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作者： Riccardo Bonalli Sorbonne Universite

学位级别：博士

In this work, we address the real-time optimal guidance of launch vehicles with the objective of designing an autonomous algorithm for the prediction of optimal control strategies, based on indirect methods, able to adapt itself to unpredicted changes of the original scenario. To this aim, we first provide an accurate geometric analysis in the presence of mixed control-state constraints to recover a well-posed framework and correctly apply indirect methods. A practical numerical integration of the problem is proposed by efficiently combining indirect methods with homotopy procedures, increasing robustness and computational speed. Moreover, we improve dynamical models by considering delays. More specifically, we introduce a rigorous and well-posed homotopy framework to recover solutions for optimal control problems with delays via indirect methods. All our contributions made possible the development of a fully automatic, independent and self-regulating software, today property of ONERA-The French Aerospace Lab, for general realistic endo-atmospheric launch vehicle applications focused on optimal missile interception scenarios.

关键词： Nonlinear optimal control Geometric control control and state constraints control and state delays Shooting methods Homotopy and continuation methods Optimal guidance Endo-atmospheric launch vehicles Interceptor mis-siles

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Error estimates for parabolic optimal control problems with control and state constraints

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2013年第1期56卷 131-151页

作者： Gong, Wei Hinze, Michael Chinese Acad Sci LSEC Inst Computat Math Acad Math & Syst Sci Beijing 100190 Peoples R China Univ Hamburg Bereich Optimierung & Approximat D-20146 Hamburg Germany

The numerical approximation to a parabolic control problem with control and state constraints is studied in this paper. We use standard piecewise linear and continuous finite elements for the space discretization of the state, while the dG(0) method is used for time discretization. A priori error estimates for control and state are obtained by an improved maximum error estimate for the corresponding discretized state equation. Numerical experiments are provided which support our theoretical results.

关键词： Optimal control problem Finite element method A priori error estimate Parabolic equation control and state constraints

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ON A DIFFERENTIAL GENERALIZED NASH EQUILIBRIUM PROBLEM WITH MEAN FIELD INTERACTION

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SIAM JOURNAL ON OPTIMIZATION 2024年第3期34卷 2821-2855页

作者： Hintermueller, Michael Surowiec, Thomas m. Theis, Mike Weierstrass Inst Appl Anal & Stochast D-10117 Berlin Germany Simula Res Lab Numer Anal & Sci Comp N-0164 Oslo Norway

We consider a class of N-player linear quadratic differential generalized Nash equilibrium problems (GNEPs) with bound constraints on the individual control and state variables. In addition, we assume the individual players' optimal control problems are coupled through their dynamics and objectives via a time-dependent mean field interaction term. This assumption allows us to model the realistic setting that strategic players in large games cannot observe the individual states of their competitors. We observe that the GNEPs require a constraint qualification, which necessitates sufficient robustness of the individuals, in order to prove the existence of an open-loop pure strategy Nash equilibrium and to derive optimality conditions. In order to gain qualitative insight into the N-player game, we assume that players are identical and pass to the limit in N to derive a type of first-order constrained mean field game (MFG). We prove that the mean field interaction terms converge to an absolutely continuous curve of probability measures on the set of possible state trajectories. Using variational convergence methods, we show that the optimal control problems converge to a representative agent problem. Under additional regularity assumptions, we provide an explicit form for the mean field term as the solution of a continuity equation and demonstrate the link back to the N-player GNEP.

关键词： differential games generalized Nash equilibrium problems mean field games control and state constraints gradient flows of probability measures

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Optimal Energy Trajectory Planning and control for Automatic Ship Berthing 39

Optimal Energy Trajectory Planning and Control for Automatic...

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39th Chinese control Conference (CCC)

作者： Liu, Xinzhao Ren, Junsheng Wang, Hui Dalian Maritime Univ Nav Coll Dalian 116026 Peoples R China

ISBN: (纸本)9789881563903

This paper proposes an optimization method for the ship's optimal berth trajectory based on the ship dynamics. By introducing a mathematical dynamic model which helps to describe the nonlinear dynamic system of a ship, this paper attempts to solve the problem of optimal trajectory planning for ship berthing. Under the condition of system constraint, environment constraint, nonlinear constraint and non-convexity of state space equation, in order to achieve a minimum energy consumption, this paper adopts the interior penalty function method, which manages to optimize the ship berthing trajectory and obtains the optimal trajectory under the constraint condition. Finally, a container ship is taken as simulation objects, the research results show that the optimization of ship automatic berthing trajectory has high application value and reference value in both energy saving and practical life.

关键词： Automatic Ship Berthing Optimal Energy Interior Penalty Function Method Nonlinear System control and state constraints

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Optimal Energy Trajectory Planning and control for Automatic Ship Berthing

Optimal Energy Trajectory Planning and Control for Automatic...

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第三十九届中国控制会议

作者： Xinzhao Liu Junsheng Ren Hui Wang Navigation College Dalian Maritime University

This paper proposes an optimization method for the ship’s optimal berth trajectory based on the ship *** introducing a mathematical dynamic model which helps to describe the nonlinear dynamic system of a ship,this paper attempts to solve the problem of optimal trajectory planning for ship *** the condition of system constraint,environment constraint,nonlinear constraint and non-convexity of state space equation,in order to achieve a minimum energy consumption,this paper adopts the interior penalty function method,which manages to optimize the ship berthing trajectory and obtains the optimal trajectory under the constraint ***,a container ship is taken as simulation objects,the research results show that the optimization of ship automatic berthing trajectory has high application value and reference value in both energy saving and practical life.

关键词： Automatic Ship Berthing Optimal Energy Interior Penalty Function Method Nonlinear System control and state constraints

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PRECONDITIONED CONJUGATE GRADIENT METHOD FOR OPTIMAL control PROBLEMS WITH control and state constraints

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2010年第5期31卷 2291-2317页

作者： Herzog, Roland Sachs, Ekkehard Tech Univ Chemnitz Fac Math D-09107 Chemnitz Germany Univ Trier Dept Math D-54286 Trier Germany

Optimality systems and their linearizations arising in optimal control of partial differential equations with pointwise control and (regularized) state constraints are considered. The preconditioned conjugate gradient (PCG) method in a nonstandard inner product is employed for their efficient solution. Preconditioned condition numbers are estimated for problems with pointwise control constraints, mixed control-state constraints, and of Moreau-Yosida penalty type. Numerical results for elliptic problems demonstrate the performance of the PCG iteration. Regularized state-constrained problems in three dimensions with more than 750,000 variables are solved.

关键词： preconditioned conjugate gradient method saddle point problems optimal control of partial differential equations control and state constraints multigrid method

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Sensitivity analysis and the adjoint update strategy for an optimal control problem with mixed control-state constraints

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2009年第1期44卷 57-81页

作者： Griesse, Roland Wachsmuth, Daniel Tech Univ Berlin D-10623 Berlin Germany Austrian Acad Sci Johann Radon Inst Computat & Appl Math A-4040 Linz Austria

In this article, an optimal control problem subject to a semilinear elliptic equation and mixed control-state constraints is investigated. The problem data depends on certain parameters. Under an assumption of separation of the active sets and a second-order sufficient optimality condition, Bouligand-differentiability (B-differentiability) of the solutions with respect to the parameter is established. Furthermore, an adjoint update strategy is proposed which yields a better approximation of the optimal controls and multipliers than the classical Taylor expansion, with remainder terms vanishing in L (a).

关键词： Optimal control control and state constraints Bouligand derivative Taylor expansion

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On Vector-Valued Approximation of state Constrained Optimal control Problems for Nonlinear Hyperbolic Conservation Laws

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JOURNAL OF DYNAMICAL AND control SYSTEMS 2013年第3期19卷 381-404页

作者： Kogut, P. I. Manzo, R. Dnepropetrovsk Natl Univ Dept Differential Equat Dnepropetrovsk Ukraine Univ Salerno Dipartimento Ingn Elettron & Ingn Informat Fisciano SA Italy

We study one class of nonlinear fluid dynamic models with controls in the initial condition and the source term. The model is described by a nonlinear inhomogeneous hyperbolic conservation law with state and control constraints. We consider the case when the greatest lower bound of the cost functional can be unattainable on the set I of admissible pairs or the set I is possibly empty. Using the methods of vector-valued optimization theory, we show that this optimal control problem admits the existence of the so-called weakened approximate solution which can be interpreted as generalized solution to some vector optimization problem of special form.

关键词： Nonlinear conservation laws control and state constraints vector optimization problem weakened approximate solutions entropy solutions

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Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method

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ANNUAL REVIEWS IN control 2010年第1期34卷 32-51页

作者： Cimen, Tayfun ROKETSAN Missiles Ind Inc Ankara Turkey

Since the 1990s, state-dependent Riccati equation (SORE) strategies have emerged as general design methods that provide a systematic and effective means of designing nonlinear controllers, observers and filters These methods overcome many of the difficulties and shortcomings of existing methodologies, and deliver computationally simple algorithms that have been highly effective in a variety of practical and meaningful applications in very diverse fields of study. These include missiles, aircraft, unmanned aerial vehicles, satellites and spacecraft, ships, autonomous underwater vehicles, automotive systems, biomedical systems, process control, and robotics, along with various benchmark problems, as well as nonlinear systems exhibiting several interesting phenomena such as parasitic effects of friction and backlash, unstable nonminimum-phase dynamics, time-delay, vibration and chaotic behavior SORE controllers, in particular, have become very popular within the control community, providing attractive stability, optimality, robustness and computational properties, making real-time implementation in feedback form feasible. However, despite a documented history of SORE control in the literature, there is a significant lack of theoretical justification for logical choices of the design matrices, which have depended on intuitive rules of thumb and extensive simulation for evaluation and performance. In this paper, the capabilities and design flexibility of SORE control are emphasized, addressing the issues on systematic selection of the design matrices and going into detail concerning the art of systematically carrying out an effective SORE design for systems that both do and do not conform to the basic structure and conditions required by the method. Several situations that prevent the direct application of the SDRE technique, such as the presence of control and state constraints, are addressed, demonstrating how these situations can be readily handled using the method In

关键词： control applications controller design control and state constraints Implementation Nonlinear systems Optimal control Real-time systems Riccati equation

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Evolutionary search for globally optimal constrained stable cycles

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CHEMICAL ENGINEERING SCIENCE 2006年第24期61卷 7924-7932页

作者： Skowron, M. Styczen, K. Wroclaw Univ Technol Inst Comp Engn Control & Robot PL-50372 Wroclaw Poland

The problem of finding globally optimal constrained stable periodic control processes (globally optimal cycles) arising from the optimization of some chemical, biotechnological, and flight processes is considered. An evolutionary optimization algorithm dealing with a population of cycles evolving by the crossing, and the mutation operations is developed. It incorporates various constraints imposed on the optimized cycles such as the averaged control constraints, the pointwise state constraints, and the stability requirements formulated as the maximal admissible level of the modulus of the Floquet's multipliers. The proposed method is applied to the global periodic optimization of some constrained chemical production processes. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： periodic control process global optimization evolutionary algorithm control and state constraints stability requirements

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