Jul 2026· 2026 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)· pp. 1-6· 0 citations· 22 references
Abstract
Online dynamic mode decomposition with control (DMDc) commonly relies on least-squares-based online updates whose numerical behavior can become fragile when the data stream is not persistently excited. In such cases, the regressor covariance may become rank-deficient or poorly conditioned, resulting in numerically unstable estimates. This paper proposes a regularized online DMDc (RO-DMDc) algorithm based on an exponentially weighted least-squares formulation with ridge regularization around a nominal model. The resulting identification law admits a closed-form recursion with a forgetting factor and fixed memory requirements, enabling real-time updates without storing past snapshots. A Lyapunov-based analysis is developed to establish deterministic boundedness of the estimation error under arbitrary excitation levels, including rank-deficient regimes. Simulations on a lane-keeping bicycle model with intermittent excitation and abrupt cornering-stiffness changes demonstrate that RO-DMDc mitigates drift and large spikes observed in a conventional online DMDc during weakly excited operation. Thus, RO-DMDc enables reliable real-time identification for adaptive control and monitoring under limited excitation.
In the digital twin paradigm, online parameter updating is essential. Unlike a static model, a digital twin must continuously adapt to the evolving dynamics of the system it represents. Adaptive observers, which jointly estimate states and parameters from online data, are therefore an increasingly important tool. In this work, we formulate a mode-wise adaptive observer for a class of autonomous switched nonlinear systems with switched unknown parameters. The main challenges are twofold: removing the disturbance that switching injects into the parameter-error dynamics and guaranteeing persistence of excitation over a finite-time window without relying on an input signal. To address them, we assign a dedicated adaptive observer to each mode, active only on its corresponding interval, which directly removes the zero-input disturbance caused by switching. We then introduce a finite-window persistence-of-excitation condition together with a minimum dwell-time condition, under which the parameter estimation error is contractive and the state estimation error is bounded within the active interval of each mode. The performance of the proposed approach is illustrated with an academic example and with a practical example of evolutionary therapies.
This paper introduces Projection-Regularized Predictive Control (PRPC), retaining the fundamental-lemma weight vector via a regularized projection analytically condensed into an efficient, fixed-dimension covariance update.
Actuator dead-zones are a common and troublesome nonlinearity in motion control: a band of commanded effort over which the plant does not respond, leaving a steady-state offset or a limit cycle. This paper proposes a data-driven architecture that compensates such mismatches without a model of the plant and without any parameterization of the dead-zone. The central idea is to identify, alongside the velocity-form predictor used for control, a second absolute subspace predictor. Because the absolute predictor carries no integral action, it behaves as a data-driven steady-state sensor, so a persistent actuator mismatch appears as a proportional prediction residual. Embedding this residual as a proxy in a behavioral Hankel matrix reduces the mismatch estimate to a single fixed orthogonal projection evaluated online, with no dynamic estimator, no injected probing signal, and no run-time prediction-error computation. Integrated into a subspace predictive controller, the framework is shown to be recursively feasible and practically input-to-state stable, and it recovers offset-free tracking once the dead-band traversal settles. The approach is validated in real time on a sixth-order, lightly damped Quanser multi-DOF torsion system, whose complex-conjugate poles give a lightly damped open-loop response, achieving offset-free tracking across a $\pm 0.18$\,V actuator dead-band. A second study on a high-precision power amplifier shows that the same architecture rejects dead-time-induced nonlinearities in fast-switching power electronics.
In adaptive control, parametric uncertainties in linear-in-parameter form consist of unknown parameters and known regressor signals. Convergence of the unknown parameters to their ideal values requires the regressor to satisfy a persistent excitation (PE) condition, which depends on future data and is therefore infeasible to guarantee online. Memory-based parameter update laws address this by enabling ideal parameter convergence under the online-verifiable finite excitation (FE) condition. In this paper, a new algorithm is proposed to construct a memory term via the Modified Gram-Schmidt orthogonalization procedure for a class of multi-input multi-output nonlinear systems with an unknown diagonal control effectiveness matrix and bounded nonparametric uncertainties. Under the finite excitation condition, the constructed memory term yields an identity coefficient matrix in the parameter estimation error dynamics. The identity coefficient matrix eliminates the need for time-varying adaptation gains, enables an explicit ultimate bound on the parameter estimation error, and preserves the structure of the nonparametric uncertainty bound under the memory term. Building on this, a combined adaptation law is developed for controller gain estimation under FE. The closed-loop tracking and estimation errors are shown to decay exponentially to a neighborhood of the origin, characterized by an explicit ultimate bound, with a decay rate that depends solely on user-defined gains and system constants, independent of the level of regressor excitation. This removes the dependence of the convergence rate on the level of regressor excitation, a key limitation of existing approaches such as concurrent learning, memory regressor extension, and DREM.
For systems with unknown parameters, finite excitation and concurrent learning can potentially yield parameter convergence without persistent excitation but the regressor may still depend on inaccessible states, leading to regressor mismatch. In this paper, this problem is addressed for a class of nonlinear systems with one-sided Lipschitz properties and quadratically inner-bounded nonlinearities with bounded disturbances and linearly parametrized uncertainties. To this aim, an output-integral regression is utilized by using measured outputs and estimated states, and history-stack residual is explicitly bounded in terms of state-estimation error and disturbance. Furthermore, a perturbation bound between the estimated-state and true-state information matrices is derived. Additionally, an OSL-QIB LMI condition is applied for the observer design and a projected adaptive law is designed without needing exact output matching. Stability analysis's results indicate the proposed observer and parameter estimation outperform observers without history-stack learning term.
Intermittent state measurements pose fundamental challenges to model predictive control of constrained nonlinear systems because prediction uncertainty grows during feedback outages and measurement-triggered resets disrupt nominal state propagation, potentially compromising closed-loop stability and recursive feasibility. This paper develops a Koopman-based stochastic MPC framework with probabilistically truncated soft constraints. Specifically, a Lipschitz-constrained deep Koopman model provides a linear latent predictor, enabling computationally efficient online optimization. The intermittent measurement process is modeled as a two-mode discrete-time Markov chain, yielding a unified Markov jump error model for open-loop propagation and measurement-triggered resets. Under numerically verifiable sufficient conditions, the prediction error is shown to be mean-square ultimately bounded, and an explicit uniform second-moment bound is obtained. A distribution-free probabilistic error radius is then constructed for a prescribed confidence level and used to truncate dropout-dependent constraint tightening. An exact-penalty soft-constraint mechanism accommodates reset-induced jumps and prolonged dropouts. Under the stated terminal compatibility and bounded-disturbance conditions, recursive feasibility and mean-square ultimate boundedness of the closed-loop regulation error are established. Numerical simulations on a visual-servoing tracking task corroborate these theoretical results and demonstrate effective tracking under stochastic measurement unavailability.
Guanzhi Liu, Tong Wu, Lixian Zhang et al.· 0 citations
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