The Experts below are selected from a list of 50961 Experts worldwide ranked by ideXlab platform
Javad Lavaei - One of the best experts on this subject based on the ideXlab platform.
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on the exponential number of connected components for the feasible set of optimal Decentralized Control problems
Advances in Computing and Communications, 2019Co-Authors: Han Feng, Javad LavaeiAbstract:The optimal Decentralized Control (ODC) problem is known to be NP-hard and many sufficient tractability conditions have been derived in the literature for its convex reformulations or approximations. To better understand the root cause of the non-existence of efficient methods for solving ODC, we propose a measure of problem complexity in terms of connectivity, and show that there is no polynomial upper bound on the number of connected components for the set of static stabilizing Decentralized Controllers. Specifically, we present a subclass of problems for which the number of connected components is exponential in the order of the system and, in particular, any point in each of these components is the unique solution of the ODC problem for some quadratic objective functional. The results of this paper have two implications. First, the recent effort in machine learning advocating the use of local search algorithms for non-convex problems, which has also been successful for the optimal centralized Control problem, fails to work for ODC since it needs an exponential number of initializations. Second, no reformulation of the problem through a smooth change of variables can reduce the complexity since it maintains the number of connected components. On the positive side, we show that structural assumptions can reduce the connectivity complexity of ODC, one such structure is the system being highly damped.
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on the convexity of optimal Decentralized Control problem and sparsity path
Advances in Computing and Communications, 2017Co-Authors: Salar Fattahi, Javad LavaeiAbstract:This paper is concerned with an important special case of the stochastic optimal Decentralized Control (SODC) problem, where the objective is to design a static structurally constrained Controller for a stable stochastic system. This problem is non-convex and hard to solve in general. We show that if either the measurement noise covariance or the input weighting matrix is not too small, the problem is locally convex. Under such circumstances, the design of a Decentralized Controller with a bounded norm subject to an arbitrary sparsity pattern is naturally a convex problem. We also study the problem of designing a sparse Controller using a regularization technique, where the Control structure is not pre-specified but penalized in the objective function. Under some genericity assumptions, we prove that this method is able to design a Decentralized Controller with any arbitrary sparsity level. Although this paper is focused on stable systems, the results can be generalized to unstable systems as long as an initial stabilizing Controller with a desirable structure is known a priori.
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optimal Decentralized Control problem as a rank constrained optimization
Allerton Conference on Communication Control and Computing, 2013Co-Authors: Javad LavaeiAbstract:This paper is concerned with the long-standing optimal Decentralized Control (ODC) problem. The objective is to design a fixed-order Decentralized Controller for a discrete-time system to minimize a given finite-time cost function subject to norm constraints on the input and output of the system. We cast this NP-hard problem as a quadratically-constrained quadratic program, and then reformulate it as a rank-constrained optimization. The reformulated problem is a semidefinite program (SDP) after removing its rank-1 constraint. Whenever the SDP relaxation has a rank-1 solution, a globally optimal Decentralized Controller can be recovered from this solution. This paper studies the rank of the minimum-rank solution of the SDP relaxation since this number may provide rich information about the level of the approximation needed to make the ODC problem tractable. Using our recently developed notion of “nonlinear optimization over graph”, we propose a methodology to compute the rank of the minimum-rank solution of the SDP relaxation. In particular, we show that in the case where the unknown Decentralized Controller being sought needs to be static with a diagonal matrix gain, this rank is upper bounded by 4. Since the upper bound is close to 1 and does not depend on the order of the system, the ODC problem may not be as hard as it is thought to be. This paper also proposes a penalized SDP relaxation to heuristically enforce the few unwanted nonzero eigenvalues of the solution to diminish.
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A Model Predictive Decentralized Control Scheme With Reduced Communication Requirement for Spacecraft Formation
IEEE Transactions on Control Systems Technology, 2008Co-Authors: Javad Lavaei, Ahmadreza Momeni, Amir G. AghdamAbstract:This brief investigates the Control problem for a number of cooperative spacecraft with communication constraints. It is assumed that a set of cooperative local Controllers corresponding to the individual spacecraft is given which satisfies the desired objectives of the formation. It is to be noted that due to the information exchange between the local Controllers, the overall Control structure can be considered centralized in general. However, communication in flight formation is expensive. Thus, it is desired to have some form of decentralization in Control structure, which has a lower communication requirement. This Decentralized Controller consists of local estimators inherently, so that each local Controller estimates the state of the whole formation. Necessary and sufficient conditions for the stability of the formation under the proposed Decentralized Controller are obtained. It is shown that the Decentralized Control system, if stable, behaves almost the same as its centralized counterpart. Moreover, robustness of the Decentralized Controller is studied and compared to that of the corresponding centralized Controller. It is finally shown that the proposed Decentralized Controller comprises most of the features of its centralized counterpart. The efficacy of the proposed method is demonstrated through simulations.
Tong Heng Lee - One of the best experts on this subject based on the ideXlab platform.
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optimal Decentralized Control for uncertain systems by symmetric gauss seidel semi proximal alm
arXiv: Optimization and Control, 2020Co-Authors: Zilong Cheng, Xiaoxue Zhang, Masayoshi Tomizuka, Tong Heng LeeAbstract:The H2 guaranteed cost Decentralized Control problem is investigated in this work. More specifically, on the basis of an appropriate H2 re-formulation that we put in place, the optimal Control problem in the presence of parameter uncertainties is then suitably characterized by convex restriction and solved in parameter space. It is shown that a set of stabilizing Decentralized Controller gains for the uncertain system is parameterized in a convex set through appropriate convex restriction, and then an approximated conic optimization problem is constructed. This facilitates the use of the symmetric Gauss-Seidel (sGS) semi-proximal augmented Lagrangian method (ALM), which attains high computational effectiveness. A comprehensive analysis is given on the application of the approach in solving the optimal Decentralized Control problem; and subsequently, the preserved Decentralized structure, robust stability, and robust performance are all suitably guaranteed with the proposed methodology. Furthermore, an illustrative example is presented to demonstrate the effectiveness of the proposed optimization approach.
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optimal Decentralized Control for uncertain systems by symmetric gauss seidel semi proximal alm
IEEE Transactions on Automatic Control, 2020Co-Authors: Zilong Cheng, Xiaoxue Zhang, Masayoshi Tomizuka, Tong Heng LeeAbstract:The $H_{2}$ guaranteed cost Decentralized Control problem is investigated in this work. More specifically, on the basis of an appropriate H2 re-formulation that we put in place, the optimal Control problem in the presence of parameter uncertainties is solved in parameter space. It is shown that a set of stabilizing Decentralized Controller gains for the uncertain system is parameterized in a convex set through appropriate convex restriction, and then an approximated conic optimization problem is constructed. It facilitates the use of the symmetric Gauss-Seidel (sGS) semi-proximal augmented Lagrangian method (ALM), which attains high computational efficiency. A comprehensive analysis is given on the application of the approach in solving the optimal Decentralized Control problem; and subsequently, the preserved Decentralized structure, robust stability, and robust performance are all suitably guaranteed with the proposed methodology. Furthermore, illustrative examples are presented to demonstrate the effectiveness of the proposed optimization approach.
Babak Parkhideh - One of the best experts on this subject based on the ideXlab platform.
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Decentralized Control Strategy for AC-Stacked PV Inverter Architecture Under Grid Background Harmonics
IEEE Journal of Emerging and Selected Topics in Power Electronics, 2018Co-Authors: Hamidreza Jafarian, Namwon Kim, Babak ParkhidehAbstract:Grid background harmonics cause harmonic distortion on the output current of grid-tied inverters, and they require the inverter to have harmonic mitigation Control. The main object of this paper is to propose a Decentralized Control strategy for mitigation of the impact of distorted grid on ac-stacked photovoltaic inverter architecture. Two Control schemes for this architecture are proposed and analyzed in this paper to mitigate the harmonic current caused by distorted grid voltage without any handshaking among the inverter members and supervisory Control center. The proposed Control method improves the reliability of the architecture by increasing the operating margin and it improves the power quality by reducing the harmonic content of the output current. The proposed methods are analyzed by frequency analysis and grid disturbance impedance analysis. The feasibility and effectiveness of the proposed Control scheme has been demonstrated and verified through a Control-hardware-in-the-loop experiment.
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hybrid current voltage mode Control scheme for distributed ac stacked pv inverter with low bandwidth communication requirements
IEEE Transactions on Industrial Electronics, 2018Co-Authors: Hamidreza Jafarian, Shibashis Bhowmik, Babak ParkhidehAbstract:This paper shows the feasibility of a novel Decentralized Control scheme for the grid-tied ac-stacked photovoltaic (PV) inverter architecture. The proposed Decentralized Control scheme with low-bandwidth communications requirements enables a fully distributed PV inverter architecture. Detailed modeling and theoretical analyses will be provided to support the existence of such Decentralized Control scheme. Simulation and experimental results on a representative laboratory-scale prototype will be presented under symmetrical and asymmetrical conditions as well as 10% grid voltage sag to show the effectiveness of the proposed Control scheme in different operating conditions.
Guanghong Yang - One of the best experts on this subject based on the ideXlab platform.
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adaptive Decentralized Control for a class of interconnected nonlinear systems via backstepping approach and graph theory
Automatica, 2017Co-Authors: Xiaojian Li, Guanghong YangAbstract:Abstract This paper is concerned with the adaptive Decentralized Control problem for a class of interconnected nonlinear systems, where the interconnections are assumed to be unknown and completely nonlinear. In addition, the interconnections and their bounds are allowed to contain the states of all subsystems. The main contribution is that, a strictly Decentralized Control scheme with compensation mechanism is developed to achieve the desirable tracking performance. More specifically, a smooth switching function is introduced to construct adaptive Control laws, where the compensation mechanism is activated only if the immediate variable involved in the backstepping design exceeds a given constant, otherwise it will be turned-off. Furthermore, by combining graph theory and Lyapunov analysis method, it is proved that all the signals of the resulting closed-loop system are globally bounded, and the tracking errors of subsystems exponentially converge to a compact set, whose radius is adjustable by choosing different Controller design parameters. Finally, the effectiveness of the proposed adaptive Decentralized Control scheme is illustrated with a simulated example.
Sanjay Lall - One of the best experts on this subject based on the ideXlab platform.
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optimal Controller synthesis for a Decentralized two player linear quadratic regulator via spectral factorization
2012Co-Authors: John Swigart, Sanjay LallAbstract:We develop Controller synthesis algorithms for Decentralized Control problems. The particular system considered here consists of two interconnected linear subsystems, with communication allowed in only one direction.We develop the concept of spectral factorization, which is the approach used to construct the optimal Controllers. Explicit state-space formulae are provided, and we show that each player has to do more than simply estimate the states that they cannot observe. In other words, the simplest separation principle does not hold for this Decentralized Control problem. Some intuition into the Control policies is provided, and the order of the optimal Controllers is established.
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an explicit dynamic programming solution for a de centralized two player optimal linear quadratic regulator
2010Co-Authors: John Swigart, Sanjay LallAbstract:We develop optimal Controller synthesis algorithms for Decentralized Control problems, in which individual subsystems are connected over a network. We consider a simple information structure, consisting of two interconnected linear systems, and construct the optimal Controller subject to a decentralization constraint via a novel dynamic programming method. We provide explicit state-space formulae for the optimal Controller, and show that each player has to do more than simply estimate the states that they cannot observe. In other words, the simplest separation principle does not hold for this Decentralized Control problem.
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an approximate dynamic programming approach to Decentralized Control of stochastic systems
Lecture Notes in Control and Information Sciences, 2006Co-Authors: Randy Cogill, Michael Rotkowitz, Sanjay LallAbstract:We consider the problem of computing Decentralized Control policies for stochastic systems with finite state and action spaces. Synthesis of optimal Decentralized policies for such problems is known to be NP-hard [1]. Here we focus on methods for efficiently computing meaningful suboptimal Decentralized Control policies. The algorithms we present here are based on approximation of optimal Q-functions. We show that the performance loss associated with choosing Decentralized policies with respect to an approximate Q-function is related to the approximation error.
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a characterization of convex problems in Decentralized Control ast
IEEE Transactions on Automatic Control, 2005Co-Authors: M Rotkowitz, Sanjay LallAbstract:We consider the problem of constructing optimal Decentralized Controllers. We formulate this problem as one of minimizing the closed-loop norm of a feedback system subject to constraints on the Controller structure. We define the notion of quadratic invariance of a constraint set with respect to a system, and show that if the constraint set has this property, then the constrained minimum-norm problem may be solved via convex programming. We also show that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. These results are developed in a very general framework, and are shown to hold in both continuous and discrete time, for both stable and unstable systems, and for any norm. This notion unifies many previous results identifying specific tractable Decentralized Control problems, and delineates the largest known class of convex problems in Decentralized Control. As an example, we show that optimal stabilizing Controllers may be efficiently computed in the case where distributed Controllers can communicate faster than their dynamics propagate. We also show that symmetric synthesis is included in this classification, and provide a test for sparsity constraints to be quadratically invariant, and thus amenable to convex synthesis.
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Decentralized Control information structures preserved under feedback
Conference on Decision and Control, 2002Co-Authors: Michael Rotkowitz, Sanjay LallAbstract:We consider the problem of constructing Decentralized Control systems. We formulate this problem as one of minimizing the closed-loop norm of a feedback system subject to constraints on the Controller structure. We define the notion of quadratic invariance of a constraint set with respect to a system, and show that if the constraint set has this property, then the constrained minimum norm problem may be solved via convex programming. We also show that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. We develop necessary and sufficient conditions under which the constraint set is quadratically invariant, and show that many examples of Decentralized synthesis which have been proven to be solvable in the literature are quadratically invariant. As an example, we show that a Controller which minimizes the norm of the closed-loop map may be efficiently computed in the case where distributed Controllers can communicate faster than the propagation delay of the plant dynamics.
