# 2010 Research Summary

## Optimal control of switched nonlinear dynamical systems

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Maryam Kamgarpour and Claire Tomlin

National Science and Engineering Research Canada (NSERC) and AFOSR PRET Grant 18796-S2

Optimal control of hybrid systems is proven to be difficult due to the problem of optimal discrete mode scheduling. In this work we focus on the subset of hybrid systems referred to as switched systems, in which the sequence of the discrete modes is fixed. The optimal control problem is finding a switching law to determine when each subsystem should be active as well as a continuous input for control of each active subsystem. We derive first order necessary optimality conditions for the continuous input and switch times. In general, due to non-convexity of the cost function and nonlinearity of dynamics globally optimal solution is difficult to compute. Based on the derived necessary conditions, we develop an algorithm that converges to a local optimum.

- [1]
- M. Kamgarpour and C. J. Tomlin, “Optimal Control of Switched Systems”, Control and Decision Conference 2010, In preparation.