LMI conditions for topology preservation: applications to multi-agent tasks

International audienceIn this work we present several implementation strategies answering to different classical problems in multi-agent systems. The model under consideration consists of a discrete-time dynamics multi-agent system in which two agents are able to communicate when an algebraic relation between their states is satisfied. As emphasized in the literature, the connectivity of the communication network is essential for global coordination objectives. Thus, the primary goal of our methodology is to characterize the controllers that preserve a given topology allowing the global coordination. In a second step we choose the controller appropriated to the main agreement objective by solving a convex optimization problem associated to the minimization of a well-chosen cost function. Examples concerning full or partial consensus of agents with double integrator dynamics illustrate the implementation of the proposed methodology

Convex conditions on decentralized control for graph topology preservation

International audienceThe paper focuses on the preservation of a given graph topology which is usually chosen to ensure its connectivity. This is an essential ingredient allowing interconnected systems to accomplish tasks by using decentralized control strategies. We consider a networked system with discrete-time dynamics in which the subsystems are able to communicate if an algebraic relation between their states is satisfied. Each subsystem is called agent and the connected subsystems are called neighbors. The agents update their state in a decentralized manner by taking into account the neighbors' states. The characterization of the local control feedback gains ensuring topology preservation is provided. The results are based on invariance and set-theory and yield to conditions in Linear Matrix Inequality (LMI) form. The conditions for topology preservation are applied to an illustrative example concerning partial state consensus of agents with double integrator dynamics

Privacy-Preserving Stealthy Attack Detection in Multi-Agent Control Systems

This paper develops a glocal (global-local) attack detection framework to detect stealthy cyber-physical attacks, namely covert attack and zero-dynamics attack, against a class of multi-agent control systems seeking average consensus. The detection structure consists of a global (central) observer and local observers for the multi-agent system partitioned into clusters. The proposed structure addresses the scalability of the approach and the privacy preservation of the multi-agent system's state information. The former is addressed by using decentralized local observers, and the latter is achieved by imposing unobservability conditions at the global level. Also, the communication graph model is subject to topology switching, triggered by local observers, allowing for the detection of stealthy attacks by the global observer. Theoretical conditions are derived for detectability of the stealthy attacks using the proposed detection framework. Finally, a numerical simulation is provided to validate the theoretical findings.Comment: to appear in IEEE CD

Optimal Control Design for Multiterminal HVDC

This thesis proposes an optimal-control based design for distributed frequency control in multi-terminal high voltage direct current (MTDC) systems. The current power grid has become overstressed by rapid growth in the demand for electric power and penetration of renewable energy. To address these challenges, MTDC technology has been developed, which has the potential to increase the flexibility and reliability of power transmission in the grid. Several control strategies have been proposed to regulate the MTDC system and its interaction with connected AC systems. However, all the existing control strategies are based on proportional and integral (PI) control with predetermined controller structures. The objective of the thesis is to first determine if existing control structures are optimal, and if improved controller structures can be developed.The thesis proposes a general framework to determine the optimal structure for the control system in MTDC transmission through optimal feedback control. The proposed method is validated and demonstrated using an example of frequency control in a MTDC system connecting five AC areas

Distributed optimal and predictive control methods for networks of dynamic systems

Several recent approaches to distributed control design over networks of interconnected dynamic systems rely on certain assumptions, such as identical subsystem dynamics, absence of dynamical couplings, linear dynamics and undirected interaction schemes. In this thesis, we investigate systematic methods for relaxing a number of simplifying factors leading to a unifying approach for solving general distributed-control stabilization problems of networks of dynamic agents. We show that the gain-margin property of LQR control holds for complex multiplicative input perturbations and a generic symmetric positive definite input weighting matrix. Proving also that the potentially non-simple structure of the Laplacian matrix can be neglected for stability analysis and control design, we extend two well-known distributed LQR-based control methods originally established for undirected networks of identical linear systems, to the directed case. We then propose a distributed feedback method for tackling large-scale regulation problems of a general class of interconnected non-identical dynamic agents with undirected and directed topology. In particular, we assume that local agents share a minimal set of structural properties, such as input dimension, state dimension and controllability indices. Our approach relies on the solution of certain model matching type problems using local linear state-feedback and input matrix transformations which map the agent dynamics to a target system, selected to minimize the joint control effort of the local feedback-control schemes. By adapting well-established distributed LQR control design methodologies to our framework, the stabilization problem of a network of non-identical dynamical agents is solved. We thereafter consider a networked scheme synthesized by multiple agents with nonlinear dynamics. Assuming that agents are feedback linearizable in a neighborhood near their equilibrium points, we propose a nonlinear model matching control design for stabilizing networks of multiple heterogeneous nonlinear agents. Motivated by the structure of a large-scale LQR optimal problem, we propose a stabilizing distributed state-feedback controller for networks of identical dynamically coupled linear agents. First, a fully centralized controller is designed which is subsequently substituted by a distributed state-feedback gain with sparse structure. The control scheme is obtained byoptimizing an LQR performance index with a tuning parameter utilized to emphasize/deemphasize relative state difference between coupled systems. Sufficient conditions for stability of the proposed scheme are derived based on the inertia of a convex combination of two Hurwitz matrices. An extended simulation study involving distributed load frequency control design of a multi-area power network, illustrates the applicability of the proposed method. Finally, we propose a fully distributed consensus-based model matching scheme adapted to a model predictive control setting for tackling a structured receding horizon regulation problem

Mathematical optimization and robust control synthesis

Nowadays, performance requirements imposed on system control designs have become more and more complicated. For many problems, it is very hard or even impossible to obtain analytic solutions. In recent years, powerful numerical computational tools for solving mathematical programming/optimization problems have been developed. This makes it possible to formulate control design problems as mathematical programming problems and then solve them using numerical optimization techniques. In this thesis, we show that two classes of important robust control design problems can be tackled by employing some newly-emerged mathematical optimization techniques.;In the first part of the thesis, we present a methodology to address the general multiobjective (GMO) control problem involving the ℓ 1 norm, H2 norm, Hinfinity norm and time-domain constraint (TDC). We show that the auxiliary problem resulting after imposing a regularizing condition always admits an optimal solution. Suboptimal solutions with performance arbitrarily close to the optimal cost can be obtained by constructing two sequences of finite dimensional convex optimization problems whose objective values converge to the optimum from below and above. Numerical implementation of the proposed methodology is discussed and several numerical examples are presented to illustrate the effectiveness of the proposed methodology.;In the second part, we consider the integrated parameter and control (IPC) design problem where the system structure parameters enter the state-space representation of the system in a rational manner. Converging finite-dimensional sub-optimal problems are constructed and solved via a linear relaxation technique, whereby a global optimal solution to the IPC problem is computed within any given performance tolerance. Two numerical examples are provided

COOPERATIVE AND CONSENSUS-BASED CONTROL FOR A TEAM OF MULTI-AGENT SYSTEMS

Cooperative control has attracted a noticeable interest in control systems community due to its numerous applications in areas such as formation flying of unmanned aerial vehicles, cooperative attitude control of spacecraft, rendezvous of mobile robots, unmanned underwater vehicles, traffic control, data network congestion control and routing. Generally, in any cooperative control of multi-agent systems one can find a set of locally sensed information, a communication network with limited bandwidth, a decision making algorithm, and a distributed computational capability. The ultimate goal of cooperative systems is to achieve consensus or synchronization throughout the team members while meeting all communication and computational constraints. The consensus problem involves convergence of outputs or states of all agents to a common value and it is more challenging when the agents are subjected to disturbances, measurement noise, model uncertainties or they are faulty. This dissertation deals with the above mentioned challenges and has developed methods to design distributed cooperative control and fault recovery strategies in multi-agent systems. Towards this end, we first proposed a transformation for Linear Time Invariant (LTI) multi-agent systems that facilitates a systematic control design procedure and make it possible to use powerful Lyapunov stability analysis tool to guarantee its consensus achievement. Moreover, Lyapunov stability analysis techniques for switched systems are investigated and a novel method is introduced which is well suited for designing consensus algorithms for switching topology multi-agent systems. This method also makes it possible to deal with disturbances with limited root mean square (RMS) intensities. In order to decrease controller design complexity, a iii method is presented which uses algebraic connectivity of the communication network to decouple augmented dynamics of the team into lower dimensional parts, which allows one to design the consensus algorithm based on the solution to an algebraic Riccati equation with the same order as that of agent. Although our proposed decoupling method is a powerful approach to reduce the complexity of the controller design, it is possible to apply classical pole placement methods to the transformed dynamics of the team to develop and obtain controller gains. The effects of actuator faults in consensus achievement of multi-agent systems is investigated. We proposed a framework to quantitatively study actuator loss-of-effectiveness effects in multi-agent systems. A fault index is defined based on information on fault severities of agents and communication network topology, and sufficient conditions for consensus achievement of the team are derived. It is shown that the stability of the cooperative controller is linked to the fault index. An optimization problem is formulated to minimize the team fault index that leads to improvements in the performance of the team. A numerical optimization algorithm is used to obtain the solutions to the optimal problem and based on the solutions a fault recovery strategy is proposed for both actuator saturation and loss-of-effectiveness fault types. Finally, to make our proposed methodology more suitable for real life scenarios, the consensus achievement of a multi-agent team in presence of measurement noise and model uncertainties is investigated. Towards this end, first a team of LTI agents with measurement noise is considered and an observer based consensus algorithm is proposed and shown that the team can achieve H∞ output consensus in presence of both bounded RMS disturbance input and measurement noise. In the next step a multi-agent team with both linear and Lipschitz nonlinearity uncertainties is studied and a cooperative control algorithm is developed. An observer based approach is also developed to tackle consensus achievement problem in presence of both measurement noise and model uncertainties

Inter-area oscillation damping in large scale power systems with unified power flow controllers

Power system oscillations occur in power networks as a result of contingencies such as faults or sudden changes in load or generation. They are detrimental to the operation of the system since they affect system stability and the optimal power flow through it. These oscillations do not usually damp out in tie-lines unless certain controls are applied to the system. Local and inter-area oscillations have traditionally been controlled by Power System Stabilizers (PSS). However, Flexible Alternating Current Transmission Controllers (FACTS) have significant potential as alternatives to PSS. The main goal of this research is to damp inter-area oscillations by Unified Power Flow Controllers (UPFC). UPFC is a series-shunt FACTS device which is used for purposes such as the control of active and reactive power flow through the corridors of the system. However, using supplementary controls and proper coordination of UPFCs, they can be used for fast damping of inter-area oscillations in multi-area power systems --Abstract, page iv