This paper deals with the trajectory tracking control problem for a class of bilinear systems with unmeasurable states and unknown parameters. Firstly, a full-information controller is suggested that guarantees global tracking under a persistency of excitation (PE) condition on the desired trajectories. Next, a model-based observer is designed for the system, which is further developed into an adaptive observer through dynamic regressor and mixing (DREM) parameter estimator. This enables global estimation under a weaker convergence condition where the regressor is PE. The estimated states and parameters are then replaced in the full-information controller, instead of their respective unavailable states and parameters, to construct the output feedback controller and its adaptive version. The proposed algorithm is applied to control lossless power factor precompensator (PFP) circuit with an unmeasurable input current and an unknown load conductance.
Global Tracking Passivity--based PI Control of Bilinear Systems and its Application to the Boost and Modular Multilevel Converters
Laboratoire de Signaux et Systémes, Supélec（信号与系统实验室，苏佩莱克高等学院）；Dipartimento Ingegneria dell’Informazione, Università Politecnica delle Marche（信息技术工程学院，马尔凯理工学院）；Norwegian University of Science and Technology（挪威科技大学）
This paper is concerned with a bilinear control problem for enhancing convection-cooling via an incompressible velocity field. Both optimal open-loop control and closed-loop feedback control designs are addressed. First and second order optimality conditions for characterizing the optimal solution are discussed. In particular, the method of instantaneous control is applied to establish the feedback laws. Moreover, the construction of feedback laws is also investigated by directly utilizing the optimality system with appropriate numerical discretization schemes. Computationally, it is much easi…
In this work, a predictive control framework is presented for feedback stabilization of nonlinear systems. To achieve this, we integrate Koopman operator theory with Lyapunov-based model predictive control (LMPC). The main idea is to transform nonlinear dynamics from state-space to function space using Koopman eigenfunctions - for control affine systems this results in a bilinear model in the (lifted) function space. Then, a predictive controller is formulated in Koopman eigenfunction coordinates which uses an auxiliary Control Lyapunov Function (CLF) based bounded controller as a constraint t…
The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs for dynamic systems in which the nonlinearity belongs to Lipschitz functions have been proposed. However, most of them only focus on output feedback and consequently, state feedback design remains less developed. To that end, this paper is dedicated to the problem of full-state feedback controller design for discrete-time Lipschitz nonlinear systems. In add…
An Experimental Comparison of Sliding Mode and Immersion and Invariance Adaptive Controllers forPosition-feedback Tracking of a Simple Mechanical System with Friction
Tecnológico Nacional de México / I.T. de La Laguna（墨西哥国立理工学院拉古纳技术学院）；Tecnológico Nacional de México / I.T. de La Paz（墨西哥国立理工学院拉巴斯技术学院）；Departamento de Ingeniería Eléctrica y Electrónica / I.T. Autónomo de México（墨西哥自治理工学院电气与电子工程系）
We study cooperative output feedback tracking control of stochastic linear heterogeneous leader-following multi-agent systems. Each agent has a continuous-time linear heterogeneous dynamics with incompletely measurable state, and there are additive and multiplicative noises along with information exchange among agents. We propose a set of admissible distributed observation strategies for estimating the leader's and the followers' states, and a set of admissible cooperative output feedback control strategies based on the certainty equivalence principle. By output regulation theory and stochasti…
Adaptive fuzzy control strategies are established to achieve global prescribed performance with prescribed-time convergence for strict-feedback systems with mismatched uncertainties and unknown nonlinearities. Firstly, to quantify the transient and steady performance constraints of the tracking error, a class of prescribed-time prescribed performance functions are designed, and a novel error transformation function is introduced to remove the initial value constraints and solve the singularity problem in existing works. Secondly, based on dynamic surface control methods, controllers with or wi…
Robust Global Position and Heading Tracking on SE(3) via Saturated Hybrid Feedback
Institute of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院机械工程学院）；Institute for Systems and Robotics, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院系统与机器人研究所）
This paper presents a novel Lagrangian approach to attitude tracking for rigid spacecraft using unit quaternions, where the motion equations of a spacecraft are described by a four degrees of freedom Lagrangian dynamics subject to a holonomic constraint imposed by the norm of a unit quaternion. The basic energy-conservation property as well as some additional useful properties of the Lagrangian dynamics are explored, enabling to develop quaternion-based attitude tracking controllers by taking full advantage of a broad class of tracking control designs for mechanical systems based on energy-sha…
We consider the problem of designing a state feedback control law to achieve nonovershooting tracking for feedback linearisable multiple-input multiple-output nonlinear systems. The reference signal is assumed to be obtained from a linear exosystem. The design method adopts known methods for the nonovershooting tracking of linear systems and extends them to the output regulation of feedback linearisable nonlinear systems. The method accommodates arbitrary initial conditions and offers design choice of the tracking convergence speed.
The isoline tracking of this work is concerned with the control design for a sensing vehicle to track a desired isoline of an unknown scalar field. To this end, we propose a simple PI-like controller for a Dubins vehicle in the GPS-denied environments. Our key idea lies in the design of a novel sliding surface based error in the standard PI controller. For the circular field, we show that the P-like controller can globally regulate the vehicle to the desired isoline with the steady-state error that can be arbitrarily reduced by increasing the P gain, and is eliminated by the PI-like controller…
Motivated by the goal of having a building block in the direct design of data-driven controllers for nonlinear systems, we show how, for an unknown discrete-time bilinear system, the data collected in an offline open-loop experiment enable us to design a feedback controller and provide a guaranteed under-approximation of its basin of attraction. Both can be obtained by solving a linear matrix inequality for a fixed scalar parameter, and possibly iterating on different values of that parameter. The results of this data-based approach are compared with the ideal case when the model is known perf…
There is a growing interest in data-driven control of nonlinear systems over the last years. In contrast to related works, this paper takes a step back and aims to solve the output matching problem, a problem closely related to the reference tracking control problem, for a broader class of nonlinear systems called output-generalized bilinear, thereby offering a new direction to explore for data-driven control of nonlinear systems. It is shown that discrete time linear parameter-varying systems are included in this model class, with affine systems easily shown to also be included. This paper pr…
This paper develops a new model reference adaptive control (MRAC) framework using partial-state feedback for solving a multivariable adaptive output tracking problem. The developed MRAC scheme has full capability to deal with plant uncertainties for output tracking and has desired flexibility to combine the advantages of full-state feedback MRAC and output feedback MRAC. With such a new control scheme, the plant-model matching condition is achievable as with an output or state feedback MRAC design. A stable adaptive control scheme is developed based on LDS decomposition of the plant high-frequ…
A stochastic optimal control based model with velocity tracking and internal feedback for saccadic eye movements is presented in this paper. Recent evidence from neurophysiological studies of superior colliculus suggests the presence of a dynamic input to the saccade generation system that encodes saccade velocity, rather than just the saccade amplitude and direction. The new evidence makes it imperative to test if saccade control can use a desired velocity input which is the basis for the proposed velocity tracking model. The model is validated using behavioral data of saccades generated by h…
This paper proposes a data-driven state feedback controller that enables reference tracking for nonlinear discrete-time systems. The controller is designed based on the identified inverse model of the system and a given reference model, assuming that the identification of the inverse model is carried out using only the system's state/input measurements. When its results are provided, we present conditions that guarantee a certain level of reference tracking performance, regardless of the identification method employed for the inverse model. Specifically, when Gaussian process regression (GPR) …
Probabilistic Data Association-Feedback Particle Filter for Multiple Target Tracking Applications
Coordinated Science Laboratory and the Department of Mechanical Science and Engineering at the University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校协同科学实验室与机械科学与工程系）
This paper proposes a feedback linearizing law for single-track dynamic models, allowing the design of a trajectory tracking controller exploiting linear control theory. The main characteristics of this algorithm are its simplicity, its independence from any vehicle model parameter, apart from the position of the center of mass, and its robustness. In particular, a numerical bifurcation analysis demonstrates that, for physically meaningful values of the center of mass deviation, the equilibrium is structurally asymptotically stable. Experimental results, concerning the linearising law and its …
This paper presents a novel adaptive feedforward controller design for reset control systems. The combination of feedforward and reset feedback control promises high performance as the feedforward guarantees reference tracking, while the non-linear feedback element rejects disturbances. To overcome inevitable model mismatches, the feedforward controller adapts to increase precision in reference tracking. Where linear existing adaptive feedforward controllers do not guarantee convergence in the presence of reset, this work presents a novel adaptive law based on converging and diverging regions …
Southern University of Science and Technology（南方科技大学）
This paper studies stabilizer design for position-controlled humanoid robots. Stabilizers are an essential part for position-controlled humanoids, whose primary objective is to adjust the control input sent to the robot to assist the tracking controller to better follow the planned reference trajectory. To achieve this goal, this paper develops a novel force-feedback based whole-body stabilizer that fully exploits the six-dimensional force measurement information and the whole-body dynamics to improve tracking performance. Relying on rigorous analysis of whole-body dynamics of position-control…
A Koopman Set-Membership Approach for Nonlinear Data-Driven Control with Stability Guarantees
University of Stuttgart（斯图加特大学）；Center for Integrated Quantum Science and Technology (IQST), University of Stuttgart（斯图加特大学综合量子科学与技术中心）；University of Oxford（牛津大学）
We study the problem of optimal state-feedback tracking control for unknown discrete-time deterministic systems with input constraints. To handle input constraints, state-of-art methods utilize a certain nonquadratic stage cost function, which is sometimes limiting real systems. Furthermore, it is well known that Policy Iteration (PI) and Value Iteration (VI), two widely used algorithms in data-driven control, offer complementary strengths and weaknesses. In this work, a two-step transformation is employed, which converts the constrained-input optimal tracking problem to an unconstrained augme…
Stable Gaussian Process based Tracking Control of Euler-Lagrange Systems
Chair of Information-oriented Control (ITR), Department of Electrical and Computer Engineering, Technical University of Munich（信息导向控制研究所（ITR），电气与计算机工程系，慕尼黑技术大学）；Adaptive Systems Laboratory, Department of Electrical and Computer Engineering, University of Waterloo（自适应系统实验室，电气与计算机工程系，滑铁卢大学）
Western University（韦仕敦大学）；Lakehead University（湖首大学）
We introduce a new hybrid control strategy, which is conceptually different from the commonly used synergistic hybrid approaches, to efficiently deal with the problem of the undesired equilibria that precludes smooth vectors fields on $SO(3)$ from achieving global stability. The key idea consists in constructing a suitable potential function on $SO(3)\times \mathbb{R}$ involving an auxiliary scalar variable, with flow and jump dynamics, which keeps the state away from the undesired critical points while, at the same time, guarantees a decrease of the potential function over the flows and jumps…
Learning and Control Beyond Linearity: Towards a Non-asymptotic Theory for Bilinear Systems
Cornell University（康奈尔大学）；Imperial College London（帝国理工学院）；University of Stuttgart（斯图加特大学）；University of Washington Seattle（华盛顿大学西雅图分校）；Amazon Inc.（亚马逊公司）
