Agent-level optimal LQG control of dynamically decoupled systems with processing delays

We consider the problem of controlling a set of dynamically decoupled plants where the plants' subcontrollers communicate with each other according to a fixed and known network topology. We assume the communication to be instantaneous but there is a fixed processing delay associated with incoming transmissions. We provide explicit closed-form expressions for the optimal decentralized controller under these communication constraints and using standard LQG assumptions for the plants and cost function. Although this problem is convex, it is challenging due to the irrationality of continuous-time delays and the decentralized information-sharing pattern. We show that the optimal subcontrollers each have an observer-regulator architecture containing LTI and FIR blocks and we characterize the signals that subcontrollers should transmit to each other across the network

Optimal Control of Multi-Agent Systems with Processing Delays

In this article, we consider a cooperative control problem involving \blue{a heterogeneous network of dynamically decoupled continuous-time linear plants. The (output-feedback) controllers for each plant may communicate with each other according to a fixed and known transitively closed directed graph. Each transmission incurs a fixed and known time delay.} We provide an explicit closed-form expression for the optimal decentralized controller and its associated cost under these communication constraints and standard linear quadratic Gaussian (LQG) assumptions for the plants and cost function. We find the exact solution without discretizing or otherwise approximating the delays. We also present an implementation of each sub-controller that is efficiently computable, and is composed of standard finite-dimensional linear time-invariant (LTI) and finite impulse response (FIR) components, and has an intuitive observer-regulator architecture reminiscent of the classical separation principle

Optimal Decentralized State-Feedback Control with Sparsity and Delays

This work presents the solution to a class of decentralized linear quadratic state-feedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition of the noise history, the control problem is split into independent subproblems that are solved using dynamic programming. The approach presented herein both unifies and generalizes many existing results

The ℋ_2 Control Problem for Quadratically Invariant Systems With Delays

This technical note gives a new solution to the output feedback ℋ_2 problem for quadratically invariant communication delay patterns. A characterization of all stabilizing controllers satisfying the delay constraints is given and the decentralized ℋ_2 problem is cast as a convex model matching problem. The main result shows that the model matching problem can be reduced to a finite-dimensional quadratic program. A recursive state-space method for computing the optimal controller based on vectorization is given

STABILITY AND PERFORMANCE OF NETWORKED CONTROL SYSTEMS

Network control systems (NCSs), as one of the most active research areas, are arousing comprehensive concerns along with the rapid development of network. This dissertation mainly discusses the stability and performance of NCSs into the following two parts. In the first part, a new approach is proposed to reduce the data transmitted in networked control systems (NCSs) via model reduction method. Up to our best knowledge, we are the first to propose this new approach in the scientific and engineering society. The "unimportant" information of system states vector is truncated by balanced truncation method (BTM) before sending to the networked controller via network based on the balance property of the remote controlled plant controllability and observability. Then, the exponential stability condition of the truncated NCSs is derived via linear matrix inequality (LMI) forms. This method of data truncation can usually reduce the time delay and further improve the performance of the NCSs. In addition, all the above results are extended to the switched NCSs. The second part presents a new robust sliding mode control (SMC) method for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise (Wiener process). The key features of the proposed method are to apply singular value decomposition (SVD) to all structural uncertainties, to introduce adjustable parameters for control design along with the SMC method, and new Lyapunov-type functional. Then, a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems are derived via linear matrix inequality (LMI) forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1 by the proposed control rule. Furthermore, the novel Lyapunov-type functional for the uncertain stochastic systems is used to design a new robust control for the general case where the derivative of time-varying delay can be any bounded value (e.g., greater than one). It is theoretically proved that the conservatism of the proposed method is less than the previous methods. All theoretical proofs are presented in the dissertation. The simulations validate the correctness of the theoretical results and have better performance than the existing results

Contributions to shared control and coordination of single and multiple robots

L’ensemble des travaux présentés dans cette habilitation traite de l'interface entre un d'un opérateur humain avec un ou plusieurs robots semi-autonomes aussi connu comme le problème du « contrôle partagé ».Le premier chapitre traite de la possibilité de fournir des repères visuels / vestibulaires à un opérateur humain pour la commande à distance de robots mobiles.Le second chapitre aborde le problème, plus classique, de la mise à disposition à l’opérateur d’indices visuels ou de retour haptique pour la commande d’un ou plusieurs robots mobiles (en particulier pour les drones quadri-rotors).Le troisième chapitre se concentre sur certains des défis algorithmiques rencontrés lors de l'élaboration de techniques de coordination multi-robots.Le quatrième chapitre introduit une nouvelle conception mécanique pour un drone quadrirotor sur-actionné avec pour objectif de pouvoir, à terme, avoir 6 degrés de liberté sur une plateforme quadrirotor classique (mais sous-actionné).Enfin, le cinquième chapitre présente une cadre général pour la vision active permettant, en optimisant les mouvements de la caméra, l’optimisation en ligne des performances (en terme de vitesse de convergence et de précision finale) de processus d’estimation « basés vision »