Hiroshi Okajima

Hiroshi Okajima

This paper studies closed-loop identification of linear periodically time-varying (LPTV) plants, with emphasis on open-loop unstable plants for which open-loop experiments are not practically available. The central contribution is an exact algebraic plant-extraction theorem for cycled closed-loop realizations: for square strictly proper plants and a controller path satisfying an invertibility condition, the cycled plant transfer matrix is recovered from a shared state-space realization of the stable closed-loop maps from the external reference to the plant output and to the control input, without state augmentation, and without requiring the recovered plant realization to be stable. Thus, the stability requirement for data generation is shifted from the open-loop plant to the internally stable closed-loop system. Building on this result, a closed-loop identification algorithm is constructed that takes the reference, output, and input signals as data, applies standard subspace identification to the cycled signals, performs the algebraic plant extraction, and recovers the LPTV plant state-space parameters via a coordinate transformation; the conditioning of the inverse controller path governs the reliability of the extraction step. Numerical examples demonstrate the recovery of stable and open-loop unstable SISO LPTV plants and validate a MIMO case through coordinate-invariant Markov-parameter comparisons.

Hiroshi Okajima, Shun Shirahama, Tatsunori Hayashi et al.

Model-based robust control requires not only accurate nominal models but also systematic uncertainty representations to guarantee stability and performance. However, constructing polytopic uncertainty models typically demands multiple experiments or a priori structural assumptions.This paper proposes an identification framework based on intentional periodicity induction, in which cyclic reformulation with period $N$ is applied to a linear time-invariant system to interpret noise-induced parameter fluctuations as a structured manifestation of estimation uncertainty. The $N$ parameter sets obtained from a single identification experiment -- which would coincide in the noise-free case -- are used as polytope vertices, providing systematic control over the granularity of the uncertainty description through the choice of $N$. The practical utility of the constructed polytope is demonstrated through robust $H_\infty$ state-feedback synthesis via LMI optimization at the polytope vertices; the synthesis uses only noisy identification data and is shown across Monte Carlo trials to stabilize the true plant with only marginal conservatism. Complementarily, a diagnostic assessment based on the best in-polytope point confirms that the polytope captures meaningful uncertainty information. For a third-order system under Gaussian and uniform noise, a comparison with bootstrap-inspired resampling baselines indicates that cyclic reformulation provides a competitive or favorable trade-off by utilizing the full data record; the construction is further validated on a fourth-order MIMO system.

Hiroshi Okajima

This paper presents an LMI-based design framework for multirate steady-state Kalman filters in systems with sensors operating at different sampling rates. The multirate system is formulated as a periodic time-varying system, where the Kalman gains converge to periodic steady-state values that repeat every frame period. Cyclic reformulation transforms this into a time-invariant problem; however, the resulting measurement noise covariance becomes semidefinite rather than positive definite, preventing direct application of standard Riccati equation methods. I address this through a dual LQR formulation with LMI optimization that naturally handles semidefinite covariances. The framework enables multi-objective design, supporting pole placement for guaranteed convergence rates and $l_2$-induced norm constraints for balancing average and worst-case performance. Numerical validation using an automotive navigation system with GPS and wheel speed sensors, including Monte Carlo simulation with 500 independent noise realizations, demonstrates that the proposed filter achieves a position RMSE well below the GPS noise level through effective multirate sensor fusion, and that the LMI solution provides valid upper bounds on the estimation error covariance.

Hiroshi Okajima

Stable inverse systems for periodically time-varying plants are essential for feedforward control and iterative learning control of multirate and periodic systems, yet existing approaches either require complex-valued Floquet factors and noncausal processing or operate on a block time scale via lifting. This paper proposes a systematic method for constructing stable inverse systems for discrete-time linear periodically time-varying (LPTV) systems that avoids these limitations. The proposed approach proceeds in three steps: (i) cyclic reformulation transforms the LPTV system into an equivalent LTI representation; (ii) the inverse of the resulting LTI system is constructed using standard LTI inversion theory; and (iii) the periodically time-varying inverse matrices are recovered from the block structure of the cycled inverse through parameter extraction. For the fundamental case of relative degree zero, where the output depends directly on the current input, the inverse system is obtained as an explicit closed-form time-varying matrix expression. For systems with periodic relative degree r >= 1, the r-step-delayed inverse is similarly obtained in explicit closed form via the periodic Markov parameters. The stability of the resulting inverse system is characterized by the transmission zeros of the cycled plant, generalizing the minimum phase condition from the LTI case. Numerical examples for both relative degree zero and higher relative degree systems confirm the validity of the stability conditions and demonstrate the effectiveness of the proposed framework, including exact input reconstruction via causal real-valued inverse systems.

Rentaro Iwai, Natsuki Hikasa, Hiroshi Okajima

This paper presents a robust path following control method for vehicles that explicitly considers steering resistance dynamics to improve tracking accuracy. Conventional methods typically treat the steering angle as a direct control input; however, this approach introduces the steering angle as a state variable and incorporates the steering resistance effect into the control model. The steering resistance is modeled as a function of vehicle speed and steering angle, whereas in practice it varies depending on road conditions. To address the resulting model inaccuracies, a Model Error Compensator (MEC) is introduced, mitigating the effects of variations in steering resistance and enhancing the adaptability of the system to different environments. Since the steering resistance coefficient depends on road surface properties and is difficult to determine precisely, the proposed method treats it as an uncertain parameter and compensates for the resulting model error via MEC. Numerical simulations are conducted to evaluate the performance of the proposed method under varying degrees of parameter mismatch, demonstrating that the proposed method substantially reduces the maximum tracking error in representative mismatched cases compared to the conventional method. The results indicate that explicitly modeling steering resistance dynamics and compensating for model errors improve path following performance in numerical simulations compared to conventional approaches.