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Register a new userPeriodic event-triggered output regulation for linear multi-agent systems
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This study considers the problem of periodic event-triggered (PET) cooperative output regulation for a class of linear multi-agent systems. The advantage of the PET output regulation is that the data transmission and triggered condition are only needed to be monitored at discrete sampling instants. It is assumed that only a small number of agents can have access to the system matrix and states of the leader. Meanwhile, the PET mechanism is considered not only in the communication between various agents, but also in the sensor-to-controller and controller-to-actuator transmission channels for each agent. The above problem set-up will bring some challenges to the controller design and stability analysis. Based on a novel PET distributed observer, a PET dynamic output feedback control method is developed for each follower. Compared with the existing works, our method can naturally exclude the Zeno behavior, and the inter-event time becomes multiples of the sampling period. Furthermore, for every follower, the minimum inter-event time can be determined textit{a prior}, and computed directly without the knowledge of the leader information. An example is given to verify and illustrate the effectiveness of the new design scheme.
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In linear systems theory its a well known fact that a regulator given by the cascade of an oscillatory dynamics, driven by some regulated variables, and of a stabiliser stabilising the cascade of the plant and of the oscillators has the ability of blocking on the steady state of the regulated variables any harmonics matched with the ones of the oscillators. This is the well-celebrated internal model principle. In this paper we are interested to follow the same design route for a controlled plant that is a nonlinear and periodic system with period T : we add a bunch of linear oscillators, embedding n o harmonics that are multiple of 2$pi$/T , driven by a regulated variable of the nonlinear system, we look for a stabiliser for the nonlinear cascade of the plant and the oscillators, and we study the asymptotic properties of the resulting closedloop regulated variable. In this framework the contributions of the paper are multiple: for specific class of minimum-phase systems we present a systematic way of designing a stabiliser, which is uniform with respect to n o , by using a mix of high-gain and forwarding techniques; we prove that the resulting closed-loop system has a periodic steady state with period T with a domain of attraction not shrinking with n o ; similarly to the linear case, we also show that the spectrum of the steady state closed-loop regulated variable does not contain the n harmonics embedded in the bunch of oscillators and that the L 2 norm of the regulated variable is a monotonically decreasing function of n o. The results are robust, namely the asymptotic properties on the regulated variable hold also in presence of any uncertainties in the controlled plant not destroying closed-loop stability.
Recently, there have been efforts towards understanding the sampling behaviour of event-triggered control (ETC), for obtaining metrics on its sampling performance and predicting its sampling patterns. Finite-state abstractions, capturing the sampling behaviour of ETC systems, have proven promising in this respect. So far, such abstractions have been constructed for non-stochastic systems. Here, inspired by this framework, we abstract the sampling behaviour of stochastic narrow-sense linear periodic ETC (PETC) systems via Interval Markov Chains (IMCs). Particularly, we define functions over sequences of state-measurements and interevent times that can be expressed as discounted cumulative sums of rewards, and compute bounds on their expected values by constructing appropriate IMCs and equipping them with suitable rewards. Finally, we argue that our results are extendable to more general forms of functions, thus providing a generic framework to define and study various ETC sampling indicators.
In this paper, an optimal output consensus problem is studied for discrete-time linear multiagent systems subject to external disturbances. Each agent is assigned with a local cost function which is known only to itself. Distributed protocols are to be designed to guarantee an output consensus for these high-order agents and meanwhile minimize the aggregate cost as the sum of these local costs. To overcome the difficulties brought by high-order dynamics and external disturbances, we develop an embedded design and constructively present a distributed rule to solve this problem. The proposed control includes three terms: an optimal signal generator under a directed information graph, an observer-based compensator to reject these disturbances, and a reference tracking controller for these linear agents. It is shown to solve the formulated problem with some mild assumptions. A numerical example is also provided to illustrate the effectiveness of our proposed distributed control laws.
This paper investigates an optimal consensus problem for a group of uncertain linear multi-agent systems. All agents are allowed to possess parametric uncertainties that range over an arbitrarily large compact set. The goal is to collectively minimize a sum of local costs in a distributed fashion and finally achieve an output consensus on this optimal point using only output information of agents. By adding an optimal signal generator to generate the global optimal point, we convert this problem to several decentralized robust tracking problems. Output feedback integral control is constructively given to achieve an optimal consensus under a mild graph connectivity condition. The efficacy of this control is verified by a numerical example.
This paper proposes decentralized resource-aware coordination schemes for solving network optimization problems defined by objective functions which combine locally evaluable costs with network-wide coupling components. These methods are well suited for a group of supervised agents trying to solve an optimization problem under mild coordination requirements. Each agent has information on its local cost and coordinates with the network supervisor for information about the coupling term of the cost. The proposed approach is feedback-based and asynchronous by design, guarantees anytime feasibility, and ensures the asymptotic convergence of the network state to the desired optimizer. Numerical simulations on a power system example illustrate our results.
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