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1. Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty

   https://doi.org/10.23919/ACC53348.2022.9867457  

   Sinha, Rohan; Harrison, James; Richards, Spencer M.; Pavone, Marco (June 2022, American Control Conference)

   We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems commonly model the nonlinear effects of an unknown environment on a nominal system. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws pioneered in classical adaptive control to achieve significant performance improvements in the presence of uncertainties of large magnitude, a setting in which existing learning-based predictive control algorithms often struggle to guarantee safety. In contrast to previous work in robust adaptive MPC, our approach allows us to take advantage of structure (i.e., the numerical predictions) in the a priori unknown dynamics learned online through function approximation. Our approach also extends typical nonlinear adaptive control methods to systems with state and input constraints even when we cannot directly cancel the additive uncertain function from the dynamics. Moreover, we apply contemporary statistical estimation techniques to certify the system’s safety through persistent constraint satisfaction with high probability. Finally, we show in simulation that our method can accommodate more significant unknown dynamics terms than existing methods. 

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2. When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems

   https://doi.org/10.1088/1361-6420/aca55b  

   Arnold, Andrea (December 2022, Inverse Problems)

   Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of these problems includes time-varying parameters with unknown evolution models that often cannot be directly observed. This work develops a systematic particle filtering approach that reframes the idea behind artificial parameter evolution to estimate time-varying parameters in nonstationary inverse problems arising from deterministic dynamical systems. Focusing on systems modeled by ordinary differential equations, we present two particle filter algorithms for time-varying parameter estimation: one that relies on a fixed value for the noise variance of a parameter random walk; another that employs online estimation of the parameter evolution noise variance along with the time-varying parameter of interest. Several computed examples demonstrate the capability of the proposed algorithms in estimating time-varying parameters with different underlying functional forms and different relationships with the system states (i.e. additive vs. multiplicative). 

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3. Feedback control of transitional flows: A framework for controller verification using quadratic constraints

   https://doi.org/10.2514/6.2021-2825  

   Mushtaq, Talha; Seiler, Peter; Hemati, Maziar (July 2021, AIAA AVIATION 2021 FORUM)

   The dynamics of incompressible fluid flows are governed by a non-normal linear dynamical system in feedback with a static energy-conserving nonlinearity. These dynamics can be altered using feedback control but verifying performance of a given control law can be challenging. The conventional approach is to perform a campaign of high-fidelity direct numerical simulations to assess performance over a wide range of parameters and disturbance scenarios. In this paper, we propose an alternative simulation-free approach for controller verification. The incompressible Navier-Stokes equations are modeled as a linear system in feedback with a static and quadratic nonlinearity. The energy conserving property of this nonlinearity can be expressed as a set of quadratic constraints on the system, which allows us to perform a nonlinear stability analysis of the fluid dynamics with minimal complexity. In addition, the Reynolds number variations only influence the linear dynamics in the Navier-Stokes equations. Therefore, the fluid flow can be modeled as a parameter-varying linear system (with Reynolds number as the parameter) in feedback with a quadratic nonlinearity. The quadratic constraint framework is used to determine the range of Reynolds numbers over which a given flow will be stable, without resorting to numerical simulations. We demonstrate the framework on a reduced-order model of plane Couette flow. We show that our proposed method allows us to determine the critical Reynolds number, largest initial disturbance, and a range of parameter variations over which a given controller will stabilize the nonlinear dynamics. 

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4. Adaptive Dynamic Programming for Decentralized Stabilization of Uncertain Nonlinear Large-Scale Systems With Mismatched Interconnections

   https://doi.org/10.1109/TSMC.2018.2837899  

   Yang, Xiong; He, Haibo (October 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems)

   This paper presents a novel decentralized control strategy for a class of uncertain nonlinear large-scale systems with mismatched interconnections. First, it is shown that the decentralized controller for the overall system can be represented by an array of optimal control policies of auxiliary subsystems. Then, within the framework of adaptive dynamic programming, a simultaneous policy iteration (SPI) algorithm is developed to solve the Hamilton–Jacobi–Bellman equations associated with auxiliary subsystem optimal control policies. The convergence of the SPI algorithm is guaranteed by an equivalence relationship. To implement the present SPI algorithm, actor and critic neural networks are applied to approximate the optimal control policies and the optimal value functions, respectively. Meanwhile, both the least squares method and the Monte Carlo integration technique are employed to derive the unknown weight parameters. Furthermore, by using Lyapunov’s direct method, the overall system with the obtained decentralized controller is proved to be asymptotically stable. Finally, the effectiveness of the proposed decentralized control scheme is illustrated via simulations for nonlinear plants and unstable power systems. 

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5. Adaptive Control of a Two-Link Robot Using Batch Least-Square Identifier

   https://doi.org/10.1109/JAS.2020.1003459  

   Bagheri, Mostafa; Karafyllis, Iasson; Naseradinmousavi, Peiman; Krstic, Miroslav. (January 2021, IEEECAA journal of automatica sinica)

   Liu, Tengfei; Ou, Yan. (Ed.)

   We design a regulation-triggered adaptive controller for robot manipulators to efficiently estimate unknown parameters and to achieve asymptotic stability in the presence of coupled uncertainties. Robot manipulators are widely used in telemanipulation systems where they are subject to model and environmental uncertainties. Using conventional control algorithms on such systems can cause not only poor control performance, but also expensive computational costs and catastrophic instabilities. Therefore, system uncertainties need to be estimated through designing a computationally efficient adaptive control law. We focus on robot manipulators as an example of a highly nonlinear system. As a case study, a 2-DOF manipulator subject to four parametric uncertainties is investigated. First, the dynamic equations of the manipulator are derived, and the corresponding regressor matrix is constructed for the unknown parameters. For a general nonlinear system, a theorem is presented to guarantee the asymptotic stability of the system and the convergence of parameters’ estimations. Finally, simulation results are discussed for a two-link manipulator, and the performance of the proposed scheme is thoroughly evaluated. 

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