arXiv subjects

Hiroshi Okajima

Publications and source records attributed to Hiroshi Okajima.

8 recordsLinked to original sources

arXiv2026

Robust Path Following Control for Vehicles with Uncertain Steering Resistance Using Model Error Compensation

This paper presents a robust path following control method for vehicles that explicitly incorporates steering torque dynamics into the control model. Unlike conventional approaches that treat the steering angle as a direct control input, this study models the steering angle as a state variable driven by a torque-proportional steering command against a speed- and angle-dependent resistance term. Since the resistance coefficient depends on road surface properties and is difficult to determine precisely, it is treated as an uncertain parameter. To compensate for the resulting model error, a Model Error Compensator (MEC) is employed as an add-on compensator that feeds back the discrepancy between the actual plant and a nominal model running in parallel, without requiring an explicit plant inverse or a specific canonical form. The zero dynamics arising from the path following formulation are formally analyzed, and it is shown that they are stable for any positive rear cornering power. Numerical simulations under systematic parameter mismatch conditions (C/C_M=0.5 to 2.0) demonstrate that the proposed method reduces the maximum following error by more than 90\% compared to the conventional method without MEC throughout the tested mismatch range, and maintains practical tracking performance within a mismatch range of 0.75 <= C/C_M <= 1.25. These results confirm that MEC effectively suppresses the influence of steering torque uncertainty, significantly enhancing path following robustness.

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arXiv2026

Stable Inversion of Discrete-Time Linear Periodically Time-Varying Systems via Cyclic Reformulation

Inverse systems for discrete-time linear periodically time-varying (LPTV) plants are fundamental to feedforward control and iterative learning control of multirate and periodic systems. Building on the classical cyclic reformulation, which converts an N-periodic system into an equivalent LTI system at the original sampling rate, this paper derives an explicit closed-form N-periodic state-space realization of the inverse for an arbitrary uniform periodic relative degree r >= 0 (defined through the periodic Markov parameters). The key technical result is a structure-preservation property: after absorbing a phase shift for r >= 1, the LTI inverse of the cycled plant provably retains the cyclic (block-circulant/block-diagonal) structure, so that the periodic inverse matrices can be read off block-by-block. The resulting inverse system is real-valued, causal for r = 0 and r-step-delayed for r >= 1, operates at the original sampling rate, and reconstructs the input exactly under matched initial conditions, with geometric error decay otherwise. Its stability is characterized by the invariant zeros of the cycled plant, generalizing the minimum phase condition of the LTI case. Numerical examples illustrate the construction, the stability characterization, and the implementation as an online periodic filter.

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arXiv2026

Cyclic Reformulation-Based Identification and Polytopic Uncertainty Modeling for Multirate Systems

Modern control systems increasingly rely on heterogeneous sensors operating at different sampling rates, where intermittently missing outputs pose fundamental challenges for system identification. This paper proposes a non-iterative, control-oriented identification method for multirate systems based on cyclic reformulation. The method transforms multirate data into an expanded time-invariant representation and yields M parameter sets from a single input-output dataset, where M is the least common multiple of the sensor sampling periods. These parameter sets are used in two complementary ways: their centroid serves as a noise-reduced nominal model, while their convex hull gives a polytopic uncertainty model compatible with vertex-based LMI robust control design. Building on the noise-free structural recovery theorem of the authors' preceding work, which is restated here in the notation of the present paper, the present paper newly introduces the centroid and polytopic models derived from the M parameter sets; finite-noise behavior is treated as an empirical observation and is evaluated numerically. Numerical simulations support both models: an illustrative SISO example shows that the centroid attains higher validation FIT than the best individual vertex and substantially outperforms an interpolation-based baseline, while a MIMO multirate sensing example confirms, in line with the LTI counterpart, that the constructed polytope contains models whose validation FIT exceeds 95\% on average even at the highest tested noise level. The polytope is interpreted cautiously, with finite-noise behavior assessed through output-level validation statistics rather than realization-dependent matrix-coordinate distances. The proposed framework therefore links multirate system identification with robust-control-oriented uncertainty modeling without iterative EM-type optimization.

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arXiv2026

Closed-Loop Identification of Periodically Time-Varying Systems via Cyclic Reformulation

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.

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arXiv2026

From Noise to Knowledge: System Identification with Systematic Polytope Construction via Cyclic Reformulation

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.

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arXiv2026

LMI Optimization Based Multirate Steady-State Kalman Filter Design

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.

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arXiv2025

System Identification Under Multi-rate Sensing Environment

This paper proposes a system identification algorithm for systems with multi-rate sensors in a discrete-time framework. It is challenging to obtain an accurate mathematical model when the ratios of inputs and outputs are different in the system. A cyclic reformulation-based model for multi-rate systems is formulated, and the multi-rate system can be reduced to a linear time-invariant system to derive the model under the multi-rate sensing environment. The proposed algorithm integrates a cyclic reformulation with a state coordinate transformation of the cycled system to enable precise identification of systems under the multi-rate sensing environment. The effectiveness of the proposed system identification method is demonstrated using numerical simulations.

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arXiv2024

Cyclic Reformulation Based System Identification for Periodically Time-varying Systems

This paper addresses a system identification for linear periodically time-varying plants in the discrete-time setting. A system identification algorithm for linear, periodically time-varying plants is introduced based on a cyclic reformulation and a state coordinate transformation of the cycled system. By using our system identification algorithm, the high-accuracy model of the periodically time-varying plant can be obtained without using specific periodic input signals. The effectiveness of the proposed algorithm is demonstrated with numerical examples.

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