1. Gabatarwa
Sarrafa Tsinkayen Samfurin (MPC) wata ƙaƙƙarfan dabarar sarrafawa ce ta ci gaba wacce aka sani da ikonta na sarrafa tsarin masu yawan masu canji tare da ƙuntatawa. Duk da haka, dogaro da ita akan warware matsalar haɓakawa a kan layi a kowane lokaci yana haifar da babban nauyin lissafi. Wannan iyakancewa yana da tsanani musamman ga tsarin da ke da ƙarancin albarkatun lissafi, kamar tsarin da aka saka, jirage marasa matuki, ko na'urorin lissafi na gefe. Hanyoyin gargajiya don rage wannan—kamar rage tsayin hasashe—sau da yawa suna lalata garantin aiki kamar haɗuwa zuwa matsayin tsayayya. Tsarin MPC mai sanin matsayin tsayayya, wanda aka gabatar a matsayin mafita, yana tabbatar da bin sawun fitarwa da haɗuwa zuwa ma'aunin da ake so ba tare da ƙarin lissafi a kan layi ba. Duk da haka, lahani mai mahimmanci shi ne rashin ƙarfi a kan rikice-rikice na waje, wanda ba za a iya yin shawarwari ba don aiwatarwa a duniyar gaske. Wannan takarda ta magance wannan gibi kai tsaye ta hanyar haɗa fasahohin sarrafa ƙarfi na tushen bututu cikin tsarin MPC mai sanin matsayin tsayayya, ƙirƙirar hanyar da ke da ingantaccen lissafi kuma mai jure rikici.
2. Bayanai na Farko & Bayanin Matsala
Takardar tayi la'akari da tsarin lokaci mai rarrabuwa mai zaman kansa (LTI) wanda ke ƙarƙashin ƙarar ƙari da ƙuntatawa na yanayi/shigarwa. Matsalar cibiyar ita ce tsara dokar MPC wacce: 1) Tana aiki da gajeren tsayin hasashe mai ƙayyadaddun tsayi don iyakance lissafi a kan layi. 2) Tana tabbatar da gamsuwa da ƙuntatawa a kowane lokaci. 3) Tana tabbatar da haɗuwa zuwa matsayin tsayayya da ake so. 4) Tana da ƙarfi ga rikice-rikice na waje masu dorewa, masu iyaka. An ƙirƙira tsarin kamar haka: $x_{k+1} = Ax_k + Bu_k + w_k$, inda $x_k \in \mathbb{R}^n$, $u_k \in \mathbb{R}^m$, kuma $w_k \in \mathbb{W} \subset \mathbb{R}^n$ rikici ne mai iyaka. Rukunonin $\mathbb{X}$ da $\mathbb{U}$ suna ayyana ƙuntatawa na yanayi da shigarwa, bi da bi.
3. Tsarin MPC Mai Ƙarfi da Sanin Matsayin Tsayayya da aka Tsara
3.1 Tsarin Cibiyar
Mai sarrafa da aka tsara ya ginu akan MPC na al'ada mai sanin matsayin tsayayya. Mahimmin abu shine ƙayyadaddun hanyar yanayin da aka hasashe don fitar da tsarin zuwa matsayin tsayayya mai yiwuwa $(x_s, u_s)$. An tsara matsalar haɓakawa a kan layi don rage aikin farashi a kan gajeren tsayi yayin aiwatar da ƙuntatawa na ƙarshe waɗanda ke haɗa yanayin da aka hasashe na ƙarshe zuwa wannan matsayin tsayayya, yana tabbatar da kaddarorin haɗuwa na dogon tsayi duk da gajeren taga hasashe.
3.2 Sarrafa Rikici na Tushen Bututu
Don gabatar da ƙarfi, marubutan suna amfani da dabarar MPC na tushen bututu. Ra'ayin cibiyar shine rarraba manufar sarrafawa zuwa sassa biyu: shigarwar al'ada wacce aka lissafta ta hanyar warware MPC mai sanin matsayin tsayayya don samfurin mara rikici, da dokar amsawa ta taimako wacce aka tsara a kashe layi don kiyaye ainihin yanayin da aka rikita a cikin "bututu" mai iyaka a kusa da hanyar al'ada. Wannan bututu, wanda sau da yawa aka ayyana shi azaman Saitin Mai Ƙarfi Mai Ingantawa (RPI), yana tabbatar da cewa idan yanayin al'ada ya gamsu da ƙuntatawa mai ƙarfi, ainihin yanayin zai gamsu da ƙuntatawa na asali duk da rikice-rikice. Wannan rabuwa mai kyau yana nufin cewa an yi sarrafa ƙuntatawa mai ƙarfi a kashe layi, yana kiyaye sauƙin lissafi a kan layi na mai sarrafa al'ada.
4. Bincike na Ka'idar
4.1 Yin Maimaitawa Mai Yiwuwa
Takardar ta ba da cikakkiyar hujja cewa idan matsalar haɓakawa tana da yiwuwa a lokacin matakin farko, za ta kasance mai yiwuwa ga duk matakan lokaci na gaba a ƙarƙashin aikin dokar sarrafa da aka tsara kuma a gaban rikice-rikice masu iyaka. Wannan wata muhimmiyar buƙata ce ga kowane aiwatarwar MPC mai amfani.
4.2 Kwanciyar Hankali na Rufe-Madauki
Ta amfani da ka'idar kwanciyar hankali ta Lyapunov, marubutan sun nuna cewa tsarin rufe-madauki yana da Kwanciyar Hankali na Shigarwa-zuwa-Yanayi (ISS) dangane da rikici. Wannan yana nufin yanayin tsarin a ƙarshe zai haɗu zuwa yanki mai iyaka a kusa da matsayin tsayayya da ake so, tare da girman wannan yanki daidai da iyaka akan rikice-rikice.
5. Sakamakon Kwaikwayo
An yi amfani da kwaikwayon lambobi akan tsarin ma'auni (misali, mai haɗawa biyu) don tabbatar da aikin mai sarrafa. Ma'auni masu mahimmanci sun haɗa da: keta ƙuntatawa (babu wanda aka gani), kuskuren haɗuwa (mai iyaka a cikin bututun ka'idar), da lokacin lissafi kowane matakin sarrafawa (ƙasa sosai fiye da MPC mai ƙarfi mai tsayi). Sakamakon ya nuna a zahiri yadda ainihin hanyar yanayi ta kasance a cikin bututun da aka lissafta a kusa da hanyar al'ada, ko da a ƙarƙashin rikice-rikice masu dorewa.
6. Tabbatar da Gwaji akan Parrot Bebop 2
An gwada amfanin hanyar da aka tsara akan jirgin mara matuki na quadrotor Parrot Bebop 2, dandamali mai ƙarancin ƙarfin sarrafa kan jirgin. Manufar sarrafawa ita ce bin sawun hanya (misali, tsarin takwas) a gaban iskar da aka kwaikwaya (wanda aka ƙirƙira a matsayin rikice-rikice). Bayanan gwaji sun nuna cewa MPC mai ƙarfi mai sanin matsayin tsayayya ya yi nasarar kiyaye jirgin kusa da hanyar da ake so tare da ƙaramin karkata, yayin da amfani da CPU na kwamfutar da ke kan jirgin ya kasance cikin iyakokin da aka yarda, yana tabbatar da ingantaccen lissafi na hanyar da ƙarfinta na duniyar gaske.
7. Ƙarshe
Takardar ta gabatar da nasara sabon tsarin MPC mai ƙarfi wanda ya haɗa fa'idodin lissafi na ƙirar sanin matsayin tsayayya tare da garantin ƙarfi na MPC na tushen bututu. Tana ba da mafita mai yiwuwa don aiwatar da sarrafa mai ƙima mai ƙima, mai sanin ƙuntatawa akan tsarin da ke da ƙarancin albarkatu waɗanda ke aiki a cikin yanayi mara tabbas, kamar yadda bincike na ka'idar da gwaje-gwajen kayan aiki suka tabbatar.
8. Bincike na Asali & Sharhin Kwararre
9. Cikakkun Bayanai na Fasaha & Tsarin Lissafi
Matsalar haɓakawa a kan layi a lokacin $k$ ita ce: $$ \begin{aligned} \min_{\mathbf{u}_k, x_s, u_s} &\quad \sum_{i=0}^{N-1} \ell(\bar{x}_{i|k} - x_s, \bar{u}_{i|k} - u_s) + V_f(\bar{x}_{N|k} - x_s) \\ \text{s.t.} &\quad \bar{x}_{0|k} = \hat{x}_k, \\ &\quad \bar{x}_{i+1|k} = A \bar{x}_{i|k} + B \bar{u}_{i|k}, \\ &\quad \bar{x}_{i|k} \in \bar{\mathbb{X}} \subseteq \mathbb{X} \ominus \mathcal{Z}, \\ &\quad \bar{u}_{i|k} \in \bar{\mathbb{U}} \subseteq \mathbb{U} \ominus K\mathcal{Z}, \\ &\quad \bar{x}_{N|k} \in x_s \oplus \mathcal{X}_f, \\ &\quad (x_s, u_s) \in \mathcal{Z}_{ss}. \end{aligned} $$ Anan, $\bar{x}, \bar{u}$ sune yanayi/shigarwar al'ada, $N$ shine gajeren tsayi, $\ell$ da $V_f$ sune farashin mataki da na ƙarshe. Abubuwa masu mahimmanci sune ƙuntataccen saitin ƙuntatawa $\bar{\mathbb{X}}, \bar{\mathbb{U}}$ (saitunan asali sun ragu ta hanyar saitin RPI $\mathcal{Z}$ ta hanyar bambancin Pontryagin $\ominus$), da dokar taimako $u_k = \bar{u}_{0|k}^* + K(x_k - \bar{x}_{0|k}^*)$, inda $K$ riba ce mai daidaitawa. Saitin $\mathcal{Z}_{ss}$ yana ayyana matsayin tsayayya masu yiwuwa.
10. Tsarin Bincike: Nazarin Lamari na Ra'ayi
Yanayi: Jirgin mara matuki mai isar da kaya yana kewaya cikin kwarin birni (komputa mai ƙarancin albarkatu, rikice-rikice na iska).
Mataki 1 – Ƙira a Kashe Layi:
- Samfuri & Saitin Rikici: Gano ƙirar layi a kusa da shawagi. Siffanta iskar iska azaman saiti mai iyaka $\mathbb{W}$ (misali, ±2 m/s a cikin jirgin sama a kwance).
- Lissafa Bututu na RPI: Ƙirƙiri ribar amsawa $K$ (misali, LQR) kuma lissafa mafi ƙarancin saitin RPI $\mathcal{Z}$ don $e_{k+1} = (A+BK)e_k + w_k$. Wannan yana ayyana "bututu na kuskure."
- Ƙarfafa Ƙuntatawa: Rage titin jirgin sama (ƙuntatawa na yanayi) da iyakokin tuƙin mota (ƙuntatawa na shigarwa) ta $\mathcal{Z}$ da $K\mathcal{Z}$ don samun $\bar{\mathbb{X}}, \bar{\mathbb{U}}$.
- Ayyana Saitin Matsayin Tsayayya: $\mathcal{Z}_{ss}$ ya ƙunshi duk wuraren tsayawa a tsaye a cikin titin da aka ƙarfafa.
- Auna Yanayi: Sami matsayi/gudun jirgin na yanzu $x_k$ daga na'urori masu auna firikwensin.
- Warware MPC na Al'ada: Warware ƙaramin QP (ta amfani da $\bar{\mathbb{X}}, \bar{\mathbb{U}}, \mathcal{Z}_{ss}$) don samun shirin al'ada $\bar{u}^*$ da manufar matsayin tsayayya.
- Aiwatar da Sarrafa Haɗaka: $u_k = \bar{u}^*_{0|k} + K(x_k - \bar{x}^*_{0|k})$. Kalmar farko tana jagorantar aikin, kalmar ta biyu tana ƙin iskar iska sosai don kiyaye jirgin a cikin bututu.
11. Aikace-aikace na Gaba & Hanyoyin Bincike
- AI na Gefe & IoT: Tura sarrafa ci gaba akan na'urori masu auna firikwensin masu wayo, na'urori masu sawa, da ƙananan mutummutumi don ayyuka masu daidaito a masana'antu da kiwon lafiya.
- Ƙungiyoyin Marasa Matuki: Sarrafa ma'auni don manyan ƙungiyoyin jirage marasa matuki ko mutummutumi masu arha, masu sauƙi inda kowane wakili yana da iyakokin lissafi masu tsanani.
- Bincike na Zamani na Gaba:
- Koyon Bututu: Yin amfani da bayanan ainihin lokaci don ƙididdige saitin rikici $\mathbb{W}$ da daidaitawa da rage bututu, rage ra'ayin mazan jiya. Wannan yana haɗuwa da MPC na daidaitawa da tsarin sarrafa tushen koyo.
- Ƙari marasa Layi: Aiwatar da falsafar zuwa tsarin marasa layi ta amfani da ra'ayoyi daga MPC na bututu mara layi ko lebur, mai mahimmanci don motsa jirgin mara matuki mai ƙarfi.
- Haɗin Kayan Aiki-Software: Ƙirƙirar ƙananan guntu na musamman (FPGAs, ASICs) waɗanda aka inganta don warware takamaiman, ƙaramin QP na wannan tsarin a ƙaramin wutar lantarki.
12. Nassoshi
- Jafari Ozoumchelooei, H., & Hosseinzadeh, M. (2023). Robust Steady-State-Aware Model Predictive Control for Systems with Limited Computational Resources and External Disturbances. [Sunan Jarida].
- Mayne, D. Q., Seron, M. M., & Raković, S. V. (2005). Robust model predictive control of constrained linear systems with bounded disturbances. Automatica, 41(2), 219-224.
- Rawlings, J. B., Mayne, D. Q., & Diehl, M. M. (2017). Model Predictive Control: Theory, Computation, and Design (2nd ed.). Nob Hill Publishing.
- ETH Zurich, Laboratory na Sarrafa Kansa. (n.d.). Bayanan Lacca akan Sarrafa Tsinkayen Samfurin. An samo daga [Gidan Yanar Gizon Cibiyar].
- Hewing, L., Wabersich, K. P., Menner, M., & Zeilinger, M. N. (2020). Learning-based model predictive control: Toward safe learning in control. Annual Review of Control, Robotics, and Autonomous Systems, 3, 269-296.
Fahimtar Cibiyar: Wannan takarda ba wani ƙarin gyara ne kawai na MPC ba; yana da daidaitawar injiniyan dabaru da aka aiwatar da daidaitaccen tiyata. Marubutan sun gano ainihin ma'amalar tsaka-tsaki tsakanin iyawar lissafi da aiki mai ƙarfi don tsarin da aka saka. Sun yarda da iyakancewar gajeren tsayin hasashe—babban rangwame—amma da hazaka sun dawo da garantin da aka rasa (haɗuwa zuwa matsayin tsayayya, ƙarfi) ta hanyar ƙirar kashe layi mai wayo (saitunan bututu, ƙayyadaddun matsayin tsayayya). Wannan sarrafa injiniya ne azaman sarrafa albarkatu.
Kwararar Ma'ana: Hujjar tana da gamsarwa kuma ta layi. Fara da matsalar da ba a warware ba (gibin ƙarfi a cikin MPC mai inganci), zaɓi kayan aiki masu ma'ana na ka'idar (tube MPC) da aka sani don raba sarkakiya, kuma haɗa shi cikin sauki cikin ingantaccen tsari (MPC mai sanin matsayin tsayayya). Tabbatarwa tana ƙaruwa bisa ma'ana daga ka'idar (hujjoji) zuwa kwaikwayo (ra'ayoyi) zuwa gwaji (gaskiya akan jirgin mara matuki), yana bin ma'auni na zinariya kamar yadda aikin farko na Tube MPC na Mayne et al. (2005) a cikin Automatica ya misalta.
Ƙarfi & Kurakurai: Babban ƙarfi shine amfani. Ta hanyar amfani da hanyoyin tushen bututu, hanyar tana kaucewa buƙatar haɓakawa mai sarkakiya a kan layi, waɗanda ke hana lissafi. Amfani da jirgin mara matuki don tabbatarwa yana da kyau—dandamali ne mai daidaitawa, mai ƙarancin albarkatu. Duk da haka, lahani yana cikin ra'ayin mazan jiya da ke cikin tube MPC. Lissafin kashe layi na saitin RPI da ƙarfafa ƙuntatawa na gaba na iya rage yankin mai yiwuwa na mai sarrafa sosai, yana iyakance motsinsa. Wannan sanannen ciniki ne a cikin sarrafa ƙarfi, kamar yadda albarkatun kamar bayanan lacca na Laboratorin Sarrafa Kansa na ETH Zurich akan sarrafa ƙuntatawa suka tattauna. Takardar za ta iya ƙididdige wannan asarar aikin da fiko fiye da (mai tsada na lissafi) ingantaccen MPC mai ƙarfi.
Fahimta Mai Aiki: Ga masu aiki: Wannan shiri ne shirye-shiryen amfani don aiwatar da MPC mai ƙarfi akan na'urorin gefe. Mayar da hankali kan lissafin saitin RPI cikin inganci—yi la'akari da amfani da kusancin polytopic ko ellipsoidal don daidaita sarkakiya da ra'ayin mazan jiya. Ga masu bincike: Gaba gaba shine bututu na daidaitawa ko na koyo. Shin hanyoyin sadarwar jijiyoyi, kama da waɗanda ake amfani da su a cikin RL na tushen samfur ko wahayi ta ayyuka kamar Sarrafa Tsinkayen Samfurin na Tushen Koyo (koyawa na IEEE CDC), za su iya koyon ƙuntataccen saitin rikici a kan layi, rage ra'ayin mazan jiya yayin kiyaye ƙarfi? Wannan zai zama juyin halitta na ma'ana na wannan aikin.