Complex differential games of pursuit-evasion type with state constraints, part 1: Necessary conditions for optimal open-loop strategies

Breitner, Michael H.; Pesch, Hans Josef; Grimm, W.

doi:10.1007/bf00939876

Cited by 54 publications

(17 citation statements)

References 3 publications

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“…In the scientific literature, some special, structural characteristics of zero-sum games are responsible of a number of singular surfaces. For instance, state constraints can yield afferent and universal surfaces [8]. Nonsmooth data (e.g., a discontinuous thrust) can be responsible of discontinuities in the right hand side of the state equations and transition surfaces can arise [8].…”

Section: Formulation Of the Zero-sum Dynamic Gamementioning

confidence: 99%

“…For instance, state constraints can yield afferent and universal surfaces [8]. Nonsmooth data (e.g., a discontinuous thrust) can be responsible of discontinuities in the right hand side of the state equations and transition surfaces can arise [8]. Furthermore, control variables that appear linearly in the dynamics equations usually yield singular surfaces of several kinds [1].…”

Section: Formulation Of the Zero-sum Dynamic Gamementioning

confidence: 99%

“…Järmark, Merz, and Breakwell [7] solved a qualitatively similar air combat problem employing differential dynamic programming, and considered only coplanar situations. A pursuit-evasion problem between missile and aircraft has been solved using an indirect, multiple shooting method by Breitner, Grimm and Pesch [8,9]. Raivio and Ehtamo [10] solved a pursuit-evasion problem for a visual identification of the target by iterating a direct method.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Orbital Combat Games Involving Missiles and Spacecraft

Pontani

2011

Dyn Games Appl

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Section: Formulation Of the Zero-sum Dynamic Gamementioning

confidence: 99%

Section: Formulation Of the Zero-sum Dynamic Gamementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Orbital Combat Games Involving Missiles and Spacecraft

Pontani

2011

Dyn Games Appl

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“…Particularly surfaces with discontinuities of the value function, so-called barriers, are not detected by the proposed numerical method. Hence one has to check a posteriori if calculated trajectories intersect such barriers [Breitner, Pesch and Grimm, 1993].…”

Section: Extension To Nonlinear Robust Optimal Semiactive Control Strmentioning

confidence: 99%

Optimal and Robust Damping Control for Semi-Active Vehicle Suspension

Rettig

Stryk

2004

Progress in Industrial Mathematics at ECMI 2002

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The paper focusses on optimal control issues arising in semi-active vehicle suspension motivated by the application of continuously controllable ERF-shock absorbers. Optimality of the damping control is measured by an objective consisting of a weighted sum of criteria related to safety and comfort which depend on the state variables of the vehicle dynamics model. In the case of linear objectives and linear quarter or half car dynamics models the well-known linear quadratic regulators can be computed. However, to account for maximum robustness with respect to unknown perturbations, e.g., by the ground, linear robust-optimal H-infinity controllers are investigated which can be computed iteratively. The linear H-infinity controller can be viewed as the solution of a linear dynamic zero-sum differential game. Thus, a nonlinear H-infinity controller can be obtained in principle as the solution of a nonlinear zero-sum dynamic game problem. Such a problem formulation enables to consider nonlinear vehicle dynamics as well as nonlinear objectives and constraints. A computational method is discussed which computes approximations of robust-optimal trajectories for nonlinear damping control. The method is based on a reformulation of the dynamic game and the application of a control and state parameterization approach in combination with sparse nonlinear programming methods. Numerical results for the different approaches and their validation by software-in-the-loop simulation using a full motor vehicle dynamics model are presented.

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“…The former reduce the problem to a sequence of finite dimensional optimization problems through discretization [8], whereas the latter solves the Isaacs partial differential equation with boundary conditions using, e.g., multiple shooting [9,10], collocation [11,12], or level-set methods [3,13].…”

Section: Introductionmentioning

confidence: 99%

Incremental Sampling-Based Algorithms for a Class of Pursuit-Evasion Games

Karaman

2010

Springer Tracts in Advanced Robotics

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Pursuit-evasion games have been used for modeling various forms of conflict arising between two agents modeled as dynamical systems. Although analytical solutions of some simple pursuit-evasion games are known, most interesting instances can only be solved using numerical methods requiring significant offline computation. In this paper, a novel incremental sampling-based algorithm is presented to compute optimal open-loop solutions for the evader, assuming worst-case behavior for the pursuer. It is shown that the algorithm has probabilistic completeness and soundness guarantees. As opposed to many other numerical methods tailored to solve pursuit-evasion games, incremental sampling-based algorithms offer anytime properties, which allow their real-time implementations in online settings.

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Complex differential games of pursuit-evasion type with state constraints, part 1: Necessary conditions for optimal open-loop strategies

Cited by 54 publications

References 3 publications

Numerical Solution of Orbital Combat Games Involving Missiles and Spacecraft

Numerical Solution of Orbital Combat Games Involving Missiles and Spacecraft

Optimal and Robust Damping Control for Semi-Active Vehicle Suspension

Incremental Sampling-Based Algorithms for a Class of Pursuit-Evasion Games

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