Efficient algorithm for solving semi-infinite programming problems and their applications to nonuniform filter bank designs

An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorith

Data-driven subspace-based model predictive control

The desire to develop control systems that can be rapidly deployed has resulted in the formulation of algorithms that combine system identification with the development of control technique resulting in a single-step implementation. One such algorithm is Subspace Model Predictive Control (SMPC), which is a combination of results from subspace methods in system identification and model predictive control. In this thesis, novel algorithms of SMPC are investigated and developed. More specifically, a data filtering procedure is proposed in the computation of subspace predictor coefficients, resulting in the suppression of non-stationary disturbance in the identification data and incorporation of integrator in the predictive control law. Computational advantages of parameterization of control input trajectory using Laguerre functions are demonstrated and extended to Multi-input and Multi-output (MIMO) systems. By manipulating the unique structure of subspace data matrices, an efficient recursive algorithm for the updating of subspace predictor coefficients is investigated. This efficient algorithm is then extended to SMPC for time-varying systems, with the proposal of a novel recursive control law. The advantage of this implementation is that recursive updating is only performed when there is plant-predictor mismatch, thus input and output signals need not be persistently exciting at all times. Consequently, unnecessary fluctuations of signals are avoided, resulting in a smoother steady-state response. Finally, an implementation of a variable forgetting factor was introduced in order to facilitate faster convergence. These innovative approaches result in more efficient and reliable SMPC algorithms, thus making this design methodology a promising choice for control system design and implementation. Experimental results obtained from Permanent Magnetic Synchronous Machine and DC motor are used to demonstrate the efficacy of the proposed approaches

Towards autonomy of a quadrotor UAV

As the potential of unmanned aerial vehicles rapidly increases, there is a growing interest in rotary vehicles as well as fixed wing. The quadrotor is small agile rotary vehicle controlled by variable speed prop rotors. With no need for a swash plate the vehicle is low cost as well as dynamically simple. In order to achieve autonomous flight, any potential control algorithm must include trajectory generation and trajectory following. Trajectory generation can be done using direct or indirect methods. Indirect methods provide an optimal solution but are hard to solve for anything other than the simplest of cases. Direct methods in comparison are often sub-optimal but can be applied to a wider range of problems. Trajectory optimization is typically performed within the control space, however, by posing the problem in the output space, the problem can be simplified. Differential flatness is a property of some dynamical systems which allows dynamic inversion and hence, output space optimization. Trajectory following can be achieved through any number of linear control techniques, this is demonstrated whereby a single trajectory is followed using LQR, this scheme is limited however, as the vehicle is unable to adapt to environmental changes. Model based predictive control guarantees constraint satisfaction at every time step, this however is time consuming and therefore, a combined controller is proposed benefiting from the adaptable nature of MBPC and the robustness and simplicity of LQR control. There are numerous direct methods for trajectory optimization both in the output and control space. Taranenko’s direct method has a number of benefits over other techniques, including the use of a virtual argument, which separates the optimal path and the speed problem. This enables the algorithm to solve the optimal time problem, the optimal fuel problem or a combination of the two, without a deviation from the optimal path. In order to implement such a control scheme, the issues of feedback, communication and control action computation, require consideration. This work discusses the issues with instrumentation and communication encountered when developing the control system and provides open loop test results. This work also extends the proposed control schemes to consider the problem of multiple vehicle flight rendezvous. Specifically the problem of rendezvous when there is no communication link, limited visibility and no agreed rendezvous point. Using Taranenko’s direct method multiple vehicle rendezvous is simulated.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Analysis of Nonlinear Behaviors, Design and Control of Sigma Delta Modulators

M PhilSigma delta modulators (SDMs) have been widely applied in analogue-to-digital (A/D) conversion for many years. SDMs are becoming more and more popular in power electronic circuits because it can be viewed and applied as oversampled A/D converters with low resolution quantizers. The basic structure of an SDM under analytical investigation consists of a loop filter and a low bit quantizer connected by a negative feedback loop. Although there are numerous advantages of SDMs over other A/D converters, the application of SDMs is limited by the unboundedness of the system states and their nonlinear behaviors. It was found that complex dynamical behaviors exist in low bit SDMs, and for a bandpass SDM, the state space dynamics can be represented by elliptic fractal patterns confined within two trapezoidal regions. In all, there are three types of nonlinear behaviors, namely fixed point, limit cycle and chaotic behaviors. Related to the unboundedness issue, divergent behavior of system states is also a commonly discovered phenomenon. Consequently, how to design and control the SDM so that the system states are bounded and the unwanted nonlinear behaviors are avoided is a hot research topic worthy of investigated. In our investigation, we perform analysis on such complex behaviors and determine a control strategy to maintain the boundedness of the system states and avoid the occurrence of limit cycle behavior. For the design problem, we impose constraints based on the performance of an SDM and determine an optimal design for the SDM. The results are significantly better than the existing approaches

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Bayesian Variational Regularisation for Dark Matter Reconstruction with Uncertainty Quantification

Despite the great wealth of cosmological knowledge accumulated since the early 20th century, the nature of dark-matter, which accounts for ~85% of the matter content of the universe, remains illusive. Unfortunately, though dark-matter is scientifically interesting, with implications for our fundamental understanding of the Universe, it cannot be directly observed. Instead, dark-matter may be inferred from e.g. the optical distortion (lensing) of distant galaxies which, at linear order, manifests as a perturbation to the apparent magnitude (convergence) and ellipticity (shearing). Ensemble observations of the shear are collected and leveraged to construct estimates of the convergence, which can directly be related to the universal dark-matter distribution. Imminent stage IV surveys are forecast to accrue an unprecedented quantity of cosmological information; a discriminative partition of which is accessible through the convergence, and is disproportionately concentrated at high angular resolutions, where the echoes of cosmological evolution under gravity are most apparent. Capitalising on advances in probability concentration theory, this thesis merges the paradigms of Bayesian inference and optimisation to develop hybrid convergence inference techniques which are scalable, statistically principled, and operate over the Euclidean plane, celestial sphere, and 3-dimensional ball. Such techniques can quantify the plausibility of inferences at one-millionth the computational overhead of competing sampling methods. These Bayesian techniques are applied to the hotly debated Abell-520 merging cluster, concluding that observational catalogues contain insufficient information to determine the existence of dark-matter self-interactions. Further, these techniques were applied to all public lensing catalogues, recovering the then largest global dark-matter mass-map. The primary methodological contributions of this thesis depend only on posterior log-concavity, paving the way towards a, potentially revolutionary, complete hybridisation with artificial intelligence techniques. These next-generation techniques are the first to operate over the full 3-dimensional ball, laying the foundations for statistically principled universal dark-matter cartography, and the cosmological insights such advances may provide

Nonlinear model predictive low-level control

This dissertation focuses on the development, formalization, and systematic evaluation of a novel nonlinear model predictive control (MPC) concept with derivative-free optimization. Motivated by a real industrial application, namely the position control of a directional control valve, this control concept enables straightforward implementation from scratch, robust numerical optimization with a deterministic upper computation time bound, intuitive controller design, and offers extensions to ensure recursive feasibility and asymptotic stability by design. These beneficial controller properties result from combining adaptive input domain discretization, extreme input move-blocking, and the integration with common stabilizing terminal ingredients. The adaptive discretization of the input domain is translated into time-varying finite control sets and ensures smooth and stabilizing closed-loop control. By severely reducing the degrees of freedom in control to a single degree of freedom, the exhaustive search algorithm qualifies as an ideal optimizer. Because of the exponentially increasing combinatorial complexity, the novel control concept is suitable for systems with small input dimensions, especially single-input systems, small- to mid-sized state dimensions, and simple box-constraints. Mechatronic subsystems such as electromagnetic actuators represent this special group of nonlinear systems and contribute significantly to the overall performance of complex machinery. A major part of this dissertation addresses the step-by-step implementation and realization of the new control concept for numerical benchmark and real mechatronic systems. This dissertation investigates and elaborates on the beneficial properties of the derivative-free MPC approach and then narrows the scope of application. Since combinatorial optimization enables the straightforward inclusion of a non-smooth exact penalty function, the new control approach features a numerically robust real-time operation even when state constraint violations occur. The real-time closed-loop control performance is evaluated using the example of a directional control valve and a servomotor and shows promising results after manual controller design. Since the common theoretical closed-loop properties of MPC do not hold with input moveblocking, this dissertation provides a new approach for general input move-blocked MPC with arbitrary blocking patterns. The main idea is to integrate input move-blocking with the framework of suboptimal MPC by defining the restrictive input parameterization as a source of suboptimality. Finally, this dissertation extends the proposed derivative-free MPC approach by stabilizing warm-starts according to the suboptimal MPC formulation. The extended horizon scheme divides the receding horizon into two parts, where only the first part of variable length is subject to extreme move-blocking. A stabilizing local controller then completes the second part of the prediction. The approach involves a tailored and straightforward combinatorial optimization algorithm that searches efficiently for suboptimal horizon partitions while always reproducing the stabilizing warm-start control sequences in the nominal setup