TITLE

Optimization Techniques for State-Constrained Control and Obstacle Problems

AUTHOR(S)
Kurzhanski, A. B.; Mitchell, I. M.; Varaiya, P.
PUB. DATE
March 2006
SOURCE
Journal of Optimization Theory & Applications;Mar2006, Vol. 128 Issue 3, p499
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The design of control laws for systems subject to complex state constraints still presents a significant challenge. This paper explores a dynamic programming approach to a specific class of such problems, that of reachability under state constraints. The problems are formulated in terms of nonstandard minmax and maxmin cost functionals, and the corresponding value functions are given in terms of Hamilton-Jacobi-Bellman (HJB) equations or variational inequalities. The solution of these relations is complicated in general; however, for linear systems, the value functions may be described also in terms of duality relations of convex analysis and minmax theory. Consequently, solution techniques specific to systems with a linear structure may be designed independently of HJB theory. These techniques are illustrated through two examples.
ACCESSION #
23213261

 

Related Articles

  • ON THE RELATIVE CONTROLLABILITY AND MINIMUM ENERGY CONTROL OF SYSTEMS WITH DELAY IN STATE AND CONTROL VARIABLES. Iyai, Davies // Journal of Applied Functional Analysis;Jan2010, Vol. 5 Issue 1, p100 

    This research work establishes necessary and sufficient conditions for relative controllability and minimum control energy of linear time varying systems with delays in state and control variable. The aim is to use the integral equivalence of our system to deduce our controllability matrix and...

  • A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance. Witte, J. H.; Reisinger, C. // AIP Conference Proceedings;9/30/2010, Vol. 1281 Issue 1, p346 

    We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based)...

  • Metric viscosity solutions of Hamilton-Jacobi equations depending on local slopes. Gangbo, Wilfrid; Święch, Andrzej // Calculus of Variations & Partial Differential Equations;Sep2015, Vol. 54 Issue 1, p1183 

    We continue the study of viscosity solutions of Hamilton-Jacobi equations in metric spaces initiated in []. We present a more complete account of the theory of metric viscosity solutions based on local slopes. Several comparison and existence results are proved and the main techniques for such...

  • On Aronsson Equation and Deterministic Optimal Control. Soravia, Pierpaolo // Applied Mathematics & Optimization;Apr2009, Vol. 59 Issue 2, p175 

    When Hamiltonians are nonsmooth, we define viscosity solutions of the Aronsson equation and prove that value functions of the corresponding deterministic optimal control problems are solutions if they are bilateral viscosity solutions of the Hamilton-Jacobi-Bellman equation. We characterize such...

  • Regularity and Variationality of Solutions to Hamilton-Jacobi Equations. Part II: Variationality, Existence, Uniqueness. Mennucci, Andrea // Applied Mathematics & Optimization;Apr2011, Vol. 63 Issue 2, p191 

    We formulate an Hamilton-Jacobi partial differential equation on a n dimensional manifold M, with assumptions of convexity of the sets $\{p:H(x,p)\le 0\}\subset T^{*}_{x}M$, for all x. We reduce the above problem to a simpler problem; this shows that u may be built using an asymmetric distance...

  • SBV Regularity for Hamilton-Jacobi Equations in $${{\mathbb R}^n}$$. Bianchini, Stefano; De Lellis, Camillo; Robyr, Roger // Archive for Rational Mechanics & Analysis;Jun2011, Vol. 200 Issue 3, p1003 

    In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations In particular, under the assumption that the Hamiltonian $${H\in C^2({\mathbb R}^n)}$$ is uniformly convex, we prove that D u and ∂ u belong to the class SBV(Ω).

  • Backtracking Adaptive Search: The Distribution of the Number of Iterations to Convergence. Wood, G. R.; Bulger, D. W.; Baritompa, W. P.; Alexander, D. L. J. // Journal of Optimization Theory & Applications;Mar2006, Vol. 128 Issue 3, p547 

    Backtracking adaptive search is a simplified stochastic optimization procedure which permits the acceptance of worsening objective function values. It generalizes hesitant adaptive search, which in turn is a generalization of pure adaptive search. In this paper, we use ideas from the theory of...

  • A COMPACT UPWIND SECOND ORDER SCHEME FOR THE EIKONAL EQUATION.  // Journal of Computational Mathematics;Jul2010, Vol. 28 Issue 4, p489 

    No abstract available.

  • Pension funds with a minimum guarantee: a stochastic control approach. Di Giacinto, Marina; Federico, Salvatore; Gozzi, Fausto // Finance & Stochastics;2011, Vol. 15 Issue 2, p297 

    In this paper we propose and study a continuous-time stochastic model of optimal allocation for a defined contribution pension fund with a minimum guarantee. We adopt the point of view of a fund manager maximizing the expected utility from the fund wealth over an infinite horizon. In our model...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics