Abstract A unified theory for the time-optimal control of general linear plants with generalized constraints on the control variable is developed. The geometrical approach taken provides new insight and interpretation for some results obtained by methods of functional analysis. Theorems stating necessary and sufficient conditions for the existence and uniqueness of the optimal control function, u0, and explicit formulae for u0, are derived by exploiting the topological properties of the reachable region—the set of the output points (n-vectors) that can be reached using constrained controls. The detailed study of the conditions for the occurrence of corners and flat portions in the reachable region clarifies some “degenerate” cases for amplitude and area constraints, which have hitherto remained obscure. The synthesis problem is briefly discussed.
[1]
L. Neustadt.
Synthesizing time optimal control systems
,
1960
.
[2]
P. E. Sarachik,et al.
An Application of Functional Analysis to the Optimal Control Problem
,
1963
.
[4]
R. Gamkrelidze.
THE THEORY OF TIME OPTIMAL PROCESSES IN LINEAR SYSTEMS
,
1961
.
[5]
R. Bellman,et al.
On the “bang-bang” control problem
,
1956
.
[6]
Charles A. Desoer,et al.
The Bang Bang Servo Problem Treated by Variational Techniques
,
1959,
Inf. Control..
[7]
E. Lee,et al.
Mathematical aspects of the synthesis of linear minimum response-time controllers
,
1960
.