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

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 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

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

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 control strategies for tuberculosis treatment: a case study in Angola

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions. Numerical simulations are given using data from Angola.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201

Numerical solution of a pursuit-evasion differential game involving two spacecraft in low earth orbit

This paper considers a spacecraft pursuit-evasion problem taking place in low earth orbit. The problem is formulated as a zero-sum differential game in which there are two players, a pursuing spacecraft that attempts to minimize a payoff, and an evading spacecraft that attempts to maximize the same payoff. We introduce two associated optimal control problems and show that a saddle point for the differential game exists if and only if the two optimal control problems have the same optimal value. Then, on the basis of this result, we propose two computational methods for determining a saddle point solution: a semi-direct control parameterization method (SDCP method), which is based on a piecewise-constant control approximation scheme, and a hybrid method, which combines the new SDCP method with the multiple shooting method. Simulation results show that the proposed SDCP and hybrid methodsare superior to the semi-direct collocation nonlinear programming method (SDCNLP method), which is widely used to solve pursuit-evasion problems in the aerospace field

Using biomarkers to predict TB treatment duration (Predict TB): a prospective, randomized, noninferiority, treatment shortening clinical trial

Background : By the early 1980s, tuberculosis treatment was shortened from 24 to 6 months, maintaining relapse rates of 1-2%. Subsequent trials attempting shorter durations have failed, with 4-month arms consistently having relapse rates of 15-20%. One trial shortened treatment only among those without baseline cavity on chest x-ray and whose month 2 sputum culture converted to negative. The 4-month arm relapse rate decreased to 7% but was still significantly worse than the 6-month arm (1.6%, P<0.01).  We hypothesize that PET/CT characteristics at baseline, PET/CT changes at one month, and markers of residual bacterial load will identify patients with tuberculosis who can be cured with 4 months (16 weeks) of standard treatment.Methods: This is a prospective, multicenter, randomized, phase 2b, noninferiority clinical trial of pulmonary tuberculosis participants. Those eligible start standard of care treatment. PET/CT scans are done at weeks 0, 4, and 16 or 24. Participants who do not meet early treatment completion criteria (baseline radiologic severity, radiologic response at one month, and GeneXpert-detectable bacilli at four months) are placed in Arm A (24 weeks of standard therapy). Those who meet the early treatment completion criteria are randomized at week 16 to continue treatment to week 24 (Arm B) or complete treatment at week 16 (Arm C). The primary endpoint compares the treatment success rate at 18 months between Arms B and C.Discussion: Multiple biomarkers have been assessed to predict TB treatment outcomes. This study uses PET/CT scans and GeneXpert (Xpert) cycle threshold to risk stratify participants. PET/CT scans are not applicable to global public health but could be used in clinical trials to stratify participants and possibly become a surrogate endpoint. If the Predict TB trial is successful, other immunological biomarkers or transcriptional signatures that correlate with treatment outcome may be identified. TRIAL REGISTRATION: NCT02821832

Analysis of host responses to Mycobacterium tuberculosis antigens in a multi-site study of subjects with different TB and HIV infection states in sub-Saharan Africa.

BACKGROUND: Tuberculosis (TB) remains a global health threat with 9 million new cases and 1.4 million deaths per year. In order to develop a protective vaccine, we need to define the antigens expressed by Mycobacterium tuberculosis (Mtb), which are relevant to protective immunity in high-endemic areas. METHODS: We analysed responses to 23 Mtb antigens in a total of 1247 subjects with different HIV and TB status across 5 geographically diverse sites in Africa (South Africa, The Gambia, Ethiopia, Malawi and Uganda). We used a 7-day whole blood assay followed by IFN-γ ELISA on the supernatants. Antigens included PPD, ESAT-6 and Ag85B (dominant antigens) together with novel resuscitation-promoting factors (rpf), reactivation proteins, latency (Mtb DosR regulon-encoded) antigens, starvation-induced antigens and secreted antigens. RESULTS: There was variation between sites in responses to the antigens, presumably due to underlying genetic and environmental differences. When results from all sites were combined, HIV- subjects with active TB showed significantly lower responses compared to both TST(-) and TST(+) contacts to latency antigens (Rv0569, Rv1733, Rv1735, Rv1737) and the rpf Rv0867; whilst responses to ESAT-6/CFP-10 fusion protein (EC), PPD, Rv2029, TB10.3, and TB10.4 were significantly higher in TST(+) contacts (LTBI) compared to TB and TST(-) contacts fewer differences were seen in subjects with HIV co-infection, with responses to the mitogen PHA significantly lower in subjects with active TB compared to those with LTBI and no difference with any antigen. CONCLUSIONS: Our multi-site study design for testing novel Mtb antigens revealed promising antigens for future vaccine development. The IFN-γ ELISA is a cheap and useful tool for screening potential antigenicity in subjects with different ethnic backgrounds and across a spectrum of TB and HIV infection states. Analysis of cytokines other than IFN-γ is currently on-going to determine correlates of protection, which may be useful for vaccine efficacy trials