A necessary optimality condition for constrained optimal control of hybrid systems

2015 ◽  
Author(s):  
Andreas B. Hempel ◽  
Paul J. Goulart ◽  
John Lygeros
Keyword(s):  
Optimal Control ◽  
Hybrid Systems ◽  
Optimality Condition ◽  
Necessary Optimality Condition ◽  
Constrained Optimal Control

Constrained Optimal Control of Hybrid Systems With a Linear Performance Index

2006 ◽  
Vol 51 (12) ◽  
pp. 1903-1919 ◽  
Author(s):  
Mato Baoti ◽  
Frank J. Christophersen ◽  
Manfred Morari
Keyword(s):  
Optimal Control ◽  
Hybrid Systems ◽  
Performance Index ◽  
Constrained Optimal Control

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.

Dynamic programming for constrained optimal control of discrete-time linear hybrid systems

Automatica ◽  
2005 ◽  
Vol 41 (10) ◽  
pp. 1709-1721 ◽  
Author(s):  
Francesco Borrelli ◽  
Mato Baotić ◽  
Alberto Bemporad ◽  
Manfred Morari
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Hybrid Systems ◽  
Discrete Time ◽  
Constrained Optimal Control ◽  
Time Linear

scholarly journals Optimal Control Problem for Switched System with the Nonsmooth Cost Functional

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Shahlar Meherrem ◽  
Rufan Akbarov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Condition ◽  
Switched System ◽  
Switching Systems ◽  
Switching System ◽  
Necessary Optimality Condition ◽  
Cost Functional

We examine the relationships between lower exhausters, quasidifferentiability (in the Demyanov and Rubinov sense), and optimal control for switching systems. Firstly, we get necessary optimality condition for the optimal control problem for switching system in terms of lower exhausters. Then, by using relationships between lower exhausters and quasidifferentiability, we obtain necessary optimality condition in the case that the minimization functional satisfies quasidifferentiability condition.

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