finally, we introduce ConRad, a Python-embedded open-source software package for convex radiation treatment planning. ConRad implements the methods described above and allows users to construct and plan cases through a simple interface., Comment: 27 pages, 6 figures

CVXR is an R package that provides an object-oriented modeling language for convex optimization, similar to CVX, CVXPY, YALMIP, and Convex.jl. It allows the user to formulate convex optimization problems in a natural mathematical syntax rather than the restrictive form required by most solvers. The user specifies an objective and set of constraints by combining constants, variables, and parameters using a library of functions with known mathematical properties. CVXR then applies signed disciplined convex programming (DCP) to verify the problem's convexity. Once verified, the problem is converted into standard conic form using graph implementations and passed to a cone solver such as ECOS or SCS. We demonstrate CVXR's modeling framework with several applications., Comment: 34 pages, 9 figures

Periodic event-triggered control (PETC) is a version of event-triggered control (ETC) that only requires to measure the plant output periodically instead of continuously. In this work, we present a construction of timing models for these PETC implementations to capture the dynamics of the traffic they generate. In the construction, we employ a two-step approach. We first partition the state space into a finite number of regions. Then in each region, the event-triggering behavior is analyzed with the help of LMIs. The state transitions among different regions result from computing the reachable state set starting from each region within the computed event time intervals.

Asynchronous decentralized event-triggered control (ADETC) is an implementation of controllers characterized by decentralized event generation, asynchronous sampling updates, and dynamic quantization. Combining those elements in ADETC results in a parsimonious transmission of information which makes it suitable for wireless networked implementations. We extend the previous work on ADETC by introducing periodic sampling, denoting our proposal asynchronous decentralized periodic event-triggered control (ADPETC), and study the stability and L2-gain of ADPETC for implementations affected by disturbances. In ADPETC, at each sampling time, quantized measurements from those sensors that triggered a local event are transmitted to a dynamic controller that computes control actions; the quantized control actions are then transmitted to the corresponding actuators only if certain events are also triggered for the corresponding actuator. The developed theory is demonstrated and illustrated via a numerical example.

Energy constraint long-range wireless sensor/ actuator based solutions are theoretically the perfect choice to support the next generation of city-scale cyber-physical systems. Traditional systems adopt periodic control which increases network congestion and actuations while burdens the energy consumption. Recent control theory studies overcome these problems by introducing aperiodic strategies, such as event trigger control. In spite of the potential savings, these strategies assume actuator continuous listening while ignoring the sensing energy costs. In this paper, we fill this gap, by enabling sensing and actuator listening duty-cycling and proposing two innovative MAC protocols for three decentralized event trigger control approaches. A laboratory experimental testbed, which emulates a smart water network, was modelled and extended to evaluate the impact of system parameters and the performance of each approach. Experimental results reveal the predominance of the decentralized event-triggered control against the classic periodic control either in terms of communication or actuation by promising significant system lifetime extension.