Aspects of Adaptive Optimal Steady-State Control

1968 ◽  
Vol 90 (2) ◽  
pp. 201-207
Author(s):  
A. E. Pearson
Keyword(s):  
Optimal Control ◽  
Steady State ◽  
Periodic Function ◽  
System Performance ◽  
Optimal Control Problems ◽  
State System ◽  
Control Problems ◽  
State Control ◽  
Steady State Operation ◽  
Steady State Control

The paper extends and modifies an approach to adaptive optimal control problems proposed by Kulikowski. The emphasis at the outset is placed upon optimizing the steady-state system performance in which the desired output of the plant is a periodic function of time. The formulation for type-one plants is modified to include the optimization of the total amount of input accumulation, s=∫−∞t0u(τ)dτ, which is present at the beginning of each period of steady-state operation.

A Constraining Hyperplane Technique for State Variable Constrained Optimal Control Problems

1973 ◽  
Vol 95 (4) ◽  
pp. 380-389 ◽  
Author(s):  
K. Martensson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Dynamic Programming Algorithm ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Control Problems ◽  
State Control ◽  
Constrained Optimal Control ◽  
State Variable

A new approach to the numerical solution of optimal control problems with state-variable inequality constraints is presented. It is shown that the concept of constraining hyperplanes may be used to approximate the original problem with a problem where the constraints are of a mixed state-control variable type. The efficiency and the accuracy of the combination of constraining hyperplanes and a second-order differential dynamic programming algorithm are investigated on problems of different complexity, and comparisons are made with the slack-variable and the penalty-function techniques.

scholarly journals Sufficiency for Purely Essentially Bounded Optimal Controls

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 238
Author(s):  
Gerardo Sánchez Licea
Keyword(s):  
Nonlinear Dynamics ◽  
Optimal Control ◽  
Optimal Control Problems ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Optimal Controls ◽  
Embedding Theorems ◽  
State Control ◽  
Discontinuous Solutions ◽  
Piecewise Continuous

For optimal control problems of Bolza with variable and free end-points, nonlinear dynamics, nonlinear isoperimetric inequality and equality restrictions, and nonlinear pointwise mixed time-state-control inequality and equality constraints, sufficient conditions for strong minima are derived. The algorithm used to prove the main theorem of the paper includes a crucial symmetric inequality, making this technique an independent self-contained method of classical concepts such as embedding theorems from ordinary differential equations, Mayer fields, Riccati equations, or Hamilton–Jacobi theory. Moreover, the sufficiency theory given in this article is able to detect discontinuous solutions, that is, solutions which need to be neither continuous nor piecewise continuous but only essentially bounded.

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