Tensor Product Model Research Articles

Tensor product model transformation-based reinforcement learning neural network controller with guaranteed stability

Despite the success of neural network (NN) controllers, the stability of closed-loop NN control systems is still a major challenge. This paper proposes a constrained reinforcement learning (RL) algorithm to design optimal NN controllers for a class of nonlinear dynamical systems while guaranteeing the stability of the control systems. By representing a controlled system as a tensor product (TP) model, a sufficient stability condition for a closed-loop NN control system is derived, which is then employed as a training constraint for the NN controller throughout the training process to ensure the stability in each training step. By showing the existence of a Lyapunov function, which is also directly obtained during the training process, the stability can be theoretically confirmed. Simulation studies on various nonlinear dynamical systems illustrate that the NN controllers trained with the proposed constrained RL algorithm outperform linear–quadratic–regulator controllers and yield roughly the same performance index values as those trained with an unconstrained RL algorithm, indicating that the imposed constraint does not significantly affect the training performance. Most importantly, while simulation results show that all controllers provide closed-loop stability, only the NN controllers trained with the proposed constrained RL algorithm theoretically guarantee stability.

LMI feasibility analysis of 2DOF NATA model

AbstractPresent paper shows the different types of tensor product model based linear matrix inequality controller design and feasibility analysis of two degrees of freedom aeroelastic wing section model. The tensor product models are based on reducing or removing the nonlinear behavior of the system and weighting functions. The linear matrix inequality based method results globally asymptotically stable system. The goal of the paper is to examine that selecting and varying the transformation space influences the feasibility of the linear matrix inequality based controller. The paper gives a comparison between the different tensor product models in terms of controller performance. The linear matrix inequality gives feasible solution for the controller design if the transformation space is selected adequately.

Quadrotors’ double-loop controller design with tensor product model transformation and partial fully actuated method

In the existing work of tensor product (TP) model transformation, the TP model transformation-based work on the quadrotor’s control system design is scarce, the direct TP model transformation control strategy that applied to the quadrotor fails due to the calculation complexity, infeasibility of the huge amount of linear matrix inequalities, and the complexity of solving the linear matrix inequalities. To solve this problem, a partial TP model transformation-based double loop fuzzy controller has been studied in this work, the double-loop hybrid control scheme combines the fully actuated control method and the TP model transformation, while the fully actuated control method is used to the position subsystem control loop, and the TP model transformation based fuzzy controller is applied to the attitude control of the quadrotor. Moreover, for comparison purpose, a varying-input method based on TP model transformation is extended to the quadrotor’s system control. The double-loop hybrid control scheme could also be extended with other TP model transformation based tensor sampling methods, such as, uniform sampling method and varying-input method. At last, the proposed algorithms are evaluated and compared on Parrot Mambo Minidrone, MFP450 and CUAV V5+ based hexarotor.

Unitary (semi)causal quantum-circuit representation of black hole evaporation

A general structure of unitary evolution (evaporation) of the black hole, respecting causality imposed by the event horizon (semicausality), has been derived and presented in the language of quantum circuits. The resulting consequences for the evolution of the corresponding entanglement entropy and the entropy curve have been determined. As an illustration of the general scheme, two families of qubit toy models have been discussed: tensor product models and controlled non-product models.

A Stability Analysis Method for High-speed Magnetically Suspended Rotors Based on Tensor Product Model Transformation

A Stability Analysis Method for High-speed Magnetically Suspended Rotors Based on Tensor Product Model Transformation

The inflation hierarchy and the polarization hierarchy are complete for the quantum bilocal scenario

It is a fundamental but difficult problem to characterize the set of correlations that can be obtained by performing measurements on quantum mechanical systems. The problem is particularly challenging when the preparation procedure for quantum states is assumed to comply with a given causal structure. Recently, a first completeness result for this quantum causal compatibility problem has been given based on the so-called quantum inflation technique. However, completeness was achieved by imposing additional technical constraints, such as an upper bound on the Schmidt rank of the observables. Here, we show that these complications are unnecessary in the quantum bilocal scenario, a much-studied abstract model of entanglement swapping experiments. We prove that the quantum inflation hierarchy is complete for the bilocal scenario in the commuting observable model of locality. We also give a bilocal version of an observation by Tsirelson, namely, in finite dimensions, the commuting observable model and the tensor product model of locality coincide. These results answer questions recently posed by Renou and Xu [arXiv:2210.09065v2 (2022)]. Finally, we point out that our techniques can be interpreted more generally as giving rise to a semidefinite programming hierarchy that is complete for the problem of optimizing polynomial functions in the states of operator algebras defined by generators and relations. The completeness of this polarization hierarchy follows from a quantum de Finetti theorem for states on maximal C*-tensor products.

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi-Sugeno (T-S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

Robust H2/H DPDC dynamic output feedback controller for an uncertain tensor product model of statically unstable missile

Robust H2/H DPDC dynamic output feedback controller for an uncertain tensor product model of statically unstable missile

Retraction Note: Image processing algorithm of Hartmann method aberration automatic measurement system with tensor product model

Retraction Note: Image processing algorithm of Hartmann method aberration automatic measurement system with tensor product model

Controller design and stability analysis for spinning missiles via tensor product

In this paper, the controller design and stability analysis for the parameters time-varying model of spinning missiles are investigated. A mathematical model for the spinning missile considering the flight parameters varying with time is proposed. Based on tensor product (TP) model transformation for the spinning missile, the parallel distributed compensation (PDC) state feedback controller is designed, and the stability of the controlled system is analyzed with the tool of linear matrix inequalities (LMIs). Numerical simulations with time-varying parameters are conducted to demonstrate the effectiveness of the proposed controller. The given controller can not only guarantee the steady performance but also the decoupling performance between pitch and yaw channels when used in the flight parameters time-varying spinning missiles.

Tensor product model HOSVD based polytopic LPV controller for suspension anti-vibration system

This paper presents a polytopic linear parameter varying (LPV) controller design methodology for nonlinear anti-vibration suspension based on stochastic road identification. As the main nonlinear component in semi-active suspension, the continuous damping control (CDC) damper value is mapped by damping velocity and control current through a bench experiment. linear parameter varying gain-scheduled method is applied for dealing with the nonlinear deterministic model. As the uncertainties caused by road stochastic excitation to suspension cannot be ignored, it is essential to identify the excitation signal as a measurable variable parameter. Empirical-mode-decomposition (EMD) and support vector machine (SVM) are utilized to identify and classify the road stochastic signal input into standard level, so polytopic LPV controller can be designed with CDC damper velocity, control current, and road level as variable parameters. Meanwhile the exponential increase of high-order plant elements in multi-parameter LPV model makes it too complicated for real-time computing. Hence the tensor product model transformation is utilized to identify the orthogonal basis of system plant so that low-rank approximation of it can be implemented by truncated high-order singular value decomposition (T−HOSVD) method. Real-time simulation shows the performance and feasibility of controller, which can efficaciously identify the road stochastic excitation as measurable variable parameters for nonlinear suspension polytopic LPV control.

Local Extrema Refinement Based Tensor Product Model Transformation Controller Design with Vary Input Methods

Local Extrema Refinement Based Tensor Product Model Transformation Controller Design with Vary Input Methods

Fuzzy Support Tensor Product Adaptive Image Classification for the Internet of Things.

Computer vision is one of the hottest research directions in artificial intelligence at present, and its research goal is to give computers the ability to perceive and cognize their surroundings from a single image. Image recognition is an important research direction in the field of computer vision, which has important research significance and application value in industrial applications such as video surveillance, biometric identification, unmanned vehicles, human-computer interaction, and medical image recognition. In this article, we propose an end-to-end, pixel-to-pixel IoT-oriented fuzzy support tensor product adaptive image classification method. Considering the problem that traditional support tensor product classification methods are difficult to directly produce pixel-to-pixel classification results, the research is based on the idea of inverse convolution network design, which directly outputs dense pixel-by-pixel classification results for images to be classified of arbitrary size to achieve true end-to-end and pixel-to-pixel high-score image classification and improve the efficiency of support tensor product models for high-score image classification on a pixel-by-pixel basis. Moreover, considering that network supervised classification training using deep learning requires a large amount of labeled data as true values and obtaining a large number of labeled data sources is a difficult problem in the field of image classification, this article proposes using a large amount of unlabeled high-resolution remote sensing images for learning generic structured features through unsupervised to assist the labeled high-resolution remote sensing images for better-supervised feature extraction and classification training. By finding a balance between generic structural feature learning of images and differentiated feature learning related to the target class, the dependence of supervised classification on the number of labeled samples is reduced, and the network robustness of the support tensor product algorithm is improved under a small number of labeled training samples.

Robust Controller Designing for an Air-Breathing Hypersonic Vehicle with an HOSVD-Based LPV Model

This paper focuses on the linear parameter varying (LPV) modeling and controller design for a flexible air-breathing hypersonic vehicle (AHV). Firstly, by selecting the measurable altitude and velocity as gain-scheduled variables, the original longitudinal nonlinear model for AHV is transformed into the LPV model via average gridding division, vertex trimming, Jacobian linearization, and multiple linear regression within the entire flight envelope. Secondly, using the tensor product model transformation method, the obtained LPV model is converted into the polytopic LPV model via high-order singular value decomposition (HOSVD). Third, the validity and applicability of the HOSVD-based LPV model are further demonstrated by designing a robust controller for command tracking control during maneuvering flight over a large envelope.

Nonlocality of observable algebras in quasi-Hermitian quantum theory

Explicit construction of local observable algebras in quasi-Hermitian quantum theories is derived in both the tensor product model of locality and in models of free fermions. The latter construction is applied to several cases of a -symmetric toy model of particle-conserving free fermions on a one-dimensional lattice, with nearest neighbour interactions and open boundary conditions. Despite the locality of the Hamiltonian, local observables do not exist in generic collections of sites in the lattice. The collections of sites which do contain nontrivial observables strongly depends on the complex potential.

Robust Decentralized Formation Tracking Control for Stochastic Large-Scale Biped Robot Team System Under External Disturbance and Communication Requirements

In this study, a robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking control design is proposed to deal with the team formation tracking problem for a large-scale biped robot team system with external disturbance and communication requirement on biped robots and leader. Under the concept of virtual leader and the decentralized control approach, biped robots walking in a large-scale team formation are controlled to track their own reference paths with the robust stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking performance. Consequently, the original robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> large-scale biped robot team formation tracking control design problem can be transformed to a set of independent Hamilton-Jacobi inequality (HJI)-constrained optimization problems for each biped robot. To cope with the difficulties in solving the HJIs for the robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> team formation tracking control design, a numerical framework is introduced to approximate the walking biped robot systems. Based on the tensor-product model transformation technique, the set of independent HJI-constrained optimization problems for the robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> team formation tracking control design is converted into a set of independent linear-matrix-inequality-constrained optimization problems, which can be solved efficiently by the convex optimization methods. Since the robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> team formation tracking control can be designed individually, the magnitude of a biped robot team can be easily increased to a very large scale. Finally, a simulation example of decentralized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> formation tracking control design for a 30-scale biped robot team is given to validate the effectiveness of the proposed scheme.

Robust control design for the FLEXOP demonstrator aircraft via tensor product models

AbstractThe paper proposes a control design methodology for active flutter suppression for the aeroservoelastic (ASE) aircraft of the European project FLEXOP. The aim of the controller is to robustly stabilize the aeroelastic modes. The control design is based on a control‐oriented linear parameter‐varying (LPV) model, which is derived via “bottom–up” modeling approach and includes the parametric uncertainties of the flutter modes. The tensor product (TP) type LPV model is generated via TP model transformation. The symmetric and asymmetric flutter modes are decoupled, which allows independent control design for each. LPV observer‐based state feedback control structure is applied with constraints on the maximal control value to avoid input saturation. The scheduling parameters of the TP‐type LPV models are split into measured and uncertain parameters for robust control design. Convex hull manipulation‐based optimization and model complexity effects are investigated. The resulting controller is validated via the high‐fidelity ASE model of the FLEXOP aircraft.

Piece‐wise ellipsoidal set‐based model predictive control of linear parameter varying systems with application to a tower crane

AbstractIn this paper, a model predictive control algorithm for polytopic linear parameter varying (LPV) systems is proposed, which is based on an offline calculated sequence of robust one‐step controllable sets. At each sampling instant, a finite‐time optimal control problem is solved subject to a stabilizing constraint on the first state to ensure stability and recursive feasibility guarantees independent of the length of the prediction horizon and the cost function. An algorithm is proposed to compute a sequence of piece‐wise ellipsoidal one‐step controllable sets. The systematic application of the developed algorithm is possible via tensor product model transformation to a class of nonlinear systems. The size and shape of each set depend on the vertices of the polytopic LPV system and influences the control performance. By using the tensor product model transformation, different vertex representations can be obtained automatically. Furthermore, a trade‐off between model complexity and accuracy can be chosen, and the computational effort of the set calculation can be influenced. The developed method is applied to a tower crane system. The tower crane is modeled in a cascaded form with three separate subsystems. The couplings between the subsystems are treated as varying parameters. Each subsystem of the crane is transformed into a polytopic LPV system using the tensor product model transformation. By discarding the nonzero singular values, the complexity of the polytopic LPV model is reduced in terms of the number of vertices.

Tensor product‐based model transformation approach to tower crane systems modeling

AbstractThis paper presents the application of the tensor product (TP)‐based model transformation approach to produce Tower CRrane (TCR) systems models. The modeling approach starts with a nonlinear model of TCR systems as representative multi‐input–multi‐output controlled processes. A linear parameter‐varying model is next derived, and the modeling steps specific to TP–based model transformation are proceeded to obtain the TP model. The TP model is tested on TCR laboratory equipment in two open‐loop scenarios considering chirp signals and pseudorandom binary step signals applied to the three model inputs (control inputs). The nonlinear and TP model outputs in the two scenarios are the payload position, the cart position, and the arm angular position. The nonlinear and TP model outputs are collected, measured, and compared. The simulation results prove that the derived TP model approximately mimics the behavior of the nonlinear model; both system responses and numerical approximation errors are illustrated.

Tensor product‐based model transformation approach to cart position modeling and control in pendulum‐cart systems

AbstractThe paper presents the application of the tensor product (TP)‐based model transformation technique to model and control the cart position of single‐input multi‐output pendulum‐cart systems (PCSs). The modeling is first carried out. The derived TP model, the nonlinear model of PCS, and the laboratory equipment are tested in the same open‐loop scenario, and their corresponding outputs are collected, measured, and compared. The parallel distributed compensation (PDC) technique is next applied to TP‐based cart position controller design. A linear state feedback control design is also designed in order to conduct a comparative analysis. The two proposed control system structures are experimentally validated and tested in the same scenarios on the laboratory equipment, and their performance indices are analyzed and compared.