Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

Management of Biesboch reservoirs for quality control with special reference to eutrophication

The three Biesbosch Reservoirs are pumped storage reservoirs, fed with rather polluted and highly eutrophic water from the River Meuse. Air injection at the bottom of the reservoirs prevents thermal stratification, which would otherwise result in serious water quality deterioration. Reservoir mixing also serves as an economic algal control measure; mixing over sufficient depth causes light to play the role of limiting factor and this, combined with zooplankton grazing, keeps the biomass of phytoplankton at acceptable levels. Special problems are caused by benthic, geosmin-producing Oscillatoria species growing on the inner embankment. Rooting up the bottom with a harrow is used as the method of control, based on underwater observations by biological staff trained as SCUBA-divers. With regard to pollutant behaviour the three reservoirs act as a series of fully mixed reactors. This enables the application of kinetic models to describe their behaviour and allows the use of a selective intake policy, e.g. for suspended solids with associated contaminants, ammonia and polynuclear aromatic hydrocarbons. A combination of selective intake and self- purification processes - enhanced by the compartmentalisation of the storage volume in three reservoirs - leads to a striking improvement for many water-quality parameters.

The cost of quinine Cinchona pubescens control on Santa Cruz Island, Galapagos

We analyse the cost of controlling the invasive quinine tree Cinchona pubescens Vahl in the highlands of Santa Cruz Island, Galapagos. Control costs in ten 400 m2 plots formed the basis for estimating the cost of control over the whole island. In the plots, densities were 2100–24,000 stems/ha (stems >150 cm tall) and 55,000–138,000 stems/ha (all size classes combined). Control involved uprooting small plants, and applying of a mix of metsulfuron methyl and picloram to cut stumps or to machete cuts in the bark of larger trees. These methods are presently used by Galapagos National Park field crews to control quinine. Costs (in man hours, herbicide and US$) were related to stem density; the density of stems summed across four height classes was a better predictor of costs than density of any one size class. Regressions (on all size classes combined) formed the basis for predictive models of costs. Costs ranged from $14 to $2225 per ha depending on stem density. The amount of herbicide (active ingredient/ha) that must be applied to high density stands of quinine is higher than typical rates of application in an agricultural setting. The cost of treating all existing plants once across quinine’s known range on Santa Cruz Island (c. 11,000 ha) was estimated at c. US$1.65 million. CDF Contribution Number 1013.

Experimental investigation of 3D shock / boundary layer interaction control in transonic flows

A novel supersonic wind tunnel setup is proposed to enable the investigation of control on a normal shock wave. Previous experimental arrangements were found to suffer from shock instability. Wind tunnel tests with and without control have confirmed the capability of the new setup to stabilise a shock structure at a target position without changing the nature of the shock wave / boundary layer interaction flow at M∞ = 1.3 and M ∞ = 1.5. Flow visualisation and pressure measurements with the new setup have revealed detailed characteristics of shock wave / boundary layer interactions and a λ-shock structure as well as benefits of control in total drag reduction in the presence of 3D bump control.

Feedback control and the arrow of time

The purpose of this paper is to highlight the central role that the time asymmetry of stability plays in feedback control. We show that this provides a new perspective on the use of doubly-infinite or semi-infinite time axes for signal spaces in control theory. We then focus on the implication of this time asymmetry in modeling uncertainty, regulation and robust control. We point out that modeling uncertainty and the ease of control depend critically on the direction of time. We finally discuss the relationship of this control-based time arrow with the well-known arrows of time in physics. © 2008 IEEE.

On control of drained weights in some fishery products

Canned and frozen prawns are subjected to compulsory pre-shipment inspection, during which compliance of the products with their declared drained weights is verified. The materials used in the processing of these products being biological in origin, the drained weights are susceptible to variation due to a number of factors. Since determination of the drained weights involves destructive and time consuming procedures, application of control chart for drained weights on the processing line is not possible. The present study has shown that gross weights of the products are significantly correlated with their drained weights and since the determination of the former does not have the disadvantages of determination of the latter, the drained weights can be controlled through the application of control chart for the gross weights.

Thickness control of Molecular Beam Epitaxy grown layers at the 0.01-0.1 monolayer level

Electron tunnelling through semiconductor tunnel barriers is exponentially sensitive to the thickness of the barrier layer, and in the most common system, the AlAs tunnel barrier in GaAs, a one monolayer variation in thickness results in a 300% variation in the tunnelling current for a fixed bias voltage. We use this degree of sensitivity to demonstrate that the level of control at 0.06 monolayer can be achieved in the growth by molecular beam epitaxy, and the geometrical variation of layer thickness across a wafer at the 0.01 monolayer level can be detected.

Efficient Implementation of Spatially-Varying 3-D Ultrasound Deconvolution

Abstract—There are sometimes occasions when ultrasound beamforming is performed with only a subset of the total data that will eventually be available. The most obvious example is a mechanically-swept (wobbler) probe in which the three-dimensional data block is formed from a set of individual B-scans. In these circumstances, non-blind deconvolution can be used to improve the resolution of the data. Unfortunately, most of these situations involve large blocks of three-dimensional data. Furthermore, the ultrasound blur function varies spatially with distance from the transducer. These two facts make the deconvolution process time-consuming to implement. This paper is about ways to address this problem and produce spatially-varying deconvolution of large blocks of three-dimensional data in a matter of seconds. We present two approaches, one based on hardware and the other based on software. We compare the time they each take to achieve similar results and discuss the computational resources and form of blur model that each requires.

Performance of magnesia cements in porous blocks in acid and magnesium environments

The performance of porous blocks containing three different reactive magnesia-based cements - namely magnesia alone, magnesium oxide: Portland cement (PC) in 1:1 ratio, cured in ambient conditions, and magnesia alone, cured at elevated carbon dioxide conditions, in hydrochloric acid and magnesium sulfate solution - was investigated. Different aggressive chemical solution conditions were used, to which the samples were exposed for up to 12 months and then tested for strength and microstructure. The performance was also compared with that of standard PC-based blocks. The results showed the significant resistance to chemical attack offered by magnesia, both alone and with PC blend in the porous blocks when cured under ambient carbon dioxide conditions, and confirmed the much poorer performance of blocks made from PC alone. The blocks of solely magnesia cured in elevated carbon dioxide conditions, at 20% concentration, showed slightly lower resistance to acid attack than PC; however, the resistance to sulfate attack was much higher. © 2012 Thomas Telford Ltd.

Performance evaluation of multiplexed model predictive control for a large airliner in nominal and contingency scenarios

Model predictive control allows systematic handling of physical and operational constraints through the use of constrained optimisation. It has also been shown to successfully exploit plant redundancy to maintain a level of control in scenarios when faults are present. Unfortunately, the computational complexity of each individual iteration of the algorithm to solve the optimisation problem scales cubically with the number of plant inputs, so the computational demands are high for large MIMO plants. Multiplexed MPC only calculates changes in a subset of the plant inputs at each sampling instant, thus reducing the complexity of the optimisation. This paper demonstrates the application of multiplexed model predictive control to a large transport airliner in a nominal and a contingency scenario. The performance is compared to that obtained with a conventional synchronous model predictive controller, designed using an equivalent cost function. © 2012 AACC American Automatic Control Council).

Control of bimanual rhythmic movements: Trading efficiency for robustness depending on the context

This paper investigates how the efficiency and robustness of a skilled rhythmic task compete against each other in the control of a bimanual movement. Human subjects juggled a puck in 2D through impacts with two metallic arms, requiring rhythmic bimanual actuation. The arms kinematics were only constrained by the position, velocity and time of impacts while the rest of the trajectory did not influence the movement of the puck. In order to expose the task robustness, we manipulated the task context in two distinct manners: the task tempo was assigned at four different values (hence manipulating the time available to plan and execute each impact movement individually); and vision was withdrawn during half of the trials (hence reducing the sensory inflows). We show that when the tempo was fast, the actuation was rhythmic (no pause in the trajectory) while at slow tempo, the actuation was discrete (with pause intervals between individual movements). Moreover, the withdrawal of visual information encouraged the rhythmic behavior at the four tested tempi. The discrete versus rhythmic behavior give different answers to the efficiency/robustness trade-off: discrete movements result in energy efficient movements, while rhythmic movements impact the puck with negative acceleration, a property preserving robustness. Moreover, we report that in all conditions the impact velocity of the arms was negatively correlated with the energy of the puck. This correlation tended to stabilize the task and was influenced by vision, revealing again different control strategies. In conclusion, this task involves different modes of control that balance efficiency and robustness, depending on the context. © 2008 Springer-Verlag.

Model-based control of thermoacoustic instabilities in partially premixed lean combustion - A design case study

Self-excited oscillation is becoming a major issue in low-emission, lean partially premixed combustion systems, and active control has been shown to be a feasible method to suppress such instabilities. A number of robust control methods are employed to obtain a feedback controller and it is observed that the robustness to system uncertainty is significantly better for a low complexity controller in spite of the norms being similar. Moreover, we demonstrate that closed-loop stability for such a complex system can be proved via use of the integral quadratic constraint method. Open- and closed-loop nonlinear simulations are provided. © 2013 Copyright Taylor and Francis Group, LLC.

Quantum coherence control of solid-state charge qubit by means of a suboptimal feedback algorithm

The quantum coherence control of a solid-state charge qubit is studied by using a suboptimal continuous feedback algorithm within the Bayesian feedback scheme. For the coherent Rabi oscillation, the present algorithm suggests a simple bang-bang control protocol, in which the control parameter is modulated between two values. For the coherence protection of the idle state, the present approach is applicable to arbitrary states, including those lying on the equator of the Bloch sphere which are out of control in the previous Markovian feedback scheme.

Intelligent control of avalanched photodiode to get optimal state

To improve the sensitivity of our laser radar system, we provided a set of control method for APDs (Avalanched Photodiodes) based on single-chip computer together with the circuits dealing with noise and temperature. It adjusts the voltages intelligently and maintains the APD's optimal working status.