### Abstract

This letter details the solution to the linear quadratic (LQ) optimal control problem over a finite interval for time-varying multimodal linear systems with time-triggered jumps. By multimodal, we mean the possibility for the system state to change dimension after every jump. To this end, we introduce the multimodal jumping differential Riccati equation (MJDRE) and we show the equivalence between the solvability of the optimal control problem and the existence of a finite solution of the MJDRE. The MJDRE can be used to compute optimal tracking gains for hybrid system with state-triggered jumps, whose state dimension changes after each jump (multimodal hybrid system). This is demonstrated, in simulation, on a 2DOF dual-mass spring-damper system.

Original language | English |
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Article number | 8738826 |

Pages (from-to) | 217-222 |

Number of pages | 6 |

Journal | IEEE Control Systems Letters |

Volume | 4 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2020 |

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### Keywords

- Multimodal
- optimal control
- Riccati equation

### Cite this

*IEEE Control Systems Letters*,

*4*(1), 217-222. [8738826]. https://doi.org/10.1109/LCSYS.2019.2923474

}

*IEEE Control Systems Letters*, vol. 4, no. 1, 8738826, pp. 217-222. https://doi.org/10.1109/LCSYS.2019.2923474

**On linear quadratic optimal control for time-varying multimodal linear systems with time-triggered jumps.** / de Carolis, Giovanni (Corresponding author); Saccon, Alessandro.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - On linear quadratic optimal control for time-varying multimodal linear systems with time-triggered jumps

AU - de Carolis, Giovanni

AU - Saccon, Alessandro

PY - 2020/1/1

Y1 - 2020/1/1

N2 - This letter details the solution to the linear quadratic (LQ) optimal control problem over a finite interval for time-varying multimodal linear systems with time-triggered jumps. By multimodal, we mean the possibility for the system state to change dimension after every jump. To this end, we introduce the multimodal jumping differential Riccati equation (MJDRE) and we show the equivalence between the solvability of the optimal control problem and the existence of a finite solution of the MJDRE. The MJDRE can be used to compute optimal tracking gains for hybrid system with state-triggered jumps, whose state dimension changes after each jump (multimodal hybrid system). This is demonstrated, in simulation, on a 2DOF dual-mass spring-damper system.

AB - This letter details the solution to the linear quadratic (LQ) optimal control problem over a finite interval for time-varying multimodal linear systems with time-triggered jumps. By multimodal, we mean the possibility for the system state to change dimension after every jump. To this end, we introduce the multimodal jumping differential Riccati equation (MJDRE) and we show the equivalence between the solvability of the optimal control problem and the existence of a finite solution of the MJDRE. The MJDRE can be used to compute optimal tracking gains for hybrid system with state-triggered jumps, whose state dimension changes after each jump (multimodal hybrid system). This is demonstrated, in simulation, on a 2DOF dual-mass spring-damper system.

KW - Multimodal

KW - optimal control

KW - Riccati equation

UR - http://www.scopus.com/inward/record.url?scp=85068471231&partnerID=8YFLogxK

U2 - 10.1109/LCSYS.2019.2923474

DO - 10.1109/LCSYS.2019.2923474

M3 - Article

AN - SCOPUS:85068471231

VL - 4

SP - 217

EP - 222

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

SN - 2475-1456

IS - 1

M1 - 8738826

ER -