Two defence applications involving discrete valued optimal control

We present two examples of optimal discrete valued control problems which arise in defence applications. The first one involves the management of batteries in a submarine. In the second example, one wishes to determine an optimal transit path for a submarine through a field of sonar sensors, subject to a total time constraint. A recently developed numerical solution technique for discrete valued optimal control problems is used to solve both of these problems. We present numerical results for each example

Optimal switching instants for a switched-capacitor DC/DC power converter

We consider a switched-capacitor DC/DC power converter with variable switching instants. The determination of optimal switching instants giving low output ripple and strong load regulation is posed as a non-smooth dynamic optimization problem. By introducing a set of auxiliary differential equations and applying a time-scaling transformation, we formulate an equivalent optimization problem with semi-infinite constraints. Existing algorithms can be applied to solve this smooth semi-infinite optimization problem. The existence of an optimal solution is also established. For illustration, the optimal switching instants for a practical switched-capacitor DC/DC power converter are determined using this approach

Well-posedness of Bimodal State-based Switched Systems

AbstractIn this work, we consider the well-posedness of state-based switched systems in the sense of piecewise classical solutions which commonly arise in the control of hybrid systems. We give some necessary and sufficient conditions for the well-posedness of this class of systems. These results can be used as tools for excluding the bimodal system having a Zeno state

Multi-objective Optimization of Zero Propellant Spacecraft Attitude Maneuvers

The zero propellant maneuver (ZPM) is an advanced space station, large angle attitude maneuver technique, using only control momentum gyroscopes (CMGs). Path planning is the key to success, and this paper studies the associated multi-objective optimization problem. Three types of maneuver optimal control problem are formulated: (i) momentum-optimal, (ii) time-optimal, and (iii) energy-optimal. A sensitivity analysis approach is used to study the Pareto optimal front and allows the tradeoffs between the performance indices to be investigated. For example, it is proved that the minimum peak momentum decreases as the maneuver time increases, and the minimum maneuver energy decreases if a larger momentum is available from the CMGs. The analysis is verified and complemented by the numerical computations. Among the three types of ZPM paths, the momentum-optimal solution and the time-optimal solution generally possess the same structure, and they are singular. The energy-optimal solution saves significant energy, while generally maintaining a smooth control profile. © 2014 Springer Science+Business Media New York

The control parameterization method for nonlinear optimal control: A survey

The control parameterization method is a popular numerical technique for solving optimal control problems. The main idea of control parameterization is to discretize the control space by approximating the control function by a linear combination of basis functions. Under this approximation scheme, the optimal control problem is reduced to an approximate nonlinear optimization problem with a finite number of decision variables. This approximate problem can then be solved using nonlinear programming techniques. The aim of this paper is to introduce the fundamentals of the control parameterization method and survey its various applications to non-standard optimal control problems. Topics discussed include gradient computation, numerical convergence, variable switching times, and methods for handling state constraints. We conclude the paper with some suggestions for future research

Optimal feedback control for dynamic systems with state constraints: An exact penalty approach

In this paper, we consider a class of nonlinear dynamic systems with terminal state and continuous inequality constraints. Our aim is to design an optimal feedback controller that minimizes total system cost and ensures satisfaction of all constraints. We first formulate this problem as a semi-infinite optimization problem. We then show that by using a new exact penalty approach, this semi-infinite optimization problem can be converted into a sequence of nonlinear programming problems, each of which can be solved using standard gradient-based optimization methods.We conclude the paper by discussing applications of our work to glider control

Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

A switched system is a dynamic system that operates by switching between different subsystems or modes. Such systems exhibit both continuous and discrete characteristics—a dual nature that makes designing effective control policies a challenging task. The purpose of this paper is to review some of the latest computational techniques for generating optimal control laws for switched systems with nonlinear dynamics and continuous inequality constraints. We discuss computational strategiesfor optimizing both the times at which a switched system switches from one mode to another (the so-called switching times) and the sequence in which a switched system operates its various possible modes (the so-called switching sequence). These strategies involve novel combinations of the control parameterization method, the timescaling transformation, and bilevel programming and binary relaxation techniques. We conclude the paper by discussing a number of switched system optimal control models arising in practical applications

The Sparrow Question: Social and Scientific Accord in Britain, 1850-1900.

During the latter-half of the nineteenth century, the utility of the house sparrow (Passer domesticus) to humankind was a contentious topic. In Britain, numerous actors from various backgrounds including natural history, acclimatisation, agriculture and economic ornithology converged on the bird, as contemporaries sought to calculate its economic cost and benefit to growers. Periodicals and newspapers provided an accessible and anonymous means of expression, through which the debate raged for over 50 years. By the end of the century, sparrows had been cast as detrimental to agriculture. Yet consensus was not achieved through new scientific methods, instruments, or changes in practice. This study instead argues that the rise and fall of scientific disciplines and movements paved the way for consensus on "the sparrow question." The decline of natural history and acclimatisation stifled a raging debate, while the rising science of economic ornithology sought to align itself with agricultural interests: the latter overwhelmingly hostile to sparrows