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1. Discrete Finite-time Stable Position Tracking Control of Unmanned Vehicles

   https://doi.org/10.1109/CDC40024.2019.9029700  

   Hamrah, Reza; Sanyal, Amit K.; Prabhakaran Viswanathan, Sasi (December 2019, 2019 IEEE 58th Conference on Decision and Control (CDC))

   This paper presents a finite-time stable (FTS) position tracking control scheme in discrete time for an unmanned vehicle. The control scheme guarantees discrete-time stability of the feedback system in finite time. This scheme is developed in discrete time as it is more convenient for onboard computer implementation and guarantees stability irrespective of sampling period. Finite-time stability analysis of the discrete-time tracking control is carried out using discrete Lyapunov analysis. This tracking control scheme ensures stable convergence of position tracking errors to the desired trajectory in finite time. The advantages of finite-time stabilization in discrete time over finite-time stabilization of a sampled continuous tracking control system is addressed in this paper by a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned vehicle model. 

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2. Hölder-Continuous Finite-Time-Stable Tracking Control of Attitude Dynamics

   https://doi.org/10.2514/1.G009106  

   Wang, Ningshan; Sanyal, Amit K (September 2025, Journal of Guidance, Control, and Dynamics)

   This article presents an attitude tracking control scheme with Hölder continuity and finite-time stability. The first part of this article discusses and compares the features of first-order multivariable Hölder-continuous systems with coupled-scalar sliding-mode systems. The advantages of Hölder-continuous systems over sliding-mode systems are presented from the perspectives of control continuity and noise robustness. Thereafter, a Hölder-continuous second-order differentiator is presented with its stability and robustness properties. This is followed by its use in an attitude tracking control scheme, which is covered in the second part of the article. The proposed tracking control scheme is designed directly on the state-space of rigid-body rotational motion, which is the tangent bundle of the Lie group of 3D rotations. The control scheme design, its stability, and its robustness properties are obtained through Lyapunov stability analyses. The proposed Hölder-continuous design is compared with three comparable sliding-mode designs. Numerical simulations on a simulated CubeSat demonstrate the performance of the proposed control scheme and compare it with the sliding-mode control schemes. The numerical simulations also compare the proposed control scheme with other state-of-the-art sliding-mode control approaches in existing research publications. The comparison results demonstrate that the proposed Hölder-continuous attitude control scheme exhibits lower control efforts and tracking control errors over these sliding-mode control schemes in simulations that incorporate actuator dynamics and measurement uncertainties. 

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

   Sangli Teng, Amit K. (July 2022, 2022 American Control Conference (ACC))

   Abstract— 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 inputdependent 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 controller 

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5. 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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