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Initial Undershoot in Discrete-Time Input-Output Hammerstein systems

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IEEE OPEN JOURNAL OF control systems 2025年 4卷 30-40页

作者： Kim, Hyung Jun Kamaldar, Mohammadreza Bernstein, Dennis S. Univ Michigan Dept Aerosp Engn Ann Arbor MI 48104 USA

This paper considers initial undershoot in the step response of discrete-time, input-output Hammerstein (DIH) systems, which have linear unforced dynamics and nonlinear zero dynamics (ZD). Initial undershoot occurs when the step response of a system moves initially in a direction that is opposite to the direction of the asymptotic response. For DIH systems, the paper investigates the relationship among the existence of initial undershoot, the step height, the height-dependent delay, and the stability of the ZD. For linear, time-invariant systems, the height-dependent delay specializes to the relative degree. The main result of the paper provides conditions under which, for all sufficiently small step heights, initial undershoot in the step response of a DIH system implies instability of the ZD. Several examples of DIH systems are presented to illustrate these results.

关键词： Delays nonlinear dynamical systems Sufficient conditions Linear systems Transient analysis Aerodynamics Terminology Stability analysis Poles and zeros Standards nonlinear systems and control stability of nonlinear systems initial undershoot nonlinear zero dynamics discrete-time input-output Hammerstein system

A Multiplex Approach Against Disturbance Propagation in nonlinear Networks With Delays

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IEEE OPEN JOURNAL OF control systems 2024年 3卷 87-101页

作者： Xie, Shihao Russo, Giovanni Univ Naples Federico II Dept Elect Engn & Informat Technol Naples Italy Univ Salerno Dept Informat & Elect Engn & Appl Math Salerno Italy

We consider both leaderless and leader-follower, possibly nonlinear, networks affected by time-varying communication delays. For such systems, we give a set of sufficient conditions that guarantee the convergence of the network towards some desired behaviour while simultaneously ensuring the rejection of polynomial disturbances and the non-amplification of other classes of disturbances across the network. To fulfill these desired properties, and prove our main results, we propose the use of a control protocol that implements a multiplex architecture. The use of our results for control protocol design is then illustrated in the context of formation control. The protocols are validated both in-silico and via an experimental set-up with real robots. All experiments confirm the effectiveness of our approach.

关键词： Delays Protocols Scalability Artificial neural networks Sufficient conditions Multiplexing Robots Disturbance propagation large-scale systems multiplex networks nonlinear systems and control time delays

Adaptive control for Singularly Perturbed systems

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IEEE OPEN JOURNAL OF control systems 2024年 3卷 1-13页

作者： Eves, Kameron Valasek, John Utah Tech Univ St George UT 84770 USA Texas A&M Univ College Stn TX 77843 USA

Singularly perturbed systems are a class of mathematical systems that are not well approximated by their limits and can be used to model plants with multiple fast and slow states. Multiple-timescale systems are very common in engineering applications, but adaptive control can be sensitive to timescale effects. Recently a method called [K]control of Adaptive Multiple-timescale systems (KAMS) has shown improved performance and increased robustness for singularly perturbed systems, but it has only been studied on systems using adaptive control for the slow states. This article extends KAMS to the general case when adaptive control is used to stabilize both the slow and fast states simultaneously. This causes complex interactions between the fast state reference model and the manifold to which the fast states converge. It is proven that under certain conditions the system still converges to the reference model despite these complex interactions. This method is demonstrated on a nonlinear, nonstandard, numerical example.

关键词： Adaptive control nonlinear systems and control perturbation techniques timescales nonlinear systems and control perturbation techniques timescales

H2- and H∞ -Optimal Model Predictive controllers for Robust Legged Locomotion

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IEEE OPEN JOURNAL OF control systems 2024年 3卷 225-238页

作者： Pandala, Abhishek Ames, Aaron D. Hamed, Kaveh Akbari Virginia Tech Dept Mech Engn Blacksburg VA 24061 USA CALTECH Dept Mech & Civil Engn Pasadena CA 91125 USA

This paper formally develops robust optimal predictive control solutions that can accommodate disturbances and stabilize periodic legged locomotion. To this end, we build upon existing optimization-based control paradigms, particularly quadratic programming (QP)-based model predictive controllers (MPCs). We present conditions under which the closed-loop reduced-order systems (i.e., template models) with MPC have the continuous differentiability property on an open neighborhood of gaits. We then linearize the resulting discrete-time, closed-loop nonlinear template system around the gait to obtain a linear time-varying (LTV) system. This periodic LTV system is further transformed into a linear system with a constant state-transition matrix using discrete-time Floquet transform. The system is then analyzed to accommodate parametric uncertainties and to synthesize robust optimal H-2- and H-infinity feedback controllers via linear matrix inequalities (LMIs). The paper then extends the theoretical results to the single rigid body (SRB) template dynamics and numerically verifies them. The proposed robust optimal predictive controllers are used in a layered control structure, where the optimal reduced-order trajectories are provided to a full-order nonlinear whole-body controller (WBC) for tracking at the low level. The developed layered controllers are numerically and experimentally validated for the robust locomotion of the A1 quadrupedal robot subject to various disturbances and uneven terrains. Our numerical results suggest that the H-2- and H-infinity-optimal MPC controllers significantly improve the robust stability of the gaits compared to the normal MPC.

关键词： Legged locomotion Robots Quadrupedal robots Uncertainty control systems Robust control Real-time systems nonlinear systems and control optimal control robotics robust control stability of nonlinear systems

Generalized Functions in the Study of Signals and systems 26

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Generalized Functions in the Study of Signals and Systems

26th International Symposium on Mathematical Theory of Networks and systems (MTNS)

作者： Verriest, Erik, I Dirr, Gunther Gray, W. Steven Georgia Inst Technol Atlanta GA 30332 USA Julius Maximilians Univ D-9707 Wurzburg Germany Old Dominion Univ Norfolk VA 23529 USA

We collect three instances where the theory of generalized functions may still make contributions to the study of signals and systems. In the first, a purely algebraic approach is presented for LTI-ODE's, in terms of two operators, D and T, respectively the differentiation operator and the multiplication-by-the-independent-variable operator. This formalism adds simplicity, a duality theory, and nicely generalizes to other classes of operator equations and their solutions. In the second part we extend the classical bilateral Laplace transform to include Bohl functions with support in R by invoking Sato's hyperfunctions. Finally, in the third case we use the Colombeau algebra to allow for products of generalized functions. This is important in the study of (smooth) nonlinear systems driven by impulsive inputs, and hybrid system theory. Copyright (c) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： Algebraic systems Theory nonlinear systems and control Operator Theoretic Methods in systems Theory Generalized Functions Impulsive systems Laplace Transform

Bounds on the growth rate of time-invariant switching max-min-plus-scaling discrete-event 26

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Bounds on the growth rate of time-invariant switching max-mi...

26th International Symposium on Mathematical Theory of Networks and systems (MTNS)

作者： van den Boom, Ton Markkassery, Sreeshma De Schutter, Bart Delft Univ Technol Delft Ctr Syst & Control DCSC Delft Netherlands

We consider the growth rate of a switching max-min-plus-scaling (S-MMPS) system in a discrete-event framework. We show that an explicit, time-invariant, monotone, and arbitrarily switching MMPS system has a bounded growth rate. Further, we propose a mixed-integer linear programming problem to calculate the estimates of the smallest upper bound and the largest lower bound of the growth rate of an S-MMPS system. Copyright (c) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： Max-plus algebra Switching max-min-plus-scaling systems Algebraic systems Theory Discrete Event systems nonlinear systems and control

controlled invariant varieties for second order polynomial control systems 26

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Controlled invariant varieties for second order polynomial c...

26th International Symposium on Mathematical Theory of Networks and systems (MTNS)

作者： Harms, Melanie Zerz, Eva Herty, Michael Rhein Westfal TH Aachen Lehrstuhl Algebra & Zahlentheorie Aachen Germany Rhein Westfal TH Aachen Inst Geometrie & Prakt Math Aachen Germany

We investigate controlled invariant varieties for second order input-affine control systems with polynomial nonlinearity. For autonomous, first order systems, a variety V is said to be invariant if any trajectory starting in V remains in V for all times. We discuss how to adapt this notion in the second order case and give conditions to decide whether a variety is invariant for a second order system using symbolic computation. This results serve as a foundation to characterise controlled invariant varieties, i.e., varieties that can be rendered invariant by a polynomial state feedback. Copyright (c) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： Algebraic systems theory Applications of Algebraic and Differential Geometry in systems Theory Computations in systems Theory Feedback control systems nonlinear systems and control

nonlinear Dynamic Modeling of a Robotic Endoscopy Platform on Synthetic Tissue Substrates

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JOURNAL OF DYNAMIC systems MEASUREMENT AND control-TRANSACTIONS OF THE ASME 2021年第1期143卷 011005页

作者： Formosa, Gregory A. Prendergast, J. Micah Humbert, J. Sean Rentschler, Mark E. Univ Colorado Dept Mech Engn Adv Med Technol Lab 1111 Engn Dr427 UCB Boulder CO 80309 USA Univ Colorado Dept Mech Engn Bioinspired Percept & Robot Lab 1111 Engn Dr427 UCB Boulder CO 80309 USA

A scaled robotic endoscopy platform (REP) was previously developed to efficiently test new control schemes in a simulated colon environment. This article presents the derivation and tuning of a nonlinear model of the REP operating on various substrates. The modeling technique and novel empirical friction profiling demonstrated here are useful for a wide variety of devices interacting with unconventional substrates. The model is first derived from the REP drivetrain inertial characteristics, and then the interaction with synthetic tissue is quantified by an automated traction measurement system for multiple substrates. The resulting model is then used with ground-truth VICON and sensor data to optimize uncertain parameters by minimizing pose error over a variety of tests and substrates. The results show an average error reduction of 67% over all tests and substrates, with a worst-case 10% open-loop final position error. The success of these results proves a robust dynamic model of the REP and its tissue interactions without the need to model complex and computationally expensive viscoelastic material properties or discrete/nonlinear events such as stalling. The resulting model will be used to develop model-based feedback control for estimation, disturbance rejection, and autonomy for the REP in an actuated colon simulator.

关键词： modeling of dynamic systems mechatronics robotics system identification nonlinear systems and control

Bounds on the growth rate of time-invariant switching max-min-plus-scaling discrete-event systems

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IFAC-PapersOnLine 2024年第17期58卷 404-409页

作者： Ton van den Boom Sreeshma Markkassery Bart De Schutter Delft Center for Systems and Control (DCSC) TU Delft The Netherlands

关键词： Max-plus algebra Switching max-min-plus-scaling systems Algebraic systems Theory Discrete Event systems nonlinear systems and control