کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
843522 908557 2009 32 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Some results on optimal control with unilateral state constraints
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Some results on optimal control with unilateral state constraints
چکیده انگلیسی

In this paper, we study the problem of quadratic optimal control with state variables unilateral constraints, for linear time-invariant systems. The necessary conditions are formulated as a linear invariant system with complementary slackness conditions. Some structural properties of this system are examined. Then it is shown that the problem can benefit from the higher order Moreau’s sweeping process, that is, a specific distributional differential inclusion, and from ten Dam’s geometric theory [A.A. ten Dam, K.F. Dwarshuis, J.C. Willems, The contact problem for linear continuous-time dynamical systems: A geometric approach, IEEE Trans. Automat. Control 42 (4) (1997) 458–472; A.A. ten Dam, Unilaterally Constrained Dynamical Systems, Ph.D. Thesis, Rijsuniversiteit Groningen, NL, available at http://irs.ub.rug.nl/ppn/159407869, 1997] for partitioning of the admissible domain boundary (in particular for the case of multivariable systems). In fact, the first step may be also seen as follows: does the higher order Moreau’s sweeping process (developed in Acary et al. [V. Acary, B. Brogliato, D. Goeleven, Higher order Moreau’s sweeping process: Mathematical formulation and numerical simulation, Math. Programm. A 113 (2008) 133–217]) correspond to the necessary conditions of some optimal control problem with an extended integral action? The knowledge of the qualitative behaviour of optimal trajectories at junction times is improved with the approach, which also paves the way towards efficient time-stepping numerical algorithms to solve the optimal control boundary value problem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 70, Issue 10, 15 May 2009, Pages 3626–3657
نویسندگان
,