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SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 597 (24 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
PROBLEM FORMULATION FOR MULTIDISCIPLINARY OPTIMIZATION
, 1994
"... This paper is about multidisciplinary (design) optimization, or MDO, the coupling of two or more analysis disciplines with numerical optimization. The paper has three goals. First, it is an expository introduction to MDO aimed at those who do research on optimization algorithms, since the optimizati ..."
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Cited by 137 (9 self)
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This paper is about multidisciplinary (design) optimization, or MDO, the coupling of two or more analysis disciplines with numerical optimization. The paper has three goals. First, it is an expository introduction to MDO aimed at those who do research on optimization algorithms, since the optimization community has much to contribute to this important class of computational engineering problems. Second, this paper presents to the MDO research community a new abstraction for multidisciplinary analysis and design problems as well as new decomposition formulations for these problems. Third, the "individual discipline feasible " (IDF) approaches introduced here make use of existing specialized analysis codes, and they introduce significant opportunities for coarsegrained computational parallelism particularly well suited to heterogeneous computing environments. The key distinguishing characteristic of the three fundamental approaches to MDO formulation discussed here is the kind of disciplinary feasibility that must be maintained at each optimization iteration. Other formulation issues, such as the sensitivities required, are also considered. This discussion highlights the tradeoffs between reuse of existing software, computational requirements, and probability of success.
A New Computational Approach to RealTime Trajectory Generation for Constrained Mechanical Systems
, 2000
"... Preliminary results of a new computational approach to generate aggressive trajectories in realtime for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that rea ..."
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Cited by 115 (23 self)
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Preliminary results of a new computational approach to generate aggressive trajectories in realtime for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that realtime trajectory generation for constrained mechanical systems is possible by mapping the problem to one of finding trajectory curves in a lower dimensional space. Performance of the algorithm is compared with existing optimal trajectory generation techniques. Numerical results are reported using the NTG software package. Keywords: Realtime optimization, nonlinear control design, optimal control, constrained trajectory generation, guidance. 1
Autonomous Vehicle Technologies for Small Fixed Wing UAVs
 AIAA JOURNAL OF AEROSPACE COMPUTING, INFORMATION, AND COMMUNICATION
, 2003
"... Autonomous unmanned air vehicle flight control systems require robust path generation to account for terrain obstructions, weather, and moving threats such as radar, jammers, and unfriendly aircraft. In this paper, we outline a feasible, hierarchal approach for realtime motion planning of small aut ..."
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Cited by 97 (28 self)
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Autonomous unmanned air vehicle flight control systems require robust path generation to account for terrain obstructions, weather, and moving threats such as radar, jammers, and unfriendly aircraft. In this paper, we outline a feasible, hierarchal approach for realtime motion planning of small autonomous fixedwing UAVs. The approach divides the trajectory generation into four tasks: waypoint path planning, dynamic trajectory smoothing, trajectory tracking, and lowlevel autopilot compensation. The waypoint path planner determines the vehicle 's route without regard for the dynamic constraints of the vehicle. This results in a significant reduction in the path search space, enabling the generation of complicated paths that account for popup and dynamically moving threats. Kinematic constraints are satisfied using a trajectory smoother which has the same kinematic structure as the physical vehicle. The third step of the approach uses a novel tracking algorithm to generate a feasible state trajectory that can be followed by a standard autopilot. MonteCarlo simulations were done to analyze the performance and feasibility of the approach and determine realtime computation requirements. A planar version of the algorithm has also been implemented and tested in a lowcost microcontroller. The paper describes a custom UAV built to test the algorithms.
Numerical solution of optimal control problems by direct collocation
, 1991
"... By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard SQPmethods [10]. Convergence properties of the discretization are derived. From a solution of this method ..."
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Cited by 68 (2 self)
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By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard SQPmethods [10]. Convergence properties of the discretization are derived. From a solution of this method known as direct collocation, these properties are used to obtain reliable estimates of adjoint variables. In the presence of active state constraints, these estimates can be significantly improved by including the switching structure of the state constraint into the optimization procedure. Two numerical examples are presented.
Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method
 Journal of Guidance, Control, and Dynamics
"... ENGINEERING NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes should not exceed 2500 words (where a figure or table counts as 200 words). Following informal review by the Editors, they may be published within a few months of the date of ..."
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Cited by 60 (33 self)
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ENGINEERING NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes should not exceed 2500 words (where a figure or table counts as 200 words). Following informal review by the Editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover).
Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment
 Multidisciplinary Design Optimization: State of the Art
, 1996
"... Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for largescale distributed analysis applications. In this approach, a complex problem is hierarchically decomposed along disciplinary boundaries into a number of su ..."
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Cited by 57 (3 self)
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Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for largescale distributed analysis applications. In this approach, a complex problem is hierarchically decomposed along disciplinary boundaries into a number of subproblems which are brought into multidisciplinary agreement by a systemlevel coordination process. When applied to problems in a multidisciplinary design environment, this scheme has several advantages over traditional solution strategies. These advantageous features include reducing the amount of information transferred between disciplines, the removal of large iterationloops, allowing the use of different subspace optimizers among the various analysis groups, an analysis framework which is easily parallelized and can operate on heterogenous equipment, and a structural framework that is wellsuited for conventional disciplinary organizations. In this article, the collaborative architectu...
Theory and implementation of numerical methods based on RungeKutta integration for solving optimal control problems
, 1996
"... ..."
SQP Methods And Their Application To Numerical Optimal Control
, 1997
"... . In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown ..."
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Cited by 37 (0 self)
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. In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown to converge to a solution under very mild conditions on the problem. Some practical and theoretical aspects of applying generalpurpose SQP methods to optimal control problems are discussed, including the influence of the problem discretization and the zero/nonzero structure of the problem derivatives. We conclude with some recent approaches that tailor the SQP method to the control problem. Key words. largescale optimization, sequential quadratic programming (SQP) methods, optimal control problems, multiple shooting methods, single shooting methods, collocation methods AMS subject classifications. 49J20, 49J15, 49M37, 49D37, 65F05, 65K05, 90C30 1. Introduction. Recently there has been c...
Online control customization via optimizationbased control
 in SoftwareEnabled Control: Information Technology for Dynamical Systems
, 2003
"... An advanced control technology that has had tremendous practical impact over the last two decades or so is model predictive control (MPC). By embedding an optimization solution in each sampling instant within the control calculation, MPC applications have demonstrated dramatic improvements in contr ..."
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Cited by 30 (14 self)
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An advanced control technology that has had tremendous practical impact over the last two decades or so is model predictive control (MPC). By embedding an optimization solution in each sampling instant within the control calculation, MPC applications have demonstrated dramatic improvements in control performance. To date, this impact has largely been limited to the process industries. The reasons for the domainspecific benefit have to do with the relatively slow time constants of most industrial processes and their relatively benign dynamics (e.g., their openloop stability). For aerospace systems to avail of the promise of MPC, research is needed in extending the technology so that it can be applied to systems with nonlinear, unstable, and fast dynamics. This chapter presents a new framework for MPC and optimizationbased control for flight control applications. The MPC formulation replaces the traditional terminal constraint with a terminal cost based on a control Lyapunov function. This reduces computational requirements and allows proofs of stability under a variety of realistic assumptions on computation. The authors also show how differential flatness system can be used to computational advantage. (A system is differentially flat if, roughly, it can be modeled as a dynamical equation in one variable and its derivatives.) In this case the optimization can be done over a space of parametrized basis functions and a constrained nonlinear program can be solved using collocation points. A software package has been developed to implement these theoretical developments. There is an experimental component to this research as well. A tethered ducted fan testbed has been developed at Caltech that mimics the longitudinal dynamics of an aircraft. Highperformance maneuvers can safely be flown with the ducted fan and an interface to highend workstations allows complex control schemes to be solved in realtime. The chapter presents results from several * Research supported in part by DARPA contract F3361598C3613.