Analysis of Optimal Control Problems for Hybrid Systems with One State Variable

2019 ◽  
Author(s):  
Puduru Viswanadha Reddy ◽  
J.M. (Hans) Schumacher ◽  
Jacob C. Engwerda
Keyword(s):  
Optimal Control ◽  
Hybrid Systems ◽  
Optimal Control Problems ◽  
Control Problems ◽  
State Variable

Analysis of Optimal Control Problems for Hybrid Systems with One State Variable

2020 ◽  
Vol 58 (6) ◽  
pp. 3262-3292 ◽  
Author(s):  
Puduru Viswanadha Reddy ◽  
Johannes M. Schumacher ◽  
Jacob C. Engwerda
Keyword(s):  
Optimal Control ◽  
Hybrid Systems ◽  
Optimal Control Problems ◽  
Control Problems ◽  
State Variable

scholarly journals Efficient Solution of Optimal Control Problems Using Hybrid Systems

2005 ◽  
Vol 43 (6) ◽  
pp. 1923-1952 ◽  
Author(s):  
Mireille Broucke ◽  
Maria Domenica Di Benedetto ◽  
Stefano Di Gennaro ◽  
Alberto Sangiovanni-Vincentelli
Keyword(s):  
Optimal Control ◽  
Hybrid Systems ◽  
Efficient Solution ◽  
Optimal Control Problems ◽  
Control Problems

scholarly journals Optimality Condition-Based Sensitivity Analysis of Optimal Control for Hybrid Systems and Its Application

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Chunyue Song
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Hybrid Systems ◽  
Optimality Condition ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Equivalent Transformation ◽  
Control Problems ◽  
Continuous Control ◽  
Mode Transition

Gradient-based algorithms are efficient to compute numerical solutions of optimal control problems for hybrid systems (OCPHS), and the key point is how to get the sensitivity analysis of the optimal control problems. In this paper, optimality condition-based sensitivity analysis of optimal control for hybrid systems with mode invariants and control constraints is addressed under a priori fixed mode transition order. The decision variables are the mode transition instant sequence and admissible continuous control functions. After equivalent transformation of the original problem, the derivatives of the objective functional with respect to control variables are established based on optimal necessary conditions. By using the obtained derivatives, a control vector parametrization method is implemented to obtain the numerical solution to the OCPHS. Examples are given to illustrate the results.

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.

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