Sufficient Conditions for Local Optimality in Multidimensional Control Problems with State Restrictions

1991 ◽  
Vol 10 (3) ◽  
pp. 397-405 ◽  
Author(s):  
Sabine Pickenhain ◽  
Klaus Tammer
Keyword(s):  
Sufficient Conditions ◽  
Control Problems ◽  
Local Optimality ◽  
Multidimensional Control Problems ◽  
State Restrictions

scholarly journals Singular extremals in L1-optimal control problems: sufficient optimality conditions

2020 ◽  
Vol 26 ◽  
pp. 99
Author(s):  
Francesca C. Chittaro ◽  
Laura Poggiolini
Keyword(s):  
Optimal Control Problems ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Sufficient Optimality Conditions ◽  
Local Optimality ◽  
Second Variation ◽  
Absolute Value ◽  
Singular Extremals ◽  
Hamiltonian Methods ◽  
The Second Variation

In this paper we are concerned with generalised L1-minimisation problems, i.e. Bolza problems involving the absolute value of the control with a control-affine dynamics. We establish sufficient conditions for the strong local optimality of extremals given by the concatenation of bang, singular and inactive (zero) arcs. The sufficiency of such conditions is proved by means of Hamiltonian methods. As a by-product of the result, we provide an explicit invariant formula for the second variation along the singular arc.

scholarly journals On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question

2014 ◽  
Vol 24 (4) ◽  
pp. 723-733
Author(s):  
K.Maciej Przyłuski
Keyword(s):  
Minimum Energy ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Minimum Norm Solution ◽  
Quadratic Problem ◽  
Infinite Dimensional ◽  
Necessary And Sufficient ◽  
Quadratic Control Problems

Abstract In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

Formation-containment control of sampled-data second-order multi-agent systems with sampling delay

2018 ◽  
Vol 40 (16) ◽  
pp. 4369-4381 ◽  
Author(s):  
Baojie Zheng ◽  
Xiaowu Mu
Keyword(s):  
Matrix Theory ◽  
Sufficient Conditions ◽  
Second Order ◽  
Control Problems ◽  
Sampled Data ◽  
Multi Agent Systems ◽  
Containment Control ◽  
Agent Systems ◽  
Multi Agent ◽  
Theoretical Results

The formation-containment control problems of sampled-data second-order multi-agent systems with sampling delay are studied. In this paper, we assume that there exist interactions among leaders and that the leader’s neighbours are only leaders. Firstly, two different control protocols with sampling delay are presented for followers and leaders, respectively. Then, by utilizing the algebraic graph theory and matrix theory, several sufficient conditions are obtained to ensure that the leaders achieve a desired formation and that the states of the followers converge to the convex hull formed by the states of the leaders, i.e. the multi-agent systems achieve formation containment. Furthermore, an explicit expression of the formation position function is derived for each leader. An algorithm is provided to design the gain parameters in the protocols. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.

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