47 research outputs found
Control Theory: A Mathematical Perspective on Cyber-Physical Systems
Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control
Output Consensus Control for Heterogeneous Multi-Agent Systems
We study distributed output feedback control of a heterogeneous multi-agent system (MAS), consisting of N different continuous-time linear dynamical systems. For achieving output consensus, a virtual reference model is assumed to generate the desired trajectory for which the MAS is required to track and synchronize. A full information (FI) protocol is assumed for consensus control. This protocol includes information exchange with the feed-forward signals. In this dissertation we study two different kinds of consensus problems. First, we study the consensus control over the topology involving time delays and prove that consensus is independent of delay lengths. Second, we study the consensus under communication constraints. In contrast to the existing work, the reference trajectory is transmitted to only one or a few agents and no local reference models are employed in the feedback controllers thereby eliminating synchronization of the local reference models. Both significantly lower the communication overhead. In addition, our study is focused on the case when the available output measurements contain only relative information from the neighboring agents and reference signal. Conditions are derived for the existence of distributed output feedback control protocols, and solutions are proposed to synthesize the stabilizing and consensus control protocol over a given connected digraph. It is shown that the H-inf loop shaping and LQG/LTR techniques from robust control can be directly applied to design the consensus output feedback control protocol. The results in this dissertation complement the existing ones, and are illustrated by a numerical example. The MAS approach developed in this dissertation is then applied to the development of autonomous aircraft traffic control system. The development of such systems have already started to replace the current clearance-based operations to trajectory based operations. Such systems will help to reduce human errors, increase efficiency, provide safe flight path, and improve the performance of the future flight
Problems in Control, Estimation, and Learning in Complex Robotic Systems
In this dissertation, we consider a range of different problems in systems, control, and learning theory and practice. In Part I, we look at problems in control of complex networks. In Chapter 1, we consider the performance analysis of a class of linear noisy dynamical systems. In Chapter 2, we look at the optimal design problems for these networks. In Chapter 3, we consider dynamical networks where interactions between the networks occur randomly in time. And in the last chapter of this part, in Chapter 4, we look at dynamical networks wherein coupling between the subsystems (or agents) changes nonlinearly based on the difference between the state of the subsystems. In Part II, we consider estimation problems wherein we deal with a large body of variables (i.e., at large scale). This part starts with Chapter 5, in which we consider the problem of sampling from a dynamical network in space and time for initial state recovery. In Chapter 6, we consider a similar problem with the difference that the observations instead of point samples become continuous observations that happen in Lebesgue measurable observations. In Chapter 7, we consider an estimation problem in which the location of a robot during the navigation is estimated using the information of a large number of surrounding features and we would like to select the most informative features using an efficient algorithm. In Part III, we look at active perception problems, which are approached using reinforcement learning techniques. This part starts with Chapter 8, in which we tackle the problem of multi-agent reinforcement learning where the agents communicate and classify as a team. In Chapter 9, we consider a single agent version of the same problem, wherein a layered architecture replaces the architectures of the previous chapter. Then, we use reinforcement learning to design the meta-layer (to select goals), action-layer (to select local actions), and perception-layer (to conduct classification)
Robust Distributed Stabilization of Interconnected Multiagent Systems
Many large-scale systems can be modeled as groups of individual dynamics, e.g., multi-vehicle systems, as well as interconnected multiagent systems, power systems and biological networks as a few examples. Due to the high-dimension and complexity in configuration of these infrastructures, only a few internal variables of each agent might be measurable and the exact knowledge of the model might be unavailable for the control design purpose. The collective objectives may range from consensus to decoupling, stabilization, reference tracking, and global performance guarantees. Depending on the objectives, the designer may choose agent-level low-dimension or multiagent system-level high-dimension approaches to develop distributed algorithms. With an inappropriately designed algorithm, the effect of modeling uncertainty may propagate over the communication and coupling topologies and degrade the overall performance of the system. We address this problem by proposing single- and multi-layer structures. The former is used for both individual and interconnected multiagent systems. The latter, inspired by cyber-physical systems, is devoted to the interconnected multiagent systems. We focus on developing a single control-theoretic tool to be used for the relative information-based distributed control design purpose for any combinations of the aforementioned configuration, objective, and approach. This systematic framework guarantees robust stability and performance of the closed-loop multiagent systems. We validate these theoretical results through various simulation studies
Distance-Based Formation Control of Multi-Agent Systems
This Ph.D. dissertation studies the distance-based formation control of multi-agent systems. A new approach to the distance-based formation control problem is proposed in this thesis. We formulated distance-based formation in a nonlinear optimal control framework and used the state-dependent Riccati equation (SDRE) technique as the primary tool for solving the optimal control problem. In general, a distance-based formation can be undirected, where distance constraints between pairs of agents are actively controlled by both adjacent agents, or directed, where just one of the neighboring agents is responsible for maintaining the desired distance. This thesis presents both, undirected and directed formations, and provides extensive simulations to verify the theoretical results.
For undirected topologies, we studied the formation control problem where we showed that the proposed control law results in the global asymptotic stability of the closed-loop system under certain conditions. The formation tracking problem was studied, and the uniform ultimate boundedness of the solutions is rigorously proven. The proposed method guarantees collision avoidance among neighboring agents and prevents depletion of the agents' energy. In the directed distance-based formation control case, we developed a distributed, hierarchical control scheme for a particular class of directed graphs, namely directed triangulated and trilateral Laman graphs. The proposed controller ensures the global asymptotic stability of the desired formation. Rigorous stability analyses are carried out in all cases. Moreover, we addressed the flip-ambiguity issue by using the signed area and signed volume constraints. Additionally, we introduced a performance index for a formation mission that can indicate the controller's overall performance.
We also studied the distance-based formation control of nonlinear agents. We proposed a method that can guarantee asymptotic stability of the distance-based formation for a broad category of nonlinear systems. Furthermore, we studied a distance-based formation control of uncertain nonlinear agents. Based on the combination of integral sliding mode control (ISMC) theory with the SDRE method, we developed a robust optimal formation control scheme that guarantees asymptotic stability of the desired distance-based formation in the presence of bounded uncertainties. We have shown that the proposed controller can compensate for the effect of uncertainties in individual agents on the overall formation
Control Of Nonh=holonomic Systems
Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles\u27 kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs
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
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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
New decentralized algorithms for spacecraft formation control based on a cyclic approach
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 223-231).When considering the formation control problem for large number of spacecraft, the advantages of implementing control approaches with a centralized coordination mechanism can be outpaced by the risks associated with having a primary vital control unit. Additionally, in formations with a large number of spacecraft, a centralized approach implies an inherent difficulty in gathering and broadcasting information from/to the overall system. Therefore, there is a need to explore efficient decentralized control approaches. In this thesis a new approach to spacecraft formation control is formulated by exploring and enhancing the recent results on the theory of convergence to geometric patterns and exploring the analysis of this approach using the tools of contracting theory. First, an extensive analysis of the cyclic pursuit dynamics leads to developing control laws useful for spacecraft formation flight which, as opposed to the most common approaches in the literature, do not track fixed relative trajectories and therefore, reduce the global coordination requirements. The proposed approach leads to local control laws that verify global emergent behaviors specified as convergence to a particular manifold. A generalized analysis of such control approach by using tools of partial contraction theory is performed, producing important convergence results. By applying and extending results from the theory of partially contracting systems, an approach to deriving sufficient conditions for convergence is formulated. Its use is demonstrated by analyzing several examples and obtaining global convergence results for nonlinear, time varying and more complex interconnected distributed controllers. Experimental results of the implementation of these algorithms were obtained using the SPHERES testbed on board the International Space Station, validating many of the important properties of this decentralized control approach. They are believed to be the first implementation of decentralized formation flight in space. To complement the results we also consider a short analysis of the advantages of decentralized versus centralized approach by comparing the optimal performance and the effects of complexity and robustness for different architectures and address the issues of implementing decentralized algorithms in a inherently coupled system like the Electromagnetic Formation Flight.by Jaime Luís Ramírez Riberos.Ph.D
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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