This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. A small gain approach is used to evaluate the performance of the given quantum system. In order to get improved control performance, we propose two methods to design a coherent controller for the system. One is to formulate a static quantum controller by adding a controller Hamiltonian to the given system, and the other is to build a dynamic quantum controller which is directly coupled to the given system. Both controller design methods are given in terms of LMIs and a non-convex equality. Hence, a rank constrained LMI method is used as a numerical procedure. An illustrative example is given to demonstrate the proposed methods and also to make a performance comparison with different controller design methods. Results show that for the same uncertain quantum system, the dynamic quantum controller can offer an improvement in performance over the static quantum controller.
We propose a tube-based guaranteed cost model predictive controller considering a homothetic formulation for constrained linear systems subject to multiplicative structured norm-bounded uncertainties. It provides an upper bound to the general min-max model predictive control. The invariance property of the proposed tube holds for any arbitrary scaling. It yields a second-order cone programming problem which is less computationally expensive than standard semi-definite programming problems. We also present a numerical example with a comparative study among the proposed approach, an open-loop gu…
Guaranteed Cost Tracking for Uncertain Coupled Multi-agent Systems Using Consensus over a Directed Graph
The University of New South Wales at the Australian Defence Force Academy（澳大利亚国防军学院新南威尔士大学）；Australian National University（澳大利亚国立大学）；Southeast University（东南大学）
It is nontrivial to achieve global zero-error regulation for uncertain nonlinear systems. The underlying problem becomes even more challenging if mismatched uncertainties and unknown time-varying control gain are involved, yet certain performance specifications are also pursued. In this work, we present an adaptive control method, which, without the persistent excitation (PE) condition, is able to ensure global zero-error regulation with guaranteed output performance for parametric strict-feedback systems involving fast time-varying parameters in the feedback path and input path. The developme…
Katholieke Universiteit Leuven（鲁汶天主教大学）；University of Melbourne（墨尔本大学）
We propose a safety-guaranteed planning and control framework for unmanned surface vessels (USVs), using Gaussian processes (GPs) to learn uncertainties. The uncertainties encountered by USVs, including external disturbances and model mismatches, are potentially state-dependent, time-varying, and hard to capture with constant models. GP is a powerful learning-based tool that can be integrated with a model-based planning and control framework, which employs a Hamilton-Jacobi differential game formulation. Such a combination yields less conservative trajectories and safety-guaranteeing control s…
Guaranteed Time Control using Linear Matrix Inequalities
Universidade Federal de Minas Gerais（米纳斯吉拉斯联邦大学）；Instituto Federal de Minas Gerais（米纳斯吉拉斯联邦理工学院）；University of São Paulo（圣保罗大学）；Université Polytechnique Hauts-de-France（上法兰西理工大学）
A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled, the proposed method aims at propagating uncertainties effectively and optimizing control parameters to satisfy the probabilistic requirements directly. To achieve this, the sensitivities of violation probabilities are evaluated by the expansion coefficients and the fourth moment method for reliability analysis, after which an optimization that minimizes failur…
Towards Guaranteed Optimal PID Tuning for Uncertain Nonlinear Systems
State Key Laboratory of Mathematical Sciences, AMSS, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学国家重点实验室）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
This paper involves the innovative development of a symmetric Gauss-Seidel ADMM algorithm to solve the H-infinity guaranteed cost control problem. In the presence of parametric uncertainties, the H-infinity guaranteed cost control problem generally leads to the large-scale optimization. This is due to the exponential growth of the number of the extreme systems involved with respect to the number of parametric uncertainties. In this work, through a variant of the Youla-Kucera parameterization, the stabilizing controllers are parameterized in a convex set; yielding the outcome that the H-infinit…
University of California San Diego（加州大学圣地亚哥分校）；San Diego State University（圣地亚哥州立大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Safety is a critical concern for the success of urban air mobility, especially in dynamic and uncertain environments. This paper proposes a path planning algorithm based on RRT in conjunction with chance constraints in the presence of uncertain obstacles. The chance-constrained formulation for Gaussian distributed obstacles is developed by converting the probabilistic constraints to deterministic constraints in terms of distribution parameters. The probabilistic feasible region at every time step can be established through the simulation of the system state and the evaluation of convex constra…
This paper proposes an adaptive control allocation approach for uncertain over-actuated systems with actuator saturation. The proposed method does not require uncertainty estimation or a persistent excitation assumption. Using the element-wise non-symmetric projection algorithm, the adaptive parameters are restricted to satisfy certain optimality conditions leading to overall closed loop system stability. Furthermore, a sliding mode controller with a time-varying sliding surface, working in tandem with the adaptive control allocation, is proposed to guarantee the outer loop stability and refer…
University of Warwick（华威大学）；National University of Singapore（新加坡国立大学）；Macquarie University（麦考瑞大学）；Australian National University（澳大利亚国立大学）；Centre for Quantum Computation and Communication Technology, Australian Research Council（澳大利亚研究委员会量子计算与通信技术中心）
This work presents a solution to the adaptive tracking control of Euler Lagrange systems with guaranteed tracking and parameter estimation error convergence. Specifically a concurrent learning based update rule fused by the filtered version of the desired system dynamics in conjunction with a desired state based regression matrix has been utilized to ensure that both the position tracking error and parameter estimation error terms converge to origin exponentially. As the regression matrix used in proposed controller makes use of the desired versions of the system states, an initial, sufficient…
We design a controller for an agent whose mission is to reach a stationary target while avoiding a family of obstacles which are not known a-priori. The agent moves in the two dimensional plane with non-trivial double integrator dynamics and receives only local information from its surroundings. Under mild assumptions on the family of obstacles (smoothness, sufficient distance from each other, bounded curvature, etc), we prove that our control algorithm yields guaranteed obstacle avoidance and convergence to the target.
The H2 guaranteed cost decentralized control problem is investigated in this work. More specifically, on the basis of an appropriate H2 re-formulation that we put in place, the optimal control problem in the presence of parameter uncertainties is then suitably characterized by convex restriction and solved in parameter space. It is shown that a set of stabilizing decentralized controller gains for the uncertain system is parameterized in a convex set through appropriate convex restriction, and then an approximated conic optimization problem is constructed. This facilitates the use of the symme…
Optimal Control of Uncertain Nonlinear Quadratic Systems with Constrained Inputs
School of Computer；Biomedical Engineering, Universit\`a degli Studi Magna Gr cia di Catanzaro, Campus Universitario di Germaneto, 88100 Catanzaro, Italy
Set-based integration methods allow to prove properties of differential systems, which take into account bounded disturbances. The systems (either time-discrete, time-continuous or hybrid) satisfying such properties are said to be "robust". In the context of optimal control synthesis, the set-based methods are generally extensions of numerical optimal methods of two classes: first, methods based on convex optimization; second, methods based on the dynamic programming principle. Heymann et al. have recently shown that, for certain systems of low dimension, the second numerical method can give b…
Guaranteeing safety for robotic and autonomous systems in real-world environments is a challenging task that requires the mitigation of stochastic uncertainties. Control barrier functions have, in recent years, been widely used for enforcing safety related set-theoretic properties, such as forward invariance and reachability, of nonlinear dynamical systems. In this paper, we extend this rich framework to nonlinear discrete-time systems subject to stochastic uncertainty and propose a framework for assuring risk-sensitive safety in terms of coherent risk measures. To this end, we introduce risk …
University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）；Technical University of Munich（慕尼黑工业大学）；University of Toronto Robotics Institute（多伦多大学机器人研究所）；Vector Institute for Artificial Intelligence（矢量人工智能研究所）
In this work, we consider the problem of designing a safety filter for a nonlinear uncertain control system. Our goal is to augment an arbitrary controller with a safety filter such that the overall closed-loop system is guaranteed to stay within a given state constraint set, referred to as being safe. For systems with known dynamics, control barrier functions (CBFs) provide a scalar condition for determining if a system is safe. For uncertain systems, robust or adaptive CBF certification approaches have been proposed. However, these approaches can be conservative or require the system to have…
The development of control techniques to maintain vehicle stability under possible loss-of-control scenarios is essential to the safe deployment of autonomous ground vehicles in public scenarios. In this paper, we propose a tube-based guaranteed cost model predictive controller for autonomous vehicles able to avoid front and rear tire saturation and to track a provided reference trajectory up to the limits of handling of the vehicle. Such an approach ensures the vehicle will remain within its safe operational envelope; therefore, guaranteeing both stability and performance of the vehicle, incl…
Robust Beamforming Design for Coherent Distributed ISAC with Statistical RCS and Phase Synchronization Uncertainty
School of Electrical Engineering, Korea Advanced Institute of Science and Technology（韩国科学技术院电气工程学院）；Department of Electrical Engineering, Ulsan National Institute of Science and Technology（蔚山科学技术院电气工程系）；Centre for Wireless Communications, University of Oulu（奥卢大学无线通信中心）
