Non-classical problems of optimal feedback control

Bressan, Alberto; Wei, Deling

doi:10.1016/j.jde.2012.04.020

Cited by 2 publications

(3 citation statements)

References 11 publications

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“…showing the differences between the original and relaxed formulations, and the possible obstructions encountered in the approximation of solutions (1.15) with solutions of (1.9). Motivated by these examples, general results on the equivalence between the various values in (1.17) will be proved in the forthcoming paper [2]. The underlying motivation for the present analysis comes from the theory of Stackelberg solutions in closed-loop form, for differential games.…”

Section: Remarkmentioning

confidence: 98%

Examples of nonclassical feedback control problems

Bressan

Wei

2013

Nonlinear Differ. Equ. Appl.

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Abstract. We consider a control system with "nonclassical" dynamics: x, u, Dxu), where the right hand side depends also on the first order partial derivatives of the feedback control function. Given a probability distribution on the initial data, we seek a feedback u = u(t, x) which minimizes the expected value of a cost functional. Various relaxed formulations of this problem are introduced. In particular, three specific examples are studied, showing the equivalence or non-equivalence of these approximations.Mathematics Subject Classification. 49N25, 49N35.

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Section: Remarkmentioning

confidence: 98%

Examples of nonclassical feedback control problems

Bressan

Wei

2013

Nonlinear Differ. Equ. Appl.

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“…In the case where both x and ξ are assigned at the initial time t = 0 has been recently studied in [8]. See also [9] for specific examples. As anticipated in [18], if the values u 1 (t, x) of the feedback can be freely assigned, in most cases this leads to an ill posed system of equations.…”

Section: Remarkmentioning

confidence: 99%

“…As observed in [9], the term u 1,x can often be considered as an additional component of the control, which can be chosen arbitrarily large and comes with no cost. In such cases, the optimal strategy for the leading player would correspond to an impulsive dynamics and can never be exactly attained.…”

Section: Remarkmentioning

confidence: 99%

Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data

Bressan

Wei

2012

Dyn Games Appl

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The paper is concerned with Stackelberg solutions for a differential game with deterministic dynamics but random initial data, where the leading player can adopt a strategy in feedback form: u 1 = u 1 (t, x). The first main result provides the existence of a Stackelberg equilibrium solution, assuming that the family of feedback controls u 1 (t, ·) available to the leading player are constrained to a finite dimensional space. A second theorem provides necessary conditions for the optimality of a feedback strategy. Finally, in the case where the feedback u 1 is allowed to be an arbitrary function, an example illustrates a wide class of systems where the minimal cost for the leading player corresponds to an impulsive dynamics. In this case, a Stackelberg equilibrium solution does not exists, but a minimizing sequence of strategies can be described.

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Non-classical problems of optimal feedback control

Cited by 2 publications

References 11 publications

Examples of nonclassical feedback control problems

Examples of nonclassical feedback control problems

Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data

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