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A Weighted Least-Squares Method for Non-Asymptotic Identification of Markov Parameters from Multiple Trajectories

IFAC-PapersOnLine 2024年第15期58卷 169-174页

作者： Jiabao He Cristian R. Rojas Håkan Hjalmarsson Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology 100 44 Stockholm Sweden

Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step least-squares algorithms, such as Weighted Null-Space Fitting. Recently, there has been an increasing interest in non-asymptotic analysis of estimation algorithms. In this contribution we identify the Markov parameters using weighted least-squares and present non-asymptotic analysis for such estimator. To cover both stable and unstable systems, multiple trajectories are collected. We show that with the optimal weighting matrix, weighted least-squares gives a tighter error bound than ordinary least-squares for the case of non-uniformly distributed measurement errors. Moreover, as the optimal weighting matrix depends on the system’s true parameters, we introduce two methods to consistently estimate the optimal weighting matrix, where the convergence rate of these estimates is also provided. Numerical experiments demonstrate improvements of weighted least-squares over ordinary least-squares in finite sample settings.

关键词： Non-asymptotic identification Markov parameters weighted least-squares

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Design of a Mechatronic Endoskeleton Robot for Inspection Tasks: Model Reference Adaptive control (MRAC) for Serpentine Locomotion with Stability Analysis 17

Design of a Mechatronic Endoskeleton Robot for Inspection Ta...

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17th International Conference on Developments in esystems engineering, DeSE 2024

作者： Al Mhdawi, Ammar K. Wright, Nick Younis, Mohammed I. Humaidi, Amjad J. School of Engineering and Sustainable Development De Montfort University LeicesterLE19BH United Kingdom Department of Electrical and Electronic Engineering Newcastle University Newcastle United Kingdom Department of Computer Engineering University of Baghdad Iraq Department of Control and Systems Engineering University of Technology Baghdad Iraq

ISBN: (纸本)9798350368697

An advantage of bio-inspired robots is the versatility of their locomotion on a wide range of terrains that conventional robots are not able to traverse. The snake-like robot, which is a mechanism designed to move in the manner of a biological snake, is an example of a bio-inspired platform. This paper aims to implement and validate, using real and simulation tests on flat terrain, a snake-like endoskeleton robot that permits serpentine movement with adaptive control capabilities. The prototype mechatronic robot was comprised of eleven segments that were 3D printed sequentially. A simulation using Matlab’s Multibody Mechanics tool determines the necessary torques for each motor. In this simulation, a parameterized virtual model of the robot is created, where rectilinear gaits are programmed. In accordance with simulation and experimental results, the robot undertakes different times to reach the goal trajectory or end points depending on the frequency, angular position, and wave length (duty cycle). As a result, there is a high degree of similarity between the simulation tests and those conducted with the prototype endoskeleton. Furthermore, the robot is equipped with machine vision capabilities that allow it to detect faults within oil and gas pipes for the purpose of inspection and maintenance. Furthermore, a Model Reference Adaptive control (MRAC) method based on Lyapunov stability analysis and MIT rules is proposed. The theoretical analysis and numerical simulation show that the designed trajectory tracking control law can make the multi-joint snake-like robot track the trajectory of the front joint when the robot encounters disturbances and stabilize the angular position and velocity of the first two head joints when disturbances occur. © 2024 IEEE.

关键词： Model reference adaptive control

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SRG Analysis of Lur’e systems and the Generalized Circle Criterion

arXiv

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arXiv 2024年

作者： Krebbekx, Julius P.J. Tóth, Roland Das, Amritam Control Systems Group Department of Electrical Engineering Eindhoven University of Technology Netherlands Systems and Control Lab HUN-REN Institute for Computer Science and Control Budapest Hungary

Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. However, we show that the current SRG analysis suffers from some pitfalls that limit its applicability in analysing practical nonlinear systems. We overcome these pitfalls by modifying the SRG of a linear time invariant operator, combining the SRG with the Nyquist criterion, and apply our result to Lur’e systems. We thereby obtain a generalization of the celebrated circle criterion, which deals with broader class of nonlinearities, and provides (incremental) L2-gain performance bounds. We illustrate the power of the new approach on the analysis of the controlled Duffing oscillator. © 2024, CC BY.

关键词： Frequency domain analysis

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Dynamic Curing and Network Design in SIS Epidemic Processes 63

Dynamic Curing and Network Design in SIS Epidemic Processes

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63rd IEEE Conference on Decision and control, CDC 2024

作者： Yi, Yuhao Shan, Liren Pare, Philip E. Johansson, Karl H. Sichuan University Institute of Clinical Pathology West China Hospital College of Computer Science Chengdu China Toyota Technological Institute at Chicago United States Purdue University School of Electrical and Computer Engineering West LafayetteIN United States Kth Royal Institute of Technology and They Are Also Affiliated with Digital Futures Division of Decision and Control Systems School of Electrical Engineering and Computer Science StockholmSE-100 44 Sweden

ISBN: (纸本)9798350316339

This paper studies efficient algorithms for dynamic curing policies and the corresponding network design problems to guarantee fast extinction of epidemic spread in a Markov process-based susceptible-infected-susceptible (SIS) model. We provide a computationally efficient curing algorithm based on the curing policy proposed by Drakopoulos, Ozdaglar, and Tsitsiklis (2014). Since the corresponding optimization problem is NP-hard, finding optimal policies is intractable for large graphs. We provide approximation guarantees on the curing budget of the proposed dynamic curing algorithm. To avoid the waiting period included in the original curing policy, we study network design problems to reduce the total infection rate by deleting edges or reducing the weight of edges. To this end, we provide algorithms with provable guarantees. In summary, the proposed curing and network design algorithms together provide an effective and computationally efficient approach that mitigates SIS epidemic spread in networks. © 2024 IEEE.

关键词： Markov processes

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Slow Convergence of Interacting Kalman Filters in Word-of-Mouth Social Learning

Slow Convergence of Interacting Kalman Filters in Word-of-Mo...

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Annual Allerton Conference on Communication, control, and Computing

作者： Vikram Krishnamurthy Cristian R. Rojas School of Electrical and Computer Engineering Cornell University Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden

ISBN: (数字)9798331541033

ISBN: (纸本)9798331541040

We consider word-of-mouth social learning involving $m$ Kalman filter agents that operate sequentially. The first Kalman filter receives the raw observations, while each subsequent Kalman filter receives a noisy measurement of the conditional mean of the previous Kalman filter. The prior is updated by the m-th Kalman filter. When $m=2$ , and the observations are noisy measurements of a Gaussian random variable, the covariance goes to zero as $k^{-1/3}$ for $k$ observations, instead of $O(k^{-1})$ in the standard Kalman filter. In this paper we prove that for $m$ agents, the covariance decreases to zero as $k^{-(2^{m}-1)}$ , i.e, the learning slows down exponentially with the number of agents. We also show that by artificially weighing the prior at each time, the learning rate can be made optimal as $k^{-1}$ . The implication is that in word-of-mouth social learning, artificially re-weighing the prior can yield the optimal learning rate.

关键词： Random variables Kalman filters Noise measurement Standards Convergence

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Hidden Markov Models:Inverse Filtering,Belief Estimation and Privacy Protection

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Journal of systems Science & Complexity 2021年第5期34卷 1801-1820页

作者： LOURENCO Ines MATTILA Robert ROJAS Cristian R. HU Xiaoming WAHLBERG Bo Division of Decision and Control Systems School of Electrical Engineering and Computer ScienceKTH Royal Institute of TechnologyStockholmSweden Division of Optimizations and Systems Theory School of Engineering SciencesKTH Royal Institute of TechnologyStockholmSweden

A hidden Markov model(HMM)comprises a state with Markovian dynamics that can only be observed via noisy *** paper considers three problems connected to HMMs,namely,inverse filtering,belief estimation from actions,and privacy enforcement in such a ***,the authors discuss how HMM parameters and sensor measurements can be reconstructed from posterior distributions of an HMM ***,the authors consider a rational decision-maker that forms a private belief(posterior distribution)on the state of the world by filtering private *** authors show how to estimate such posterior distributions from observed optimal actions taken by the *** the setting of adversarial systems,the authors finally show how the decision-maker can protect its private belief by confusing the adversary using slightly sub-optimal *** range from financial portfolio investments to life science decision systems.

关键词： Belief estimation counter-adversarial systems hidden Markov models inverse decision making inverse filtering

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Stress Matrix-Based Formation control of Multi-Agent systems with Discrete-Time Communication 12

Stress Matrix-Based Formation Control of Multi-Agent Systems...

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2024 12th International Conference on systems and control, ICSC 2024

作者： Onuoha, Okechi Ubochi, Brendan Chijioke Kurawa, Suleiman Tang, Zezhi Wu, Changshun Dong, Yi University of Hertfordshire United Kingdom Federal University of Technology The Department of Electrical and Electronic Engineering Akure Nigeria University of Manchester The Department of Electrical Engineering United Kingdom University of Sheffield The Department of Automatic Control and Systems Engineering United Kingdom University Grenoble Alpes Grenoble38000 France The School of Electronics & Computer Science University of Southampton United Kingdom

ISBN: (纸本)9798331531812

This study addresses the affine formation maneuver control of cooperative multi-agent systems (MAS) having periodic inter-agent communication for both static and dynamic leader cases. Here, we focus on the leader-follower MASs. The primary aim of the control system is to steer the entire collection of agents to produce required patterns (geometric) along with any required maneuver through the direct control of only few a selected agents referred to as leaders. Most of the existing works are constrained to either the individual agents communicate with each other in continuous-time or the sample-data scenario where the leaders are stationary or have constant acceleration or velocities. Here, we consider the scenarios where the velocities of the leaders can be time-varying or constant. Here, different cases are addressed and some control laws are proposed. Conditions are established to help guarantee the overall stability of the systems. A simulation study is employed for the illustration of our proposed laws. © 2024 IEEE.

关键词： Continuous time systems

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Safe platooning control of connected and autonomous vehicles on curved multi-lane roads

arXiv

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arXiv 2025年

作者： Chen, Xiao Tang, Zhiqi Johansson, Karl H. Mårtensson, Jonas Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Sweden

This paper investigates the safe platoon formation tracking and merging control problem of connected and automated vehicles (CAVs) on curved multi-lane roads. The first novelty is the separation of the control designs into two distinct parts: a lateral control law that ensures a geometrical convergence towards the reference path regardless of the translational velocity, and a longitudinal control design for each vehicle to achieve the desired relative arc length and velocity with respect to its neighboring vehicle. The second novelty is exploiting the constructive barrier feedback as an additive term to the nominal tracking control, ensuring both lateral and longitudinal collision avoidance. This constructive barrier feedback acts as a dissipative term, slowing down the relative velocity toward obstacles without affecting the nominal controller’s performance. Consequently, our proposed control method enables safe platoon formation of vehicles on curved multi-lane roads, with theoretical guarantees for safety invariance and stability analysis. Simulation and experimental results on connected vehicles are provided to further validate the effectiveness of the proposed method. Copyright © 2025, The Authors. All rights reserved.

关键词： Feedback

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Stability of the distributed Kalman filter using general random coefficients

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Science China(Information Sciences) 2021年第7期64卷 66-79页

作者： Die GAN Siyu XIE Zhixin LIU Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences The Department of Electrical and Computer Engineering Wayne State University

In this paper, we propose a distributed Kalman filter(DKF) for the dynamical system with general random coefficients. In the proposed method, each estimator shares local innovation pairs with its neighbors to collectively complete the estimation task. Further, we introduce a collective random observability condition by which the Lp-stability of the covariance matrix and the Lp-exponential stability of the homogeneous part of the estimation error equation can be established. In contrast, the stringent conditions on the coefficient matrices, such as independency and stationarity are not required. Besides, the stability of the DKF, i.e., the boundedness of the filtering errors, can be established. Finally, from the simulation result,we demonstrate the cooperative effect of the sensors.

关键词： distributed Kalman filter collective random observability $L_p$-stable $L_p$-exponentially stable state estimation

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Collaborative Satisfaction of Long-Term Spatial Constraints in Multi-Agent systems: A Distributed Optimization Approach (extended version)

arXiv

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arXiv 2025年

作者： Mehdifar, Farhad Dhullipalla, Mani H. Bechlioulis, Charalampos P. Dimarogonas, Dimos V. The Division of Decision and Control Systems KTH Royal Institute of Technology Stockholm Sweden The Division of Systems and Control The Department of Electrical and Computer Engineering University of Patras Patra Greece

This paper addresses the problem of collaboratively satisfying long-term spatial constraints in multi-agent systems. Each agent is subject to spatial constraints, expressed as inequalities, which may depend on the positions of other agents with whom they may or may not have direct communication. These constraints need to be satisfied asymptotically or after an unknown finite time. The agents’ objective is to collectively achieve a formation that fulfills all constraints. The problem is initially framed as a centralized unconstrained optimization, where the solution yields the optimal configuration by maximizing an objective function that reflects the degree of constraint satisfaction. This function encourages collaboration, ensuring agents help each other meet their constraints while fulfilling their own. When the constraints are infeasible, agents converge to a least-violating solution. A distributed consensus-based optimization scheme is then introduced, which approximates the centralized solution, leading to the development of distributed controllers for single-integrator agents. Finally, simulations validate the effectiveness of the proposed approach. Copyright © 2025, The Authors. All rights reserved.

关键词： Multi agent systems

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