Optimal control of switched systems based on parameterization of the switching instants

This paper presents a new approach for solving optimal control problems for switched systems. We focus on problems in which a prespecified sequence of active subsystems is given. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. In order to sea...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2004-01, Vol.49 (1), p.2-16
Main Authors: Xuping Xu, Antsaklis, P.J.
Format: Article
Language:English
Subjects:
Applied sciences
Automobiles
Automotive engineering
Boundary value problems
Chemical processes
Closed-form solution
Computer science
control theory
systems
Control system analysis
Control system synthesis
Control theory. Systems
Cost function
Derivatives
Differential algebraic equations
Differential equations
Exact sciences and technology
Manufacturing processes
Mathematical analysis
Mathematical models
Optimal control
Optimization
Parametrization
Studies
Switched systems
Switching
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Summary:This paper presents a new approach for solving optimal control problems for switched systems. We focus on problems in which a prespecified sequence of active subsystems is given. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. In order to search for the optimal switching instants, the derivatives of the optimal cost with respect to the switching instants need to be known. The most important contribution of the paper is a method which first transcribes an optimal control problem into an equivalent problem parameterized by the switching instants and then obtains the values of the derivatives based on the solution of a two point boundary value differential algebraic equation formed by the state, costate, stationarity equations, the boundary and continuity conditions, along with their differentiations. This method is applied to general switched linear quadratic problems and an efficient method based on the solution of an initial value ordinary differential equation is developed. An extension of the method is also applied to problems with internally forced switching. Examples are shown to illustrate the results in the paper.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2003.821417