Research about Control Theory

Control engineering is an engineering field that deals with control systems, applying various control theories to controller and systems for achieving desired behaviors of plant outputs. Control engineering focuses on implementation of control systems mainly derived by mathematical modeling of various types of systems (Model-based control). The research topics of our laboratory mainly deal with control theory


日本語ホームページ(okajima lab.) 

Hiroshi Okajima

Associate Professor at Faculty of Advanced Science and Technology, Kumamoto University, Japan

He was born in 1980. He received his M.D. and Ph.D. degrees from Osaka University, Japan, in 2004 and 2007, respectively. He is presently an associate professor at Kumamoto University, Japan. His research interests include control theory and control engineering. 

Associate Professor at Faculty of Advanced Science and Technology, Kumamoto University, Japan

IFAC TC 2.2. Linear Control Systems

IFAC 2023 Publicity Member (twitter)

SICE JCMSI AE SICE Journal of Control, Measurement, and System Integration Editorial Board

Hiroshi Okajima - My portal - researchmap 


Google scholar

Control YouTube (main channel, 8000 subscribers, Japanese) 

Control YouTube (sub channel, 178 subscribers, English)

Github(MATLAB code about control)

Research Achievements (more than 70 papers, PDF links)


SICE Education Contribution Award (2023)

SICE 2019 Poster Presentation Award Finalist

ICCAS 2017 Outstanding Paper Award

SICE CPD Point Award (2017)

ICCAS 2016 Outstanding Paper Award

SICE CPD Point Award (2011)

SICE 2010 Young Author Award Finalist

Education Topics (Explanation page)

Linear Matrix Inequality 

Research Topics (Explanation page)

Model Error Compensator 

Dynamic Quantizer 

Vehicle Control 

My Main Works about Control Theory and Control Method

Hiroshi Okajima, Kenta Arinaga and Atsuo Hayashida, Design of observer-based feedback controller for multi-rate systems with various sampling periods using cyclic reformulation, IEEE ACCESS (2023) (Open Access) MATLAB code

Outline: Signal sensing periods typically vary depending on the sensor used and may differ even within a single control system that involves multiple sensors. Likewise, input periods can vary based on the actuator used. This paper discusses the design of observer-based feedback controllers for linear, time-invariant, discrete-time systems operating in a multi-rate sensing and actuating environment. The observation and control periods of the sensors and actuators in the plant are assumed to have mutually rational ratios. First, we reduce the multi-rate system to a periodically time-varying system and provide a linear matrix inequality (LMI) condition for analyzing the l 2 performance using cyclic reformulation, which is a type of time-invariant reformulation for periodic systems. Next, we extend the analysis method to design an observer-based feedback controller for the multi-rate system. This allows us to obtain multi-rate observer gains and feedback gains based on the l 2 -induced norm from disturbances to outputs. Finally, we present numerical results to demonstrate the effectiveness of the observer-based feedback system in the multi-rate environment.

H. Okajima, Model Error Compensator for adding Robustness toward Existing Control, Preprints of the IFAC World Congress, pp. 3998 - 4005 (2023)

Outline: This paper shows a method for adding robustness to various existing control systems. A novel system compensation structure ”model error compensator” was proposed by the authors, and it has been applied to many kinds of control systems. The control purpose of the model error compensator (MEC) is to minimize as much as possible the negative effect of the model error and the disturbance in the input-output characteristics. This compensator has a simple form and is easy to apply to various types of existing control systems, such as non-linear systems, control systems with time delay, non-minimum phase systems, MIMO systems, and so on. Various types of control schemes, such as the model predictive control, can be used together with the model error compensator and can achieve good robust performance. First, this paper presents an overview of the model error compensator and summarizes various types of previously proposed methods of the model error compensator. Moreover, a generalized version of the robust feedback linearization is proposed, and its effectiveness is illustrated using a numerical example. As the other contribution, we discuss how to integrate MEC into existing control systems in this paper. 

Hiroshi Okajima, Yohei Hosoe and Tomomichi Hagiwara, State Observer under Multi-rate Sensing Environment and Its Design using l2 -Induced Norm, IEEE ACCESS (2023) (Open Access) MATLAB code

Outline: The duration of a signal's sensing period typically relies on the sensor being used, and can vary even within a single control system that uses multiple sensors. This paper explores the design challenge of creating state observers for linear, time-invariant, discrete-time systems in a multi-rate sensing environment. We assume that the sensing periods of the plant's sensors have mutually rational ratios. First, we describe a state observer for a system with multi-rate sensing as a periodically time-varying state observer. Next, we examine the l2 performance analysis of state estimation errors using the given periodically changing state observer. A linear matrix inequality (LMI) condition is provided for this analysis. By expanding the LMI condition for analysis, we also offer a condition for multi-rate observer synthesis. We then demonstrate the effectiveness of our proposed multi-rate state observer through numerical examples. Notably, even when all sensors share the same period, sensing timing is not unique. As a result, we numerically investigate whether performance varies when the observation timing differs among multiple sensors.

Hiroshi Okajima, Yasuaki Kaneda and Nobutomo Matsunaga, State estimation method using median of multiple candidates for observation signals including outliers, SICE Journal of Control, Measurement, and System Integration, Volume 14 Issue 1 pages 257-267 (T&F, Open Access) MATLAB Code

Outline: This paper addresses the state estimation problem for systems with observation outputs that include outliers. The presence of outliers in observation outputs can significantly reduce the accuracy of state estimation. To tackle this issue, we propose a novel observer structure that employs multiple estimated state candidates. First, we generate multiple estimated state candidates, each using the sensing output value from a different detection timing. If outliers are rare, removing candidates affected by outliers helps maintain estimation accuracy. Our proposed observer then selects one estimated state candidate from the group using either a median or weighted median operation. This process ensures that the selected estimated state does not rely on outlier values. Furthermore, we present a method for designing observer gains for these estimated state candidates based on the reachable set of the estimated state error, using Lyapunov-based inequalities. The effectiveness of our proposed observer is demonstrated through numerical examples.

H. Okajima, K. Fujinami, Estimation of Robust Invariant Set for Switched Linear Systems using Recursive State Updating and Robust Invariant Ellipsoid, SICE Journal of Control, Measurement, and System Integration, Volume 14 Issue 1 Pages 97-106 (2021) (T&F, Open Access) YouTube, SupportPage 

Outline: This paper presents an analysis method for robust invariant sets in discrete-time linear switched systems with peak-bounded disturbances. Analyzing the robust invariant set in switched linear systems is more challenging than in linear time-invariant systems. We introduce a novel approach to estimate a robust invariant set by combining recursive state updating and an invariant ellipsoid for a common Lyapunov function. The accuracy and effectiveness of our proposed method are demonstrated through numerical examples.

Ryuichiro Yoshida, Hiroshi Okajima and Takumi Sato, Model error compensator design for continuous- and discrete-time non-minimum phase systems with polytopic-type uncertainties, SICE Journal of Control, Measurement, and System Integration, Volume 15 Issue 2 pags 141-153 (2022) (T&F, Open Access) MECpage 

Outline: This paper introduces a design for a model error compensator combined with a parallel feedforward compensator for continuous- and discrete-time non-minimum phase multiple input multiple output (MIMO) plants. The model error compensator can readily enhance robustness in various control systems. By adding the compensator to the actual plant, the plant's output trajectory can closely follow that of the control system with the intended nominal model. Our previous research proposed a model error compensator design using particle swarm optimization and linear matrix inequalities based on the common Lyapunov function, addressing polytopic-type uncertainties in plants. However, designing the appropriate gain for the model error compensator becomes challenging when dealing with non-minimum phase MIMO systems. In this study, we attach a parallel feedforward compensator to the model error compensator to achieve minimum phase characteristics. With some assumptions, an evaluation system incorporating a parallel feedforward compensator can be derived as a system with polytopic uncertainties. This approach simplifies the gain design of the model error compensator, ensuring robust performance. We demonstrate the effectiveness of our proposed design through numerical examples.

H. Okajima, K. Sawada and N. Matsunaga:Dynamic Quantizer Design Under Communication Rate Constraints, IEEE Transactions on Automatic Control, Vol.61, No.10, pp.3190-3196 (2016) SupportPage

Outline: Feedback-type dynamic quantizers, such as delta-sigma modulators, are often effective for converting high-resolution data into lower-resolution data. These dynamic quantizers consist of a filter and a static quantizer. When controlling under a communication rate constraint, the data rate of the quantizer output should be minimized appropriately through quantization. This technical note presents numerical methods for the comprehensive design of a type of dynamic quantizer, including the selection of all quantizer parameters to minimize a specific performance index while satisfying a communication constraint. We propose a design method for the dynamic quantizer using a particle swarm optimization (PSO) approach. Some initial quantizers in PSO are designed based on an invariant set analysis and an iteration algorithm. The effectiveness of the system employing the proposed quantizer is demonstrated through numerical examples.

H. Okajima, H. Umei, N. Matsunaga and T. Asai:A Design Method of Compensator to Minimize Model Error, SICE Journal of Control, Measurement, and System Integration, Vol.6, No.4, pp.267-275 (2013) (T&F, Open Access) MECpage  

Outline: Robust control design methods have been widely studied in recent decades. A control system performs well under modeling errors and disturbances when the controller design is based on robust control methods. However, it is well known that control systems typically face a trade-off between control performance and robustness. To address this trade-off problem, an internal model-type compensator structure that minimizes the modeling gap between the nominal model and actual plant dynamics is proposed.   By employing the proposed compensator, the dynamics of the compensated system closely match those of the nominal model. Additionally, we introduce a design method for compensator parameters aimed at minimizing a set of plant dynamics. The proposed design method can be reduced to the standard µ design control problem. Using the proposed compensator for control systems instead of the plant itself may lead to improved output performance despite plant uncertainty. As the proposed compensator can be used for controlling not only linear but also nonlinear plants, it allows for the easy achievement of robust control in nonlinear systems. The effectiveness of our proposed method is demonstrated through numerical examples.

H. Okajima and T. Asai:Performance Limitation of Tracking Control Problem for a Class of References, IEEE Transactions on Automatic Control, Vol.56, No.11, pp.2723-2727 (2011) SupportPage PDF 

Outline: This technical note focuses on the analysis of fundamental limitations in tracking control problems for single-input single-output (SISO) systems. Existing results analyze these limitations based on specific assumptions of reference signals, such as step, trigonometric signals, and others. In contrast, we define a class of reference signals in a more abstract but general way. For this general class of reference inputs, we provide an analytical solution for tracking performance limitations based on the achievable set of outputs, which are characterized by transfer functions. The analysis results clearly separate the contributions of the plant and the reference signal.

Other Researches

Model Error Compensator

Dynamic Quantizer

Multi-rate state observer