Retrofit control is a new control concept towards the control of large-scale network systems that are ** subject to change due to extension and reconstruction of local subsystems by multiple independent subsystem operators**.
The proposed approach is a control method that, rather than an entire system model, requires a model of the subsystem of interest for controller design.
The retrofit controller can guarantee robust stability in the sense that the entire closed-loop system is stable for any variations of neighboring subsystems (assembly of which is called an environment), other than the subsystem of interest, as long as the preexisting network system (the feedback system of the environment and the subsystem of interest) is originally stable.
This enables the

As theoretical achievements, we have given the parameterization of __ all the retrofit controllers in terms of a constrained version of the Youla parametrization__.
Furthermore, providing a particular design method of retrofit controllers, we have analyzed resultant system properties when multiple retrofit controllers are designed and implemented in parallel.
As further extension of theory, we have developed a design method of a generalized version of retrofit controllers where

- Takayuki Ishizaki, Tomonori Sadamoto, Jun-ichi Imura, Henrik Sandberg, Karl Henrik Johansson: Retrofit Control: Localization of Controller Design and Implementation. Automatica, 95, pp.336-346, 2018. (DOI: 10.1016/j.automatica.2018.05.033) arXiv Preprint
- Takayuki Ishizaki, Takahiro Kawaguchi, Hampei Sasahara, Jun-ichi Imura: Retrofit Control with Approximate Environment Modeling. Automatica, in press. arXiv Preprint
- Takayuki Ishizaki, Hampei Sasahara, Masaki Inoue, Jun-ichi Imura: Modularity-in-Design of Dynamical Network Systems: Retrofit Control Approach. arXiv

Smart use of renewable energy is one of the key tasks towards reductions in greenhouse gas emissions.
To push up the penetration level of renewable energy resources, it is crucial to devise a practical control method to improve the degree of power system stability because __ renewable power generation, such as photovoltaic and wind power generation, is highly volatile due to weather change__.
With this background, we have developed

- Tomonori Sadamoto, Aranya Chakrabortty, Takayuki Ishizaki, Jun-ichi Imura: Retrofit Control of Wind-Integrated Power Systems. IEEE Transactions on Power Systems, 33(3), pp.2804-2815, 2018. (DOI: 10.1109/TPWRS.2017.2750411) Preprint JST Press Release JST Press Release
- Hampei Sasahara, Takayuki Ishizaki, Tomonori Sadamoto, Taisuke Masuta, Yuzuru Ueda, Hideharu Sugihara, Nobuyuki Yamaguchi, Jun-ichi Imura: Damping Performance Improvement for PV-Integrated Power Grids via Retrofit Control. Control Engineering Practice, 84, pp.92-101, 2019. (DOI: 10.1016/j.conengprac.2018.11.004) Preprint

Conventional thermal generators generally require several hours for warm-up and cool-down.
Therefore, it is crucial to conduct __ the day-ahead scheduling of startup and shutdown of thermal generators__ to keep supply-demand balancing for volatile demand and renewable power generation, the amounts of which are also predicted the day before.
Such a scheduling problem of conventional generators under uncertainty of demand and renewable power prediction is called a

For robust unit commitment, we have proposed a novel approach that can realize stable power supply with explicit consideration of the feasibility of realtime economic dispatch in realtime operation.
In the proposed robust unit commitment problem, we aim at deciding not only the startup and shutdown schedules of thermal generators, but also __ the admissible operation ranges of generators and batteries that are sufficient for realtime adaptation to the volatility of demand and renewable power generation__.
Such an ability to realize realtime adaptation is mathematically described as

- Youngchae Cho, Takayuki Ishizaki, Nacim Ramdani, Jun-ichi Imura: Box-Based Temporal Decomposition of Multi-Period Economic Dispatch for Two-Stage Robust Unit Commitment. IEEE Transactions on Power Systems, 2019, in press. (DOI: 10.1109/TPWRS.2019.2896349) Preprint Tokyo Tech Press Release JST Press Release Tokyo Tech/JST Press Release

Sharp fluctuations in photovoltaic (PV) power generation and idiosyncratic power consumption make the exact net-demand prediction difficult.
As a relatively new approach to reliable renewable power prediction, there can be found __ interval-valued prediction methods__ that determine confidence intervals with a certain probability, e.g., 95%.
Such interval-valued net-demand prediction can be depicted as the red region in the figure below.
To comply with this type of prediction, we have formulated

- Takayuki Ishizaki, Masakazu Koike, Nacim Ramdani, Yuzuru Ueda, Taisuke Masuta, Takashi Oozeki, Tomonori Sadamoto, Jun-ichi Imura: Interval Quadratic Programming for Day-Ahead Dispatch of Uncertain Predicted Demand. Automatica, 64, pp.163-173, 2016. (DOI: 10.1016/j.automatica.2015.11.002) Preprint JST Press Release JST Press Release
- Masakazu Koike, Takayuki Ishizaki, Nacim Ramdani, Jun-ichi Imura: Optimal Scheduling of Storage Batteries and Thermal Power Plants for Supply-Demand Balance. Control Engineering Practice, 77, pp.213-224, 2018. (DOI: 10.1016/j.conengprac.2018.05.008)
- Masakazu Koike, Takayuki Ishizaki, Nacim Ramdani, Jun-ichi Imura: Optimal Scheduling of Storage Batteries and Power Generators Based on Interval Prediction of Photovoltaics -Monotonicity Analysis for State of Charge-. IEEE Control Systems Letters (L-CSS), in press.

In network science, real world networks have been extensively studied on the basis of statistics and graph theory,
and some universal properties of real world networks, such as the small-world property and the power law of degree distribution, have been found out.
Major examples of research topics in this area include *community detection*,
which is formulated as ** a problem to divide a given network into some meaningful subnetworks** in the sense of, e.g., personal human relationship.

In our work, we take an approach to the community detection problem from a viewpoint of control theory.
More specifically, assigning a state variable to each node of networks, ** we construct a set of clusters according to the similarity of state behavior for input signals**.
As a result, as shown in the figure below, we can detect a set of

- Takayuki Ishizaki, Kenji Kashima, Jun-ichi Imura, Kazuyuki Aihara: Model Reduction and Clusterization of Large-Scale Bidirectional Networks, IEEE Transactions on Automatic Control, 59(1), pp.48-63, 2014. (DOI: 10.1109/TAC.2013.2275891) Preprint
- Takayuki Ishizaki, Kenji Kashima, Antoine Girard, Jun-ichi Imura, Luonan Chen, Kazuyuki Aihara: Clustered Model Reduction of Positive Directed Networks, Automatica, 59, pp.238-247, 2015. (DOI: 10.1016/j.automatica.2015.06.027) Preprint
- Takayuki Ishizaki, Aranya Chakrabortty, Jun-ichi Imura: Graph-Theoretic Analysis of Power Systems, Proceedings of the IEEE, 106(5), pp. 931-952, 2018. (DOI: 10.1109/JPROC.2018.2812298) Tokyo Tech Press Release JST Press Release Tokyo Tech/JST Press Release

There are a number of systems having an internal state that does not escape from the nonnegative orthant.
Example of such systems include spatially-discrete reaction-diffusion systems, electric circuit systems, Markovian processes, and so forth.
In linear systems theory, this class of systems is called *positive systems*, and it is known that the positivity of systems is characterized by nonnegativity of system matrices.
Based on this characterization, a model reduction problem preserving the system positivity can be formulated as
** a problem to approximate the input-to-output mapping of systems while preserving the nonnegativity of system matrices**.
In our work, in addition to the positivity-preserving model reduction problem, we formulate a

- Takayuki Ishizaki, Kenji Kashima, Antoine Girard, Jun-ichi Imura, Luonan Chen, Kazuyuki Aihara: Clustered Model Reduction of Positive Directed Networks, Automatica, 59, pp.238-247, 2015. (DOI: 10.1016/j.automatica.2015.06.027) Preprint
- Takayuki Ishizaki, Henrik Sandberg, Kenji Kashima, Jun-ichi Imura, Kazuyuki Aihara: Dissipativity-Preserving Model Reduction for Large-Scale Distributed Control Systems, IEEE Transactions on Automatic Control, 60(4), pp.1023-1037, 2015. (DOI: 10.1109/TAC.2014.2370271 ) Preprint

A number of systematic control design methods, such as robust control, have been developed, and the efficiency of those methods has been verified from various viewpoints.
However, it is known that, for large-scale systems, such a sophisticated design method inevitably makes a resultant controller and observer high-dimensional.
In this sense, ** the implementation of control design methods for large-scale systems is not necessarily straightforward**,
and it is crucial to address the approximation problem of controllers and observers with a specified error precision.

The controller and observer reduction problem is formulated as
** a structured model reduction problem to find a lower-dimensional controller and observer preserving the signal transmission structure** shown in the figures below.
Even though this kind of structured model reduction problems is known as one of difficult problems in systems theory,
we successfully give a solution to it by utilizing our dissipativity-preserving model reduction.

- Takayuki Ishizaki, Henrik Sandberg, Kenji Kashima, Jun-ichi Imura, Kazuyuki Aihara: Dissipativity-Preserving Model Reduction for Large-Scale Distributed Control Systems, IEEE Transactions on Automatic Control, 60(4), pp.1023-1037, 2015. (DOI: 10.1109/TAC.2014.2370271 ) Preprint
- Takayuki Ishizaki, Masakazu Koike, Tomonori Sadamoto, Jun-ichi Imura: Hierarchical Decentralized Observers for Networked Linear Systems, Proc. of 2014 American Control Conference, pp.5718-5723, 2014. Preprint
- Tomonori Sadamoto, Takayuki Ishizaki, Jun-ichi Imura: Low-Dimensional Functional Observer Design for Linear Systems Via Observer Reduction Approach, Proc. of 52nd IEEE Conference on Decision and Control, pp.776-781, 2013. (DOI: 10.1109/CDC.2013.6759976) Preprint

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