Optimal solutions to differential inclusions in presence of state constraints

1984 ◽  
Vol 44 (4) ◽  
pp. 657-679 ◽  
Author(s):  
G. S. Pappas
Keyword(s):  
Differential Inclusions ◽  
State Constraints ◽  
Optimal Solutions

scholarly journals Trajectories of differential inclusions with state constraints

2011 ◽  
Vol 250 (4) ◽  
pp. 2267-2281 ◽  
Author(s):  
Alberto Bressan ◽  
Giancarlo Facchi
Keyword(s):  
Differential Inclusions ◽  
State Constraints

Distributed control of networked systems with coupling constraints

2019 ◽  
Vol 67 (12) ◽  
pp. 1007-1018
Author(s):  
Zonglin Liu ◽  
Olaf Stursberg
Keyword(s):  
Cost Reduction ◽  
State Constraints ◽  
Networked Systems ◽  
Mixed Integer ◽  
Control Problems ◽  
Optimal Solutions ◽  
Coupling Constraints ◽  
Motion Problem ◽  
Vehicle Motion ◽  
High Computational Complexity

Abstract This paper proposes algorithms for the distributed solution of control problems for networked systems with coupling constraints. This type of problem is practically relevant, e. g., for subsystems which share common resources, or need to go through a bottleneck, while considering non-convex state constraints. Centralized solution schemes, which typically first cast the non-convexities into mixed-integer formulations that are then solved by mixed-integer programming, suffer from high computational complexity for larger numbers of subsystems. The distributed solution proposed in this paper decomposes the centralized problem into a set of small subproblems to be solved in parallel. By iterating over the subproblems and exchanging information either among all subsystems, or within subsets selected by a coordinator, locally optimal solutions of the global problem are determined. The paper shows for two instances of distributed algorithms that feasibility as well as continuous cost reduction over the iterations up to termination can be guaranteed, while the solutions times are considerably shorter than for the centralized problem. These properties are illustrated for a multi-vehicle motion problem.

scholarly journals Stratified Necessary Conditions for Differential Inclusions with State Constraints

2013 ◽  
Vol 51 (5) ◽  
pp. 3903-3917 ◽  
Author(s):  
Piernicola Bettiol ◽  
Andrea Boccia ◽  
Richard B. Vinter
Keyword(s):  
Differential Inclusions ◽  
State Constraints ◽  
Necessary Conditions

scholarly journals Differential inclusions with state constraints

1989 ◽  
Vol 32 (1) ◽  
pp. 81-98 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Inclusion ◽  
Tangent Cone ◽  
Differential Inclusions ◽  
State Constraints ◽  
Tangent Cones ◽  
Viability Theory ◽  
Constraint Set

In “Viability Theory”, we select trajectories which are viable in the sense that they always satisfy a given constraint. Since the fundamental work of Nagumo [26], we know that in order to guarantee existence of viable trajectories, we need to satisfy certain tangential conditions. In the case of differential inclusions and using the modern terminology and notation of tangent cones, this condition takes the form F(t, x) ∩ TK#φ, where F(.,.) is the orientor field involved in the differential inclusion, K is the viability (constraint) set and TK(x) is the tangent cone to K at x. Results on the existence of viable solutions for differential inclusions can be found in Aubin–Cellina [2] and Papageorgiou [30,32].

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