Convex model predictive control for vehicular systems

In this work, the author presents a method called Convex Model Predictive Control (CMPC) to control systems whose states are elements of the rotation matrices SO(n) for n = 2, 3. This is done without charts or any local linearization, and instead is performed by operating over the orbitope of rotation matrices. This results in a novel model predictive control (MPC) scheme without the drawbacks associated with conventional linearization techniques such as slow computation time and local minima. Of particular emphasis is the application to aeronautical and vehicular systems, wherein the method removes many of the trigonometric terms associated with these systems’ state space equations. Furthermore, the method is shown to be compatible with many existing variants of MPC, including obstacle avoidance via Mixed Integer Linear Programming (MILP).

On the Role of Delays in Biological Systems : Analysis and Design

This work quantifies the nature of delays in genetic regulatory networks and their effect on system dynamics. It is known that a time lag can emerge from a sequence of biochemical reactions. Applying this modeling framework to the protein production processes, delay distributions are derived in a stochastic (probability density function) and deterministic setting (impulse function), whilst being shown to be equivalent under different assumptions. The dependence of the distribution properties on rate constants, gene length, and time-varying temperatures is investigated. Overall, the distribution of the delay in the context of protein production processes is shown to be highly dependent on the size of the genes and mRNA strands as well as the reaction rates. Results suggest longer genes have delay distributions with a smaller relative variance, and hence, less uncertainty in the completion times, however, they lead to larger delays. On the other hand large uncertainties may actually play a positive role, as broader distributions can lead to larger stability regions when this formalization of the protein production delays is incorporated into a feedback system.

Furthermore, evidence suggests that delays may play a role as an explicit design into existing controlling mechanisms. Accordingly, the reccurring dual-feedback motif is also investigated with delays incorporated into the feedback channels. The dual-delayed feedback is shown to have stabilizing effects through a control theoretic approach. Lastly, a distributed delay based controller design method is proposed as a potential design tool. In a preliminary study, the dual-delayed feedback system re-emerges as an effective controller design.

Distributed Control and Optimization for Communication and Power Systems

We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.

This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.

Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.

Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.

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.

Asymptotic Recovery for Discrete-Time Systems

An asymptotic recovery design procedure is proposed for square, discrete-time, linear, time-invariant multivariable systems, which allows a state-feedback design to be approximately recovered by a dynamic output feedback scheme. Both the case of negligible processing time (compared to the sampling interval) and of significant processing time are discussed. In the former case, it is possible to obtain perfect. © 1985 IEEE.

Modelling and control of nonlinear systems using Gaussian processes with partial model information

Gaussian processes are gaining increasing popularity among the control community, in particular for the modelling of discrete time state space systems. However, it has not been clear how to incorporate model information, in the form of known state relationships, when using a Gaussian process as a predictive model. An obvious example of known prior information is position and velocity related states. Incorporation of such information would be beneficial both computationally and for faster dynamics learning. This paper introduces a method of achieving this, yielding faster dynamics learning and a reduction in computational effort from O(Dn2) to O((D - F)n2) in the prediction stage for a system with D states, F known state relationships and n observations. The effectiveness of the method is demonstrated through its inclusion in the PILCO learning algorithm with application to the swing-up and balance of a torque-limited pendulum and the balancing of a robotic unicycle in simulation. © 2012 IEEE.

Robust Guaranteed Cost Control for Yaw Control of Helicopter

针对具有时变不确定性且不确定性界为椭球的线性系统提出了一种新的具有自适应机制的鲁棒保性能控制器设计方法。首先,引入一个具有可由自适应律在线调整的可调参数的目标模型,通过该参数来保证由目标模型与被控模型所获得的误差系统渐近稳定。结合保证目标模型稳定性的设计,最终形成保证闭环系统稳定且控制器增益仿射依赖于可调参数的鲁棒保性能跟踪控制器。应用于安装在试验平台上的小型直升机航向控制中,仿真试验表明了该方法的有效性。

A run-time configurable software architecture for self-managing systems

This paper describes a highly flexible component architecture, primarily designed for automotive control systems, that supports distributed dynamically- configurable context-aware behaviour. The architecture enforces a separation of design-time and run-time concerns, enabling almost all decisions concerning runtime composition and adaptation to be deferred beyond deployment. Dynamic context management contributes to flexibility. The architecture is extensible, and can embed potentially many different self-management decision technologies simultaneously. The mechanism that implements the run-time configuration has been designed to be very robust, automatically and silently handling problems arising from the evaluation of self- management logic and ensuring that in the worst case the dynamic aspects of the system collapse down to static behavior in totally predictable ways.

Plant-wide predictive control for a thermal power plant based on a physical plant model

A constrained non-linear, physical model-based, predictive control (NPMPC) strategy is developed for improved plant-wide control of a thermal power plant. The strategy makes use of successive linearisation and recursive state estimation using extended Kalman filtering to obtain a linear state-space model. The linear model and a quadratic programming routine are used to design a constrained long-range predictive controller One special feature is the careful selection of a specific set of plant model parameters for online estimation, to account for time-varying system characteristics resulting from major system disturbances and ageing. These parameters act as nonstationary stochastic states and help to provide sufficient degrees-of-freedom to obtain unbiased estimates of controlled outputs. A 14th order non-linear plant model, simulating the dominant characteristics of a 200 MW oil-fired pou er plant has been used to test the NPMPC algorithm. The control strategy gives impressive simulation results, during large system disturbances and extremely high rate of load changes, right across the operating range. These results compare favourably to those obtained with the state-space GPC method designed under similar conditions.

Synchrophasor-Based Islanding Detection for Distributed Generation Systems Using Systematic Principal Component Analysis Approaches

Systematic principal component analysis (PCA) methods are presented in this paper for reliable islanding detection for power systems with significant penetration of distributed generations (DGs), where synchrophasors recorded by Phasor Measurement Units (PMUs) are used for system monitoring. Existing islanding detection methods such as Rate-of-change-of frequency (ROCOF) and Vector Shift are fast for processing local information, however with the growth in installed capacity of DGs, they suffer from several drawbacks. Incumbent genset islanding detection cannot distinguish a system wide disturbance from an islanding event, leading to mal-operation. The problem is even more significant when the grid does not have sufficient inertia to limit frequency divergences in the system fault/stress due to the high penetration of DGs. To tackle such problems, this paper introduces PCA methods for islanding detection. Simple control chart is established for intuitive visualization of the transients. A Recursive PCA (RPCA) scheme is proposed as a reliable extension of the PCA method to reduce the false alarms for time-varying process. To further reduce the computational burden, the approximate linear dependence condition (ALDC) errors are calculated to update the associated PCA model. The proposed PCA and RPCA methods are verified by detecting abnormal transients occurring in the UK utility network.

Control of uncertain compartmental systems

Os sistemas compartimentais são frequentemente usados na modelação de diversos processos em várias áreas, tais como a biomedicina, ecologia, farmacocinética, entre outras. Na maioria das aplicações práticas, nomeadamente, aquelas que dizem respeito à administração de drogas a pacientes sujeitos a cirurgia, por exemplo, a presença de incertezas nos parâmetros do sistema ou no estado do sistema é muito comum. Ao longo dos últimos anos, a análise de sistemas compartimentais tem sido bastante desenvolvida na literatura. No entanto, a análise da sensibilidade da estabilidade destes sistemas na presença de incertezas tem recebido muito menos atenção. Nesta tese, consideramos uma lei de controlo por realimentação do estado com restrições de positividade e analisamos a sua robustez quando aplicada a sistemas compartimentais lineares e invariantes no tempo com incertezas nos parâmetros. Além disso, para sistemas lineares e invariantes no tempo com estado inicial desconhecido, combinamos esta lei de controlo com um observador do estado e a robustez da lei de controlo resultante também é analisada. O controlo do bloqueio neuromuscular por meio da infusão contínua de um relaxante muscular pode ser modelado como um sistema compartimental de três compartimentos e tem sido objecto de estudo por diversos grupos de investigação. Nesta tese, os nossos resultados são aplicados a este problema de controlo e são fornecidas estratégias para melhorar os resultados obtidos.

An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method