This technical note studies quantized output feedback control of discrete-time linear systems using a finite-level quantizer. The main objective is to find a quantization strategy which is easily ...implementable and achieves asymptotic stabilization. Based on a known logarithmic quantization scheme, we introduce a simple dynamic scaling method for the quantizer. A suboptimal approach for the optimization of the number of quantization levels and the design of a corresponding quantized dynamic output feedback controller is given. The robustness of the dynamic quantization scheme with respect to input disturbances is also examined.
The paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape. A new technique based on complex Laplacian is ...introduced to address the problems of which formation shapes specified by inter-agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability. Concerning the first question, we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex Laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter-agent specification of the formation shape is 2-rooted. Concerning the second question, a distributed and linear control law is developed based on the complex Laplacian specifying the target formation shape, and provable existence conditions of stabilizing gains to assign the eigenvalues of the closed-loop system at desired locations are given. Moreover, we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to re-design and change their control laws.
This technical note studies the quantized linear quadratic Gaussian (LQG) control problem which is generalized from the classical LQG control but with the constraint that the feedback signal is ...quantized with a fixed bit rate. We show that state feedback control, state estimation and quantization can not be fully separated in general. Only a weak separation principle holds which converts the quantized LQG control problem into a quantized state estimation problem. Further separation of estimation and quantization is not possible in general. A concrete example is provided to demonstrate this fact. It is also shown that the so-called "whitening" approach to quantized state estimation is not optimal.
This paper is concerned with the long-standing problems of linear quadratic regulation (LQR) control and stabilization for a class of discrete-time stochastic systems involving multiplicative noises ...and input delay. These fundamental problems have attracted resurgent interests due to development of networked control systems. An explicit analytical expression is given for the optimal LQR controller. More specifically, the optimal LQR controller is shown to be a linear function of the conditional expectation of the state, with the feedback gain based on a Riccati-ZXL difference equation. It is also shown that the system is stabilizable in the mean-square sense if and only if an algebraic Riccati-ZXL equation has a particular solution. These results are based on a new technical tool, which establishes a non-homogeneous relationship between the state and the costate of this class of systems, and the introduction of a new Lyapunov function for the finite-horizon optimal control design.
This paper introduces a new multi-agent control problem, called an affine formation control problem, with the objective of asymptotically reaching a configuration that preserves collinearity and ...ratios of distances with respect to a target configuration. Suppose each agent updates its own state using a weighted sum of its neighbor's relative states with possibly negative weights. Then the affine control problem can be solved for either undirected or directed interaction graphs. It is shown in this paper that an affine formation is stabilizable over an undirected graph if and only if the undirected graph is universally rigid, while an affine formation is stabilizable over a directed graph in the d-dimensional space if and only if the directed graph is (d + 1)-rooted. Rigorous analysis is provided, mainly relying on Laplacian associated with the interaction graph, which contain both positive and negative weights.
This paper concentrates on coordinate-free formation control for directed networks, for which the dynamic motion of each agent is assumed to be governed only by a local control. We develop a graph ...Laplacian approach to solve the global and exponential formation stabilization problem using merely relative position measurements between neighbors. First, to capture the sensing and control architectures that are needed to maintain the shape of a formation, a necessary and sufficient topological condition is proposed. Second, a Laplacian-based control law is developed for the stabilization problem of a group of mobile agents to a desired formation shape under both fixed and switching topologies due to temporal node failures. Simulation results are provided to demonstrate that our Laplacian-based formation control strategy is inherently fault-tolerant and robust to node failures.
In this paper, we present a fully distributed bisection algorithm for the economic dispatch problem (EDP) in a smart grid scenario, with the goal to minimize the aggregated cost of a network of ...generators, which cooperatively furnish a given amount of power within their individual capacity constraints. Our distributed algorithm adopts the method of bisection, and is based on a consensus-like iterative method, with no need for a central decision maker or a leader node. Under strong connectivity conditions and allowance for local communications, we show that the iterative solution converges to the globally optimal solution. Furthermore, two stopping criteria are presented for the practical implementation of the proposed algorithm, for which sign consensus is defined. Finally, numerical simulations based on the IEEE 14-bus and 118-bus systems are given to illustrate the performance of the algorithm.
This paper focuses on the procurement of load shifting service by optimally scheduling the charging and discharging of PEVs in a decentralized fashion. We assume that the energy flow between PEVs and ...the grid is bidirectional, i.e., PEVs can also release energy back into the grid as distributed generation, which is known as vehicle-to-grid (V2G). The optimal scheduling problem is then formulated as a mixed discrete programming (MDP) problem, which is NP-hard and extremely difficult to solve directly. To get over this difficulty, we propose a solvable approximation of the MDP problem by exploiting the shape feature of the base demand curve during the night, and develop a decentralized algorithm based on iterative water-filling. Our algorithm is decentralized in the sense that the PEVs compute locally and communicate with an aggregator. The advantages of our algorithm include reduction in computational burden and privacy preserving. Simulation results are given to show the performance of our algorithm.
This paper addresses the stability of a Kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator. We give a ...necessary condition and a sufficient condition, with a trivial gap between them, for the boundedness of the expected value of the estimation error covariance. These conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order Markov process. Hence, we extend the class of systems for which these conditions are known in two directions, namely, by including degenerate systems, and by considering network models more general than i.i.d. and Gilbert-Elliott. We show that these conditions recover known results from the literature when evaluated for non-degenerate systems under the assumption of i.i.d. or Gilbert-Elliott packet loss models.
This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to ...stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.
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