ETH Zürich, Switzerland\
    (e-mail: mkamgar@control.ee. ethz.ch).
author:
- Farbod Farshidian
- Maryam Kamgarpour
- Diego Pardo
- Jonas Buchli
bibliography:
- 'bibliography/references.bib'
title: Sequential Linear Quadratic Optimal Control for Nonlinear Switched Systems
---

Control design for hybrid systems, Switching stability and control, Optimal control of hybrid systems, Optimal control theory, Real-time control, Riccati equations, and Mobile robots.

Introduction
============

Switched systems are a subclass of a general family known as hybrid systems. Hybrid system model consists of a finite number of dynamical subsystems subjected to discrete events which cause transition between these subsystems. This transition is either triggered by an external input, or through the intersection of the continuous states trajectory to a certain manifolds known as the switching surfaces. Switched systems are usually characterized by systems that have continuous state transition during these switches. Switched system models are encountered in many practical applications such as automobiles and locomotives with different gears, DC-DC converters, manufacturing processes, biological systems, and robotics.

Our interest in switched systems originates from an application on a legged robot where we model the Center of Mass (CoM) as a switched system. The control goal is to synthesize a controller which, for a given gait, stabilizes the 