Internal approximations of reachable sets of control systems with state constraints

被引：0
作者：
M. I. Gusev
机构：
[1] Ural Branch of the Russian Academy of Sciences,Institute of Mathematics and Mechanics
[2] Ural Federal University,Institute of Mathematics and Computer Science
来源：
Proceedings of the Steklov Institute of Mathematics | 2014年 / 287卷
关键词：
control system; reachable set; state constraints; invariance; penalty function method;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the approximation problem for reachable sets of a nonlinear control system with state constraints, which are given as the solution set of a nonlinear inequality or a system of inequalities. An analog of the penalty function method is proposed, which consists in replacing the original system with state constraints by an auxiliary system without constraints by means of a restriction of the set of velocities of the original system. This restriction (the right-hand side of the auxiliary system) depends on a scalar penalty coefficient. It is proved that approximating sets converge in the Hausdorff metric to the reachable set of the original system as the penalty coefficient tends to infinity. An estimate of the convergence rate is obtained.
引用
收藏
页码：77 / 92
页数：15
相关论文
共 29 条
[1]  
Lotov A V(1975)A numerical method for constructing sets of attainability for linear controlled systems with phase constraints USSR Comp. Math. Math. Phys. 15 63-74
[2]  
Matviichuk A R(2006)On the construction of resolving controls in control problems with phase constraints J. Comput. Syst. Sci. Int. 45 1-16
[3]  
Ushakov V N(2006)Optimization techniques for state-constrained control and obstacle problems J. Optim. Theory Appl. 128 499-521
[4]  
Kurzhanski A B(2007)Stability and convergence of Euler’s method for state-constrained differential inclusions SIAM J. Optim. 18 1004-1026
[5]  
Mitchell I M(2012)Computing reachable sets as capture-viability kernels in reverse time Appl. Math. 3 1593-1597
[6]  
Varaiya P(1998)External and internal estimation of attainability domains by means of parallelotopes Vychisl. Tekhnologii 3 11-20
[7]  
Baier R(2012)External estimates of the reachability sets of nonlinear controlled systems Autom. Remote Control 73 450-461
[8]  
Chahma I A(1986)Description of a set of viable trajectories of a differential inclusion Dokl. Akad. Nauk SSSR 289 38-41
[9]  
Lempio F(1987)Description of the pencil of viable trajectories of a control system Differents. Uravneniya 23 1303-1315
[10]  
Bonneuil N(2013)On the penalty function method in the problem of constructing reachable sets for control systems with state constraints Trudy Inst. Mat. Mekh. UrO RAN 19 81-86
123