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1. Input Influence Matrix Design for MIMO Discrete-Time Ultra-Local Model

   https://doi.org/10.23919/ACC53348.2022.9867513  

   Teng, Sangli; Sanyal, Amit K.; Vasudevan, Ram; Bloch, Anthony; Ghaffari, Maani (June 2022, 2022 American Control Conference (ACC))

   Ultra-Local Models (ULM) have been applied to perform model-free control of nonlinear systems with unknown or partially known dynamics. Unfortunately, extending these methods to MIMO systems requires designing a dense input influence matrix which is challenging. This paper presents guidelines for designing an input influence matrix for discretetime, control-affine MIMO systems using an ULM-based controller. This paper analyzes the case that uses ULM and a model-free control scheme: the Hölder-continuous Finite-Time Stable (FTS) control. By comparing the ULM with the actual system dynamics, the paper describes how to extract the input-dependent part from the lumped ULM dynamics and finds that the tracking and state estimation error are coupled. The stability of the ULM-FTS error dynamics is affected by the eigenvalues of the difference (defined by matrix multiplication) between the actual and designed input influence matrix. Finally, the paper shows that a wide range of input influence matrix designs can keep the ULM-FTS error dynamics (at least locally) asymptotically stable. A numerical simulation is included to verify the result. The analysis can also be extended to other ULM-based controllers. 

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2. A Hölder-continuous Extended State Observer for Model-free Position Tracking Control

   https://doi.org/10.23919/ACC50511.2021.9483268  

   Wang, Ningshan; Sanyal, Amit K. (May 2021, 2021 American Control Conference (ACC))

   null (Ed.)

   Position tracking control in three spatial dimensions in the presence of unknown or uncertain dynamics, is applicable to unmanned aerial, ground, (under)water and space vehicles. This work gives a new approach to model-free position tracking control by designing an extended state observer to estimate the states and the uncertain dynamics, with guaranteed accuracy of estimates. The estimated states and uncertainties can be used in a control scheme in real-time for position tracking control. The uncertainty (disturbance input) estimate is provided by an extended state observer (ESO) that is finite-time stable (FTS), to provide accuracy and robustness. The ideas of homogeneous vector fields and real-valued functions are utilized for the ESO design and to prove FTS. The estimated disturbance is then utilized for compensation of this uncertainty in real-time, and to enhance the stability and robustness of the feedback tracking control scheme. 

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3. A Multirate Adaptive Control for MIMO Systems with Application to Cyber-Physical Security

   https://doi.org/10.1109/CDC.2018.8619570  

   Jafarnejadsani, Hamidreza; Lee, Hanmin; Hovakimyan, Naira; Voulgaris, Petros (December 2018, 2018 IEEE Conference on Decision and Control)

   This paper proposes a multirate output-feedback controller for multi-input multi-output (MIMO) systems, possibly with non-minimum-phase zeros, using the L1 adaptive control structure. The analysis of stability and robustness of the sampled-data controller reveals that under certain conditions the performance of a continuous-time reference system is uniformly recovered as the sampling time goes to zero. The controller is designed for detection and mitigation of actuator attacks. By considering a multirate formulation, stealthy zero-dynamics attacks become detectable. The experimental results from the flight test of a small quadrotor are provided. The tests show that the multirate L1 controller can effectively detect the zero-dynamics actuator attack and recover stability of the quadrotor. 

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4. Control-Coherent Koopman Modeling: A Physical Modeling Approach

   Asada, Harry; Solano--Castellanos, Jose (December 2024, IEEE)

   The modeling of nonlinear dynamics based on Koopman operator theory, originally applicable only to autonomous systems with no control, is extended to nonautonomous control system without approximation of the input matrix. Prevailing methods using a least square estimate of the input matrix may result in an erroneous input matrix, misinforming the controller. Here, a new method for constructing a Koopman model that yields the exact input matrix is presented. A set of state variables are introduced so that the control inputs are linearly involved in the dynamics of actuators. With these variables, a lifted linear model with the exact input matrix, called a Control-Coherent Koopman Model, is constructed by superposing control input terms, which are linear in local actuator dynamics, to the Koopman operator of the associated autonomous nonlinear system. As an example, the proposed method is applied to multi degree-of-freedom robotic arms, which are controlled with Model Predictive Control (MPC). It is demonstrated that the prevailing Dynamic Mode Decomposition with Control (DMDc) using an approximate input matrix does not provide a satisfactory result, while the Control-Coherent Koopman Model performs well with the correct input matrix, even performing better than the bilinear formulation of the Koopman operator. 

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5. Hierarchical MIMO Decoupling Control for Vehicle Roll and Planar Motions With Control Allocation

   https://doi.org/10.1109/tvt.2023.3308577  

   Wang, Fengchen; Shi, Yue; Chen, Yan (January 2024, IEEE Transactions on Vehicular Technology)

   Although many methods of ground vehicle dynamics control have been widely studied, their robustness against undesirable oscillatory coupling behaviors of planar and roll dynamics is not fully explored. To address this issue, a hierarchical multiple-input-multiple-output (MIMO) decoupling controller is proposed in this study. Based on the hierarchical control configuration, the coupled vehicle roll and planar dynamics are resolved in the high-level control, and a control allocation is utilized for tracking control in the low-level control. The decoupled internal dynamics and nominal stability are then analyzed and proved. Moreover, by using the vehicle yaw rate and load transfer ratio, a control trigger with dynamic weighting is designed to guarantee the feasibility of the MIMO decoupling control and smooth control efforts. Through the co-simulation between CarSim and MATLAB/Simulink, the feasibility and effectiveness of the proposed controller are verified. 

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