Nonholonomically Constrained Dynamics and Optimization of Rolling Isolation Systems

Rolling Isolation Systems provide a simple and effective means for protecting components from horizontal floor vibrations. In these systems a platform rolls on four steel balls which, in turn, rest within shallow bowls. The trajectories of the balls is uniquely determined by the horizontal and rotational velocity components of the rolling platform, and thus provides nonholonomic constraints. In general, the bowls are not parabolic, so the potential energy function of this system is not quadratic. This thesis presents the application of Gauss's Principle of Least Constraint to the modeling of rolling isolation platforms. The equations of motion are described in terms of a redundant set of constrained coordinates. Coordinate accelerations are uniquely determined at any point in time via Gauss's Principle by solving a linearly constrained quadratic minimization. In the absence of any modeled damping, the equations of motion conserve energy. This mathematical model is then used to find the bowl profile that minimizes response acceleration subject to displacement constraint.

Energy efficiency optimization in hardware-constrained large-scale MIMO systems

Large-scale multiple-input multiple-output (MIMO) communication systems can bring substantial improvement in spectral efficiency and/or energy efficiency, due to the excessive degrees-of-freedom and huge array gain. However, large-scale MIMO is expected to deploy lower-cost radio frequency (RF) components, which are particularly prone to hardware impairments. Unfortunately, compensation schemes are not able to remove the impact of hardware impairments completely, such that a certain amount of residual impairments always exists. In this paper, we investigate the impact of residual transmit RF impairments (RTRI) on the spectral and energy efficiency of training-based point-to-point large-scale MIMO systems, and seek to determine the optimal training length and number of antennas which maximize the energy efficiency. We derive deterministic equivalents of the signal-to-noise-and-interference ratio (SINR) with zero-forcing (ZF) receivers, as well as the corresponding spectral and energy efficiency, which are shown to be accurate even for small number of antennas. Through an iterative sequential optimization, we find that the optimal training length of systems with RTRI can be smaller compared to ideal hardware systems in the moderate SNR regime, while larger in the high SNR regime. Moreover, it is observed that RTRI can significantly decrease the optimal number of transmit and receive antennas.

Efficient Hill Climber for Constrained Pseudo-Boolean Optimization Problems

Efficient hill climbers have been recently proposed for single- and multi-objective pseudo-Boolean optimization problems. For $k$-bounded pseudo-Boolean functions where each variable appears in at most a constant number of subfunctions, it has been theoretically proven that the neighborhood of a solution can be explored in constant time. These hill climbers, combined with a high-level exploration strategy, have shown to improve state of the art methods in experimental studies and open the door to the so-called Gray Box Optimization, where part, but not all, of the details of the objective functions are used to better explore the search space. One important limitation of all the previous proposals is that they can only be applied to unconstrained pseudo-Boolean optimization problems. In this work, we address the constrained case for multi-objective $k$-bounded pseudo-Boolean optimization problems. We find that adding constraints to the pseudo-Boolean problem has a linear computational cost in the hill climber.

New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

A hybrid genetic algorithm for the optimal constrained web service selection problem in web service composition

Web service composition is an important problem in web service based systems. It is about how to build a new value-added web service using existing web services. A web service may have many implementations, all of which have the same functionality, but may have different QoS values. Thus, a significant research problem in web service composition is how to select a web service implementation for each of the web services such that the composite web service gives the best overall performance. This is so-called optimal web service selection problem. There may be mutual constraints between some web service implementations. Sometimes when an implementation is selected for one web service, a particular implementation for another web service must be selected. This is so called dependency constraint. Sometimes when an implementation for one web service is selected, a set of implementations for another web service must be excluded in the web service composition. This is so called conflict constraint. Thus, the optimal web service selection is a typical constrained ombinatorial optimization problem from the computational point of view. This paper proposes a new hybrid genetic algorithm for the optimal web service selection problem. The hybrid genetic algorithm has been implemented and evaluated. The evaluation results have shown that the hybrid genetic algorithm outperforms other two existing genetic algorithms when the number of web services and the number of constraints are large.

An Introduction to Constrained Control

An ubiquitous problem in control system design is that the system must operate subject to various constraints. Although the topic of constrained control has a long history in practice, there have been recent significant advances in the supporting theory. In this chapter, we give an introduction to constrained control. In particular, we describe contemporary work which shows that the constrained optimal control problem for discrete-time systems has an interesting geometric structure and a simple local solution. We also discuss issues associated with the output feedback solution to this class of problems, and the implication of these results in the closely related problem of anti-windup. As an application, we address the problem of rudder roll stabilization for ships.

On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.

Thrust allocation with linear constrained quadratic cost function

In this paper, a method of thrust allocation based on a linearly constrained quadratic cost function capable of handling rotating azimuths is presented. The problem formulation accounts for magnitude and rate constraints on both thruster forces and azimuth angles. The advantage of this formulation is that the solution can be found with a finite number of iterations for each time step. Experiments with a model ship are used to validate the thrust allocation system.

Open-pit block sequencing optimization: A mathematical model and solution technique

This study presents a comprehensive mathematical formulation model for a short-term open-pit mine block sequencing problem, which considers nearly all relevant technical aspects in open-pit mining. The proposed model aims to obtain the optimum extraction sequences of the original-size (smallest) blocks over short time intervals and in the presence of real-life constraints, including precedence relationship, machine capacity, grade requirements, processing demands and stockpile management. A hybrid branch-and-bound and simulated annealing algorithm is developed to solve the problem. Computational experiments show that the proposed methodology is a promising way to provide quantitative recommendations for mine planning and scheduling engineers.

Power Minimization for CDMA under Colored Noise

Rate-constrained power minimization (PMIN) over a code division multiple-access (CDMA) channel with correlated noise is studied. PMIN is. shown to be an instance of a separable convex optimization problem subject to linear ascending constraints. PMIN is further reduced to a dual problem of sum-rate maximization (RMAX). The results highlight the underlying unity between PMIN, RMAX, and a problem closely related to PMIN but with linear receiver constraints. Subsequently, conceptually simple sequence design algorithms are proposed to explicitly identify an assignment of sequences and powers that solve PMIN. The algorithms yield an upper bound of 2N - 1 on the number of distinct sequences where N is the processing gain. The sequences generated using the proposed algorithms are in general real-valued. If a rate-splitting and multi-dimensional CDMA approach is allowed, the upper bound reduces to N distinct sequences, in which case the sequences can form an orthogonal set and be binary +/- 1-valued.

Worst inputs and a bound on the highest peak statistics of a class of non-linear systems

A method is developed by which the input leading to the highest possible response in an interval of time can be determined for a class of non-linear systems. The input, if deterministic, is constrained to have a known finite energy (or norm) in the interval under consideration. In the case of random inputs, the energy is constrained to have a known probability distribution function. The approach has applications when a system has to be put to maximum advantage by getting the largest possible output or when a system has to be designed to the highest maximum response with only the input energy or the energy distribution known. The method is also useful in arriving at a bound on the highest peak distribution of the response, when the excitation is a known random process.As an illustration the Duffing oscillator has been analysed and some numerical results have also been presented.

Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

Coupled electrostatic-elastic analysis for topology optimization using material interpolation

In this paper, we present a novel analytical formulation for the coupled partial differential equations governing electrostatically actuated constrained elastic structures of inhomogeneous material composition. We also present a computationally efficient numerical framework for solving the coupled equations over a reference domain with a fixed finite-element mesh. This serves two purposes: (i) a series of problems with varying geometries and piece-wise homogeneous and/or inhomogeneous material distribution can be solved with a single pre-processing step, (ii) topology optimization methods can be easily implemented by interpolating the material at each point in the reference domain from a void to a dielectric or a conductor. This is attained by considering the steady-state electrical current conduction equation with a `leaky capacitor' model instead of the usual electrostatic equation. This formulation is amenable for both static and transient problems in the elastic domain coupled with the quasi-electrostatic electric field. The procedure is numerically implemented on the COMSOL Multiphysics (R) platform using the weak variational form of the governing equations. Examples have been presented to show the accuracy and versatility of the scheme. The accuracy of the scheme is validated for the special case of piece-wise homogeneous material in the limit of the leaky-capacitor model approaching the ideal case.

Delay constrained optimal relay placement for planned wireless sensor networks

In this paper, we study the problem of wireless sensor network design by deploying a minimum number of additional relay nodes (to minimize network design cost) at a subset of given potential relay locationsin order to convey the data from already existing sensor nodes (hereafter called source nodes) to a Base Station within a certain specified mean delay bound. We formulate this problem in two different ways, and show that the problem is NP-Hard. For a problem in which the number of existing sensor nodes and potential relay locations is n, we propose an O(n) approximation algorithm of polynomial time complexity. Results show that the algorithm performs efficiently (in over 90% of the tested scenarios, it gave solutions that were either optimal or exceeding optimal just by one relay) in various randomly generated network scenarios.