Brief paper: On optimal control of non-autonomous switched systems with a fixed mode sequence

Authors:
Maryam Kamgarpour;Claire Tomlin
Affiliations:
Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA, USA;Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA, USA
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

We consider differentiability with respect to the switch times of the value function of an optimal control problem for a non-autonomous switched system. The control variables are the switch times between the modes and the input in each mode. We provide a method to compute the derivative of the cost function given a nominal input. Then, we view the optimal control problem as a parametrized optimization problem in which the switch times are the parameters and the optimization is over the set of feasible inputs of each mode. From this point of view, we provide conditions under which the continuity and differentiability of the optimal value function, that is the cost function optimized over the inputs, can be guaranteed.