145 research outputs found

    Optimal Control Problems with Mixed and Pure State Constraints

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    This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both “pure” constraints on the state variable and “mixed” constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke's theory of “stratified” necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take into account the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints

    Optimal Control Problems with Mixed and Pure State Constraints

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    This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both ‘pure’ constraints on the state variable and also ‘mixed’ constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke’s theory of ‘stratified’ necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take account of the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to apply to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints

    On first order state constrained optimal control problems

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    We show that exact penalization techniques canbe applied to optimal control problems with state constraintsunder a hard to verify hypothesis. Investigating conditionsimplying our hypothetical hypothesis we discuss some recenttheoretical results on regularity of multipliers for optimalcontrol problem involving first order state constraints. We showby an example that known conditions asserting regularity ofthe multipliers do not prevent the appearance of atoms in themultiplier measure. Our accompanying example is treated bothnumerically and analytically. Extension to cover problems withadditional mixed state constraints is also discusse

    A new version of necessary conditions for optimal control problems with differential algebraic equations

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    Appealing to recent results for nonsmooth mixed constrained problems we derivenew variants of necessary optimality conditions for optimal control problems involving differentialalgebraic equations. The analysis is quite suitable for index one problems with no need for theintroduction of implicit functions. It is also suitable to some higher index problems

    Educating the Army's Jedi

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    This dissertation examines the decisions taken during the development of the concept for the School of Advanced Military Studies and its subsequent refinement in the first ten years of its history. The other line of inquiry in the dissertation is the development, introduction and refinement of the concept of operational art and the operational level of war into U.S. Army doctrine, primarily in the 1982, 1986 and 1993 versions of Field Manual 100-5, Operations

    A MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE AND MIXED CONSTRAINTS

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    Here we derive a variant of the nonsmooth maximum principle for optimal control problems with both pure state and mixed state and control constraints. Our necessary conditions include a Weierstrass condition together with an Euler adjoint inclusion involving the joint subdifferentials with respect to both state and control, generalizing previous results in [M.d.R. de Pinho, M.M.A. Ferreira, F.A.C.C. Fontes, Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: COCV 11 (2005) 614-632]. A notable feature is that our main results are derived combining old techniques with recent results. We use a well known penalization technique for state constrained problem together with an appeal to a recent nonsmooth maximum principle for problems with mixed constraints

    Dual weighted residual error estimation for the finite cell method

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    The paper presents a goal-oriented error control based on the dual weighted residual method (DWR) for the finite cell method (FCM), which is characterized by an enclosing domain covering the domain of the problem. The error identity derived by the DWR method allows for a combined treatment of the discretization and quadrature error introduced by the FCM. We present an adaptive strategy with the aim to balance these two error contributions. Its performance is demonstrated for some two-dimensional examples

    Differential Inclusion Approach for Mixed Constrained Problems Revisited

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    Properties of control systems described by differentialinclusions are well established in the literature. Ofspecial relevance to optimal control problems are propertiesconcerning measurability, convexity, compactness of trajectoriesand Lipschitz continuity of the multifunctions mapping defining thedifferential inclusion of interest. In this work we concentrateon dynamic control systems coupled with mixed state-controlconstraints. We characterize a class of such systems thatcan be described by an appropriate differential inclusion soas exhibit good'' properties of the multifunction.We also illustrate the importance of our findings bytreating some applications scenarios

    Future state maximisation as an intrinsic motivation for decision making

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    The concept of an “intrinsic motivation" is used in the psychology literature to distinguish between behaviour which is motivated by the expectation of an immediate, quantifiable reward (“extrinsic motivation") and behaviour which arises because it is inherently useful, interesting or enjoyable. Examples of the latter can include curiosity driven behaviour such as exploration and the accumulation of knowledge, as well as developing skills that might not be immediately useful but that have the potential to be re-used in a variety of different future situations. In this thesis, we examine a candidate for an intrinsic motivation with wide-ranging applicability which we refer to as “future state maximisation". Loosely speaking this is the idea that, taking everything else to be equal, decisions should be made so as to maximally keep one's options open, or to give the maximal amount of control over what one can potentially do in the future. Our goal is to study how this principle can be applied in a quantitative manner, as well as identifying examples of systems where doing so could be useful in either explaining or generating behaviour. We consider a number of examples, however our primary application is to a model of collective motion in which we consider a group of agents equipped with simple visual sensors, moving around in two dimensions. In this model, agents aim to make decisions about how to move so as to maximise the amount of control they have over the potential visual states that they can access in the future. We find that with each agent following this simple, low-level motivational principle a swarm spontaneously emerges in which the agents exhibit rich collective behaviour, remaining cohesive and highly-aligned. Remarkably, the emergent swarm also shares a number of features which are observed in real flocks of starlings, including scale free correlations and marginal opacity. We go on to explore how the model can be developed to allow us to manipulate and control the swarm, as well as looking at heuristics which are able to mimic future state maximisation whilst requiring significantly less computation, and so which could plausibly operate under animal cognition
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