This article treats the problems of the stability, boundedness, and stabilizing control of discrete-time semi-Markov jump systems (SMJSs) with fragmentary semi-Markov kernel (SMK) under persistent disturbances. Since the statistical characteristics of stochastic processes are difficult to describe precisely and comprehensively, the available SMK information may be fragmentary, and only a portion of the information is known. Regarding this problem, we propose new approaches that leverage all the known SMK information and derive new criteria for analysis and control. The feasibility therein can be enhanced compared to the existing approaches with inadequate utilization of the known SMK information. Additionally, a polytopic approach is proposed to approximate the unknown portion of the SMK information to enrich the information available for subsequent analysis and control design. This is achieved through constructing a polytopic quadratic Lyapunov-like function (LF), which further improves the feasibility. In this way, both the available information and the approximated unknown part about the SMK are incorporated. Meanwhile, the ultimate boundedness of the closed-loop semi-Markov jump linear system (SMJLS) is ensured in the mean-square sense without requiring the deviation between the state and its nominal one to converge at all times. We illustrate the validity and superiority of the proposed approach through a numerical example and a simulated chemical process example using a machine learning-based surrogate model.

The Koopman theory, which enables the transformation of nonlinear systems into linear representations, is a powerful and efficient tool to model and control nonlinear systems. However, the ability of the Koopman operator to model complex systems, particularly time-varying systems, is limited by the fixed linear state-space representation. To address the limitation, the large language model, Mamba, is considered a promising strategy for enhancing modeling capabilities while preserving the linear state-space structure. In this paper, we propose a new framework, the Mamba-based Koopman operator (MamKO), which provides enhanced model prediction capability and adaptability, as compared to Koopman models with constant Koopman operators. Inspired by the Mamba structure, MamKO generates Koopman operators from online data; this enables the model to effectively capture the dynamic behaviors of the nonlinear system over time. A model predictive control system is then developed based on the proposed MamKO model. The modeling and control performance of the proposed method is evaluated through experiments on benchmark time-invariant and time-varying systems. The experimental results demonstrate the superiority of the proposed approach. Additionally, we perform ablation experiments to test the effectiveness of individual components of MamKO. This approach unlocks new possibilities for integrating large language models with control frameworks, and it achieves a good balance between advanced modeling capabilities and real-time control implementation efficiency.

Time-varying systems commonly exist in modern industrial processes. This paper addresses the problem of learning-based modeling and economic control of time-varying nonlinear systems. By developing a deep time-varying Koopman operator model, the future information of the system related to economic costs and critical outputs is learned directly from data. Transformer architecture is employed to learn the observable functions and to generate time-varying Koopman operators. An efficient economic model predictive control (EMPC) problem is formulated based on the learned transformer-based Koopman model to achieve the economic operations of the system. The proposed method is applied to a membrane-based wastewater treatment process. The performance of the proposed method is compared to the baseline.

Data-enabled predictive control (DeePC) has garnered significant attention for its ability to achieve safe, data-driven optimal control without relying on explicit parametric models. Traditional DeePC methods use pre-collected input/output (I/O) data to construct a Hankel matrix offline and then formulate a predictive control framework online for linear, weakly nonlinear, and weakly stochastic systems. However, in systems with evolving dynamics, incorporating real-time data into the DeePC framework becomes crucial to enhance control performance. This paper proposes an online DeePC framework designed for strongly nonlinear and/or time-varying systems (i.e., systems with evolving dynamics), enabling the algorithm to update the Hankel matrix online by adding real-time informative signals. By exploiting the minimum non-zero singular value of the Hankel matrix, the developed online DeePC selectively integrates informative data and effectively captures evolving system dynamics. Additionally, a numerical singular value decomposition technique is introduced to reduce the computational complexity for updating a reduced-order Hankel matrix. Simulation results on three cases, linear time-varying system, vehicle anti-rollover control, and Li-ion battery fast charging, demonstrate the effectiveness of the proposed online reduced-order DeePC framework.

Optimal control schemes have achieved remarkable performance in numerous engineering applications. However, they typically require high computational cost, which has limited their use in real-world engineering systems. To address this challenge, Neighboring Extremal (NE) has been developed to adapt a pre-computed nominal control solution to perturbations from the nominal trajectory. The resulting control law is a time-varying feedback gain that can be pre-computed along with the original optimal control problem, and it takes negligible online computation. However, existing NE frameworks only deal with state perturbations while in modern applications, optimal controllers frequently incorporate preview information. Therefore, a new NE framework is needed to adapt to such preview perturbations. In this work, an extended NE (ENE) framework is developed to systematically adapt the nominal control to both state and preview perturbations. We show that the derived ENE law is two time-varying feedback gains on the state and preview perturbations. We also develop schemes to handle nominal non-optimal solutions and large perturbations to retain optimal performance and constraint satisfaction. Case study on nonlinear model predictive control is presented due to its popularity but it can be easily extended to other optimal control schemes. Promising simulation results on the cart inverted pendulum problem demonstrate the efficacy of the ENE algorithm. Note to Practitioners—Due to the vast success in predictive control and advancement in sensing, modern control applications have frequently been incorporating preview information in the control design. For example, the road profile preview obtained from vehicle crowdsourcing is exploited for simultaneous suspension control and energy harvesting, demonstrating a significant performance enhancement using the preview information despite noises in the preview (Hajidavalloo et al., 2022). Another example is thermal management for cabin and battery of hybrid electric vehicles, where traffic preview is employed in hierarchical model predictive control to improve energy efficiency (Amini et al., 2019). In Laks et al. (2011), light detection and ranging systems are used to provide wind disturbance preview to enhance the controls of turbine blades. In Yazdandoost et al. (2022), virtual water preview is employed using integrated water resources management modelling to optimize agricultural patterns and control level of water in lakes. In this work, we develop an extended neighboring extremal framework that can adapt a nominal control law to state and preview perturbations simultaneously. This setup is widely applicable as in many applications, a nominal preview is available while the preview signal can also be measured or estimated online.

In this work, we consider the problem of Koopman modeling and data-driven predictive control for a class of uncertain nonlinear systems subject to time delays. A robust deep learning-based approach–deep recurrent Koopman operator is proposed. Without requiring the knowledge of system uncertainties or information on the time delays, the proposed deep recurrent Koopman operator method is able to learn the dynamics of the nonlinear systems autonomously. A robust predictive control framework is established based on the deep Koopman operator. Conditions on the stability of the closed-loop system are presented. The proposed approach is applied to a chemical process example. The results confirm the superiority of the proposed framework as compared to baselines.

In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to select lifting functions for Koopman identification. The selected lifting functions are used to project the original nonlinear state space into a higher-dimensional linear function space, in which Koopman-based linear models may be constructed for the underlying nonlinear process. To address the potential issue of a significant increase in the dimensionality of the resulting full-order Koopman models caused by the use of lifting functions, we propose a reduced-order Koopman modeling approach based on proper orthogonal decomposition. A computationally efficient linear robust predictive control scheme is established based on the reduced-order Koopman model. A case study on a benchmark chemical process is conducted to illustrate the proposed framework.

This paper proposes a novel quantized control strategy for network-based linear systems subject to multi-input-multi-output (MIMO) quantization. A logarithmic quantization scheme is adopted for characterizing the quantization effect on system dynamics. A sufficient and necessary condition on the asymptotic stability is established for quantized MIMO systems. To improve the numerical testability of the obtained results, a polytopic approach approximating the MIMO quantization uncertainties is developed. By constructing a novel Lyapunov function that has dependence on the MIMO quantization uncertainties, asymptotic stability criteria are established for closed-loop quantized MIMO systems. The conditions on the existence of state-feedback controllers that guarantee the closed-loop stability are derived based on the proposed technique that decouples the controller gains and the parameters of MIMO quantization uncertainties. The proposed method and the associated theoretical results are extended to the disturbance attenuation case. Finally, the theoretical results are applied to a benchmark example and a converter circuit to illustrate their efficacy and superiority.

As a significant ingredient regarding health status, data-driven state of health (SOH) estimation has become dominant for lithium-ion batteries. To handle data discrepancy across batteries, current SOH estimation models engage in transfer learning (TL), which reserves a priori knowledge gained through reusing partial structures of the offline trained model. However, multiple degradation patterns of a complete life cycle of a battery make it challenging to pursue TL. The concept of the stage is introduced to describe the collection of continuous cycles that present a similar degradation pattern. A transferable multistage SOH estimation model is proposed to perform TL across batteries in the same stage, consisting of four steps. First, with identified stage information, raw cycling data from the source battery are reconstructed into the phase space with high dimensions, exploring hidden dynamics with limited sensors. Next, domain invariant representation across cycles in each stage is proposed through cycling discrepancy subspace with reconstructed data. Third, considering the unbalanced discharge cycles among different stages, a switching estimation strategy composed of a lightweight model with the long short-term memory network and a powerful model with the proposed temporal capsule network is proposed to boost estimation accuracy. Finally, an updating scheme compensates for estimation errors when the cycling consistency of target batteries drifts. The proposed method outperforms its competitive algorithms in various transfer tasks for a run-to-failure benchmark with three batteries. Especially through transferring the estimation model from batteries B7 to B6, the proposed method improves the estimation accuracy by as high as 42.6% in the third stage in terms of the root mean square error, compared to the other state-of-the-art approaches. In addition, similar conclusions can be drawn from other contributed experiments.

In this article, an event-triggered distributed state estimation mechanism is proposed for general linear systems that comprise several subsystems. Two distributed moving horizon estimation (MHE) algorithms that can handle constraints on disturbances and noise are proposed. An event scheduler is exploited to govern the evaluation of the estimators and networked information exchange between the plant and the estimators, such that good estimates can be provided while both the usage of processors and networked communication frequency can be reduced. The estimation error provided by the event-triggered estimation mechanism is proven to be convergent and bounded. A numerical example and a chemical process example are used to verify the effectiveness and applicability of the proposed method.

This paper addresses a distributed estimator design problem for linear systems deployed over sensor networks within a multiple communication channels (MCCs) framework. A practical scenario is taken into account such that the channel used for communication can be switched and the switching is governed by a Markov chain. With the existence of communicational imperfections and external disturbances, an estimation algorithm is proposed such that the developed distributed estimators are able to give accurate state estimates against the channel switching phenomenon. The distributed estimation framework is applied to a chemical process to illustrate the effectiveness of the proposed methodology and the superiority of the MCCs framework featured by channel switching.

This paper is concerned with the problem of asynchronous H∞filtering for a class of discrete-time Takagi-Sugeno fuzzy affine systems against time-varying signal transmission delays and measurement quantization. The asynchrony refers to the situation that the plant state and the filter state belong to different local state space regions, and the quantization density can be adjusted to satisfy different performance requirements at different time instants. By transforming the filtering error system into an input-output form consisting of two interconnected subsystems, sufficient conditions on the existence of the desired asynchronous filter are established via the scaled small gain theorem to ensure that the closed-loop system is asymptotically stable with a prescribed H∞performance index with the aid of a novel piecewise Lyapunov-Krasovskii functional and the S-procedure approach. Finally, a practical example of cart-pendulum with a modified model is provided to illustrate the effectiveness of the obtained theoretical results.

This paper is concerned with the problem of robust filter design for a class of discrete-time networked nonlinear systems. The Takagi-Sugeno fuzzy model is employed to represent the underlying nonlinear dynamics. A multi-channel communication scheme that involves a channel switching phenomenon described by a Markov chain is proposed for data transmission. Two typical communication imperfections, network-induced time-varying delays and packet dropouts are considered in each channel. The objective of this paper is to design an admissible filter such that the filter error system is stochastically stable and ensures a prescribed disturbance attenuation level bound. Based on the Lyapunov-Krasovskii functional method and matrix inequality techniques, sufficient conditions on the existence of the desired filter are obtained. A numerical example is provided to illustrate the effectiveness of the proposed design approach.

The global asymptotic stabilization problem is investigated for a class of stochastic nonlinear time-varying delay systems under the weaker condition on nonlinear functions. The new parameter-dependent state and output feedback controllers are, respectively, proposed. Based on the stochastic time-delay system stability criterion, by tactfully introducing a suitable Lyapunov-Krasovskii functional, the globally asymptotically stable in probability of the closed-loop system is guaranteed by rigorous proof. As a practical application, the stochastic model of a two-stage chemical reactor system is established by reasonably introducing the Gaussian white noise. The developed approach is applied to the control design for this practical system. The simulation results demonstrate the efficiency of the proposed design approach.

In this work, we investigate a state estimation problem for a full-car semi-active suspension system. To account for the complex calculation and optimization problems, a vehicle-to-cloud-to-vehicle (V2C2V) scheme is utilized. Moving horizon estimation is introduced for the state estimation system design. All the optimization problems are solved in a remotely-embedded agent with high computational ability. Measurements and state estimates are transmitted between the vehicle and the remote agent via networked communication channels. The effectiveness of the proposed method is illustrated via a set of simulations.

This study is mainly concerned with fuel efficiency modeling and prediction for common automobiles based on an informative vehicle database. The historical database is processed and the mutual information index (MII) is employed to identify a set of characteristics that significantly affect fuel efficiency. Five different machine learning techniques are exploited to build fuel efficiency prediction models. Among these techniques, quantile regression, which is a natural extension of classical least square estimation, is shown to have better performance for fuel efficiency prediction compared to other adopted techniques. It is also demonstrated that with the selected attributes based on MII, the prediction performance is almost ideal when exploiting the complete dataset.