A Generalization of the Bang-Bang Principle of Linear Control Theory*

1965 ◽  
Vol 8 (6) ◽  
pp. 783-789
Author(s):  
Richard Datko
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Matrix Function ◽  
Linear Time ◽  
Time Optimal Control ◽  
Linear Control ◽  
Dimensional Vector ◽  
R Matrix ◽  
Linear Control Theory ◽  
Time Optimal

In a paper by LaSalle [l] on linear time optimal control the following lemma is proved:Let Ω be the set of all r-dimensional vector functions U(τ) measurable on [ 0, t] with |ui(τ)≦1. Let Ωo be the subset of functions uo(τ) with |uoi(τ) = 1. Let Y(τ) be any (n × r ) matrix function in L1([ 0, t]).

Strong stability of linear parabolic time-optimal control problems

2019 ◽  
Vol 25 ◽  
pp. 1 ◽  
Author(s):  
Lucas Bonifacius ◽  
Konstantin Pieper
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Strong Stability ◽  
Time Optimal Control ◽  
Control Problems ◽  
Terminal Set ◽  
Time Optimal

Sufficient conditions for strong stability of a class of linear time-optimal control problems with general convex terminal set are derived. Strong stability in turn guarantees qualified optimality conditions. The theory is based on a characterization of weak invariance of the target set under the controlled equation. An appropriate strengthening of the resulting Hamiltonian condition ensures strong stability and yieldsa prioribounds on the size of multipliers, independent of,e.g., the initial point or the running cost. In particular, the results are applied to the control of the heat equation into anL2-ball around a desired state.

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