The effect of small-amplitude time-dependent changes to the surface morphology of a sphere

Typical approaches to manipulation of flow separation employ passive means or active techniques such as blowing and suction or plasma acceleration. Here it is demonstrated that the flow can be significantly altered by making small changes to the shape of the surface. A proof of concept experiment is performed using a very simple time-dependent perturbation to the surface of a sphere: a roughness element of 1% of the sphere diameter is moved azimuthally around a sphere surface upstream of the uncontrolled laminar separation point, with a rotational frequency as large as the vortex shedding frequency. A key finding is that the non-dimensional time to observe a large effect on the lateral force due to the perturbation produced in the sphere boundary layers as the roughness moves along the surface is ˆt =tU_(∞)/D ≈4. This slow development allows the moving element to produce a tripped boundary layer over an extended region. It is shown that a lateral force can be produced that is as large as the drag. In addition, simultaneous particle image velocimetry and force measurements reveal that a pair of counter-rotating helical vortices are produced in the wake, which have a significant effect on the forces and greatly increase the Reynolds stresses in the wake. The relatively large perturbation to the flow-field produced by the small surface disturbance permits the construction of a phase-averaged, three-dimensional (two-velocity component) wake structure from measurements in the streamwise/radial plane. The vortical structure arising due to the roughness element has implications for flow over a sphere with a nominally smooth surface or distributed roughness. In addition, it is shown that oscillating the roughness element, or shaping its trajectory, can produce a mean lateral force

Automatic Scenario Generation for Robust Optimal Control Problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness while increasing the size of the optimization problems. Mitigating the size of the problem by reducing the number of scenarios requires knowledge about how the uncertainty affects the system. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric uncertainty. We show that nonlinear robust optimal control problems are equivalent to semi-infinite optimization problems and can be solved by local reduction. By iteratively adding interim globally worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. In particular, we show that local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. The proposed approach is illustrated with a case study with both parametric and additive time-varying uncertainty. The number of scenarios obtained from local reduction is 101, smaller than in the case when all 2 14+3×192 boundary scenarios are considered. A validation with randomly-drawn scenarios shows that our proposed approach reduces the number of scenarios and ensures robustness even if local solvers are used

On Polyhedral Projection and Parametric Programming

This paper brings together two fundamental topics: polyhedral projection and parametric linear programming. First, it is shown that, given a parametric linear program (PLP), a polyhedron exists whose projection provides the solution to the PLP. Second, the converse is tackled and it is shown how to formulate a PLP whose solution is the projection of an appropriately defined polyhedron described as the intersection of a finite number of halfspaces. The input to one operation can be converted to an input of the other operation and the resulting output can be converted back to the desired form in polynomial time—this implies that algorithms for computing projections or methods for solving parametric linear programs can be applied to either problem clas

Automatic scenario generation for efficient solution of robust optimal control problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and time-varying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all 2¹⁴⁺³×¹⁹² extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive

Data-Driven Predictive Control With Improved Performance Using Segmented Trajectories

A class of data-driven control methods has recently emerged based on Willems’ fundamental lemma. Such methods can ease the modeling burden in control design but can be sensitive to disturbances acting on the system under control. In this article, we propose a restructuring of the problem to incorporate segmented prediction trajectories. The proposed segmentation leads to reduced tracking error for longer prediction horizons in the presence of unmeasured disturbance and noise when compared with an unsegmented formulation. The performance characteristics are illustrated in a set-point tracking case study in which the segmented formulation enables more consistent performance over a wide range of prediction horizons. The method is then applied to a building energy management problem using a detailed simulation environment. The case studies show that good tracking performance is achieved for a range of horizon choices, whereas performance degrades with longer horizons without segmentation

Accuracy-awareness: A pessimistic approach to optimal control of triggered mobile communication networks

We use nonlinear model predictive control to procure a joint control of mobility and transmission to minimize total network communication energy use. The nonlinear optimization problem is solved numerically in a self-triggered framework, where the next control update time depends on the predicted state trajectory and the accuracy of the numerical solution. Solution accuracy must be accounted for in any circumstance where systems are run in open-loop for long stretches of time based on potentially inaccurate predictions. These triggering conditions allow us to place wireless nodes in low energy ‘idle' states for extended periods, saving over 70% of energy compared to a periodic policy where nodes consistently use energy to receive control updates

Predictive control co-design for enhancing flexibility in residential housing with battery degradation

Buildings are responsible for about a quarter of global energy-related CO2 emissions. Consequently, the decarbonisation of the housing stock is essential in achieving net-zero carbon emissions. Global decarbonisation targets can be achieved through increased efficiency in using energy generated by intermittent resources. The paper presents a co-design framework for simultaneous optimal design and operation of residential buildings using Model Predictive Control (MPC). The framework is capable of explicitly taking into account operational constraints and pushing the system to its efficiency and performance limits in an integrated fashion. The optimality criterion minimises system cost considering time-varying electricity prices and battery degradation. A case study illustrates the potential of co-design in enhancing flexibility and self-sufficiency of a system operating under different conditions. Specifically, numerical results from a low-fidelity model show substantial carbon emission reduction and bill savings compared to an a-priori sizing approach

Innovation and opportunity: review of the UK’s national AI strategy

The publication of the UK’s National Artificial Intelligence (AI) Strategy represents a step-change in the national industrial, policy, regulatory, and geo-strategic agenda. Although there is a multiplicity of threads to explore this text can be read primarily as a ‘signalling’ document. Indeed, we read the National AI Strategy as a vision for innovation and opportunity, underpinned by a trust framework that has innovation and opportunity at the forefront. We provide an overview of the structure of the document and offer an emphasised commentary on various standouts. Our main takeaways are: Innovation First: a clear signal is that innovation is at the forefront of UK’s data priorities. Alternative Ecosystem of Trust: the UK’s regulatory-market norms becoming the preferred ecosystem is dependent upon the regulatory system and delivery frameworks required. Defence, Security and Risk: security and risk are discussed in terms of utilisation of AI and governance. Revision of Data Protection: the signal is that the UK is indeed seeking to position itself as less stringent regarding data protection and necessary documentation. EU Disalignment—Atlanticism?: questions are raised regarding a step back in terms of data protection rights. We conclude with further notes on data flow continuity, the feasibility of a sector approach to regulation, legal liability, and the lack of a method of engagement for stakeholders. Whilst the strategy sends important signals for innovation, achieving ethical innovation is a harder challenge and will require a carefully evolved framework built with appropriate expertise

Output feedback receding horizon control of constrained systems

Accepted versio

Fast and accurate method for computing non-smooth solutions to constrained control problems

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems with constraints. State-of-the-art methods use fixed mesh schemes, which cannot achieve superlinear convergence in the presence of non-smooth solutions. In this paper, we propose using a flexible mesh in an integrated residual method. The locations of the mesh nodes are introduced as decision variables, and constraints are added to set upper and lower bounds on the size of the mesh intervals. We compare our approach to a uniform fixed mesh on a real-world satellite reorientation example. This example demonstrates that the flexible mesh enables the solver to automatically locate the discontinuities in the solution, has superlinear convergence and faster solve time