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作者：Wu, Xiaotai; Shi, Peng; Tang, Yang; Mao, Shuai; Qian, Feng
作者单位：Anhui Polytechnic University; University of Adelaide; East China University of Science & Technology
摘要：The problem of exponential stability for semi-Markov jump stochastic nonlinear systems is studied in this article. Semi-Markov chain is well known as an extension of the Markov chain, whose sojourn time distribution depends on the current and next states, and is no longer limited to the exponential distribution. However, in the existing works, the independence and the distribution function limitation are imposed on the sojourn time of semi-Markov jump systems. In this article, without addition...
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作者：Caluya, Kenneth F.; Halder, Abhishek
作者单位：University of California System; University of California Santa Cruz
摘要：In this article, we study the Schrodinger bridge problem (SBP) with nonlinear prior dynamics. In control-theoretic language, this is a problem of minimum effort steering of a given joint state probability density function (PDF) to another over a finite-time horizon, subject to a controlled stochastic differential evolution of the state vector. As such, it can be seen as a stochastic optimal control problem in continuous time with endpoint density constraints-A topic that originated in the phys...
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作者：Liu, Jun-Jun; Guo, Bao-Zhu
作者单位：Taiyuan University of Technology; North China Electric Power University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this article, we consider robust output tracking for a Schrodinger equation with external disturbances in all possible channels. The challenge of the problem comes from the fact that the observation operator is unbounded and the regulated output and the control are noncollocated. An observer-based approach is adopted in investigation. We first select specially some coefficients of the disturbances to obtain a nominal system, which is a coupled PDE+ODE system. For this nominal system, we des...
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作者：Lehmann, Frederic; Pieczynski, Wojciech
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis
摘要：This article presents an optimal reduced-dimension Kalman filter for a family of triplet Markov models (TMMs). The problem is to estimate the state vector in the case when the auxiliary process in the TMM can be eliminated. Sufficient conditions for this elimination to be feasible are established and we give a selection of illustrative real-life TMM examples, where these conditions are satisfied. We subsequently show that the original TMM boils down to a pairwise Markov model (PMM) of second o...
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作者：Maity, Dipankar; Tsiotras, Panagiotis
作者单位：University of North Carolina; University of North Carolina Charlotte; University System of Georgia; Georgia Institute of Technology
摘要：In this article, we consider optimal controller synthesis of a quantized-feedback linear-quadratic-Gaussian (QF-LQG) system, where the measurements are to be quantized before being transmitted to the controller. The system is presented with several choices of quantizers, along with the cost of operating each quantizer. The objective is to jointly select the quantizers and the controller that would maintain an optimal balance between the control performance and quantization cost. Under certain ...
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作者：Serry, Mohamed; Reissig, Gunther
作者单位：University of Waterloo; Bundeswehr University Munich
摘要：We present a method to overapproximate reachable tubes over compact time intervals for linear continuous-time time-varying control systems, whose initial states and inputs are subject to compact convex uncertainty. The method uses numerical approximations of transition matrices, is convergent of first order, and assumes the ability to compute with compact convex sets in finite dimension. We also present a variant that applies to the case of zonotopic uncertainties, uses only linear algebraic o...
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作者：Cisneros-Velarde, Pedro; Jafarpour, Saber; Bullo, Francesco
作者单位：University of California System; University of California Santa Barbara
摘要：Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semicontractive) systems, the distance (resp. semidistance) between any two trajectories decreases exponentially fast. For partially contractive systems, each trajectory converges exponentially fast to an invariant subspace. In this article, we develop contraction theory on Hilbert spaces. First, we provide a novel integral condition for contractivity, and for time-invariant systems, we est...
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作者：Davydov, Alexander; Jafarpour, Saber; Bullo, Francesco
作者单位：University of California System; University of California Santa Barbara; University of California System; University of California Santa Barbara
摘要：this article, we study necessary and suffi-cient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to arbitrary norms, and charac-terize their properties. We introduce and study the sign and max pairings for the B1 and B infinity norms, respectively. Using weak pairings, we establish five equivalent character-izations for contraction, including the o...
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作者：Feng, Xinwei; Huang, Jianhui; Qiu, Zhenghong
作者单位：Shandong University; Hong Kong Polytechnic University
摘要：This article investigates a class of mixed stochastic linear-quadratic-Gaussian social optimization and Nash game in the context of a large-scale system. Two types of interactive agents are involved: a major agent and a large number of weakly coupled minor agents. All minor agents are cooperative to minimize the social cost as the sum of their individual costs, whereas such social cost is conflictive to that of the major agent. Thus, the major agent and all minor agents are further competitive...
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作者：Janak, Dylan; Garoche, Pierre-Loic; Acikmese, Behcet
作者单位：University of Washington; University of Washington Seattle; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Ecole Nationale de l'Aviation Civile (ENAC)
摘要：Set theoretic analysis plays a crucial part in understanding safety requirements for control systems. We apply the lattice theoretic insights of fixed point theorems to construct the maximal invariant set and verify safety constraint satisfaction. We present a Kleene iteration-based algorithm with a novel initialization-based on omega-limit sets-for exactly computing the maximal invariant set under a general safety constraint, and we analyze this algorithm for the special case of Markov chains...
