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 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

A neighboring extremal solution for an optimal switched impulsive control problem

This paper presents a neighboring extremal solution for a class of optimal switched impulsive control problems with perturbations in the initial state, terminal condition and system's parameters. The sequence of mode's switching is pre-specified, and the decision variables, i.e. the switching times and parameters of the system involved, have inequality constraints. It is assumed that the active status of these constraints is unchanged with the perturbations. We derive this solution by expanding the necessary conditions for optimality to first-order and then solving the resulting multiple-point boundary-value problem by the backward sweep technique. Numerical simulations are presented to illustrate this solution method

Optimal control of impulsive switched systems with minimum subsystem durations

This paper presents a new computational approach for solving optimal control problems governed by impulsive switched systems. Such systems consist of multiple subsystems operating in succession, with possible instantaneous state jumps occurring when the system switches from one subsystem to another. The control variables are the subsystem durations and a set of system parameters influencing the state jumps. In contrast with most other papers on the control of impulsive switched systems, we do not require every potential subsystem to be active during the time horizon (it may be optimal to delete certain subsystems, especially when the optimal number of switches is unknown). However, any active subsystem must be active for a minimum non-negligible duration of time. This restriction leads to a disjoint feasible region for the subsystem durations. The problem of choosing the subsystem durations and the system parameters to minimize a given cost function is a non-standard optimal control problem that cannot be solved using conventional techniques. By combining a time-scaling transformation and an exact penalty method, we develop a computational algorithm for solving this problem. We then demonstrate the effectiveness of this algorithm by considering a numerical example on the optimization of shrimp harvesting operations

A unified parameter identification method for nonlinear time-delay systems

This paper deals with the problem of identifying unknown time-delays and model parameters in a general nonlinear time-delay system. We propose a unified computational approach that involves solving a dynamic optimization problem, whose cost function measures the discrepancy between predicted and observed system output, to determine optimal values for the unknown quantities. Our main contribution is to show that the partial derivatives of this cost function can be computed by solving a set of auxiliary time-delay systems. On this basis, the parameter identification problem can be solved using existing gradient-based optimization techniques. We conclude the paper with two numerical simulations

Control parameterization for optimal control problems with continuous inequality constraints: New convergence results

Control parameterization is a powerful numerical technique for solving optimal control problems with general nonlinear constraints. The main idea of control parameterization is to discretize the control space by approximating the control by a piecewise-constant or piecewise-linear function, thereby yielding an approximate nonlinear programming problem. This approximate problem can then be solved using standard gradient-based optimization techniques. In this paper, we consider the control parameterization method for a class of optimal control problems in which the admissible controls are functions of bounded variation and the state and control are subject to continuous inequality constraints. We show that control parameterization generates a sequence of suboptimal controls whose costs converge to the true optimal cost. This result has previously only been proved for the case when the admissible controls are restricted to piecewise continuous functions

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

Miscarriage, Preterm Delivery, and Stillbirth: Large Variations in Rates within a Cohort of Australian Women

Objectives We aimed to use simple clinical questions to group women and provide their specific rates of miscarriage, preterm delivery, and stillbirth for reference. Further, our purpose was to describe who has experienced particularly low or high rates of each event. Methods Data were collected as part of the Australian Longitudinal Study on Women's Health, a national prospective cohort. Reproductive histories were obtained from 5806 women aged 31–36 years in 2009, who had self-reported an outcome for one or more pregnancy. Age at first birth, number of live births, smoking status, fertility problems, use of in vitro fertilisation (IVF), education and physical activity were the variables that best separated women into groups for calculating the rates of miscarriage, preterm delivery, and stillbirth. Results Women reported 10,247 live births, 2544 miscarriages, 1113 preterm deliveries, and 113 stillbirths. Miscarriage was correlated with stillbirth (r = 0.09, P<0.001). The calculable rate of miscarriage ranged from 11.3 to 86.5 miscarriages per 100 live births. Women who had high rates of miscarriage typically had fewer live births, were more likely to smoke and were more likely to have tried unsuccessfully to conceive for ≥12 months. The highest proportion of live preterm delivery (32.2%) occurred in women who had one live birth, had tried unsuccessfully to conceive for ≥12 months, had used IVF, and had 12 years education or equivalent. Women aged 14–19.99 years at their first birth and reported low physical activity had 38.9 stillbirths per 1000 live births, compared to the lowest rate at 5.5 per 1000 live births. Conclusion Different groups of women experience vastly different rates of each adverse pregnancy event. We have used simple questions and established reference data that will stratify women into low- and high-rate groups, which may be useful in counselling those who have experienced miscarriage, preterm delivery, or stillbirth, plus women with fertility intent

Cargo scheduling decision support for offshore oil and gas production: a case study

Woodside Energy Ltd (Woodside), Australia’s largest independent oil and gas company, operates multiple oil and gas facilities off the coast of Western Australia. These facilities require regular cargo shipments from supply vessels based in Karratha, Western Australia. In this paper, we describe a decision support model for scheduling the cargo shipments to minimize travel cost and trip duration, subject to various operational restrictions including vessel capacities, cargo demands at the facilities, time windows at the facilities, and base opening times. The model is a type of non-standard vehicle routing problem involving multiple supply vessels—a primary supply vessel that visits every facility during a round trip taking at most 1 week, and other supply vessels that are used on an ad hoc basis when the primary vessel cannot meet all cargo demands. We validate the model via test simulations using real data provided by Woodside

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