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Register a new userDiscounted Cost Linear Quadratic Gaussian Control for Descriptor Systems
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We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterize the feasibility of this problem using a linear matrix inequality. In particular, conditions for existence and uniqueness of optimal controls are derived, which are weaker compared to the standard approaches in the literature. We further show that also for the stochastic problem, the optimal control is given in terms of the stabilizing solution of the Lure equation, which generalizes the algebraic Riccati equation.
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This paper studies a class of partially observed Linear Quadratic Gaussian (LQG) problems with unknown dynamics. We establish an end-to-end sample complexity bound on learning a robust LQG controller for open-loop stable plants. This is achieved using a robust synthesis procedure, where we first estimate a model from a single input-output trajectory of finite length, identify an H-infinity bound on the estimation error, and then design a robust controller using the estimated model and its quantified uncertainty. Our synthesis procedure leverages a recent control tool called Input-Output Parameterization (IOP) that enables robust controller design using convex optimization. For open-loop stable systems, we prove that the LQG performance degrades linearly with respect to the model estimation error using the proposed synthesis procedure. Despite the hidden states in the LQG problem, the achieved scaling matches previous results on learning Linear Quadratic Regulator (LQR) controllers with full state observations.
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This paper presents a new fast and robust algorithm that provides fuel-optimal impulsive control input sequences that drive a linear time-variant system to a desired state at a specified time. This algorithm is applicable to a broad class of problems where the cost is expressed as a time-varying norm-like function of the control input, enabling inclusion of complex operational constraints in the control planning problem. First, it is shown that the reachable sets for this problem have identical properties to those in prior works using constant cost functions, enabling use of existing algorithms in conjunction with newly derived contact and support functions. By reformulating the optimal control problem as a semi-infinite convex program, it is also demonstrated that the time-invariant component of the commonly studied primer vector is an outward normal vector to the reachable set at the target state. Using this formulation, a fast and robust algorithm that provides globally optimal impulsive control input sequences is proposed. The algorithm iteratively refines estimates of an outward normal vector to the reachable set at the target state and a minimal set of control input times until the optimality criteria are satisfied to within a user-specified tolerance. Next, optimal control inputs are computed by solving a quadratic program. The algorithm is validated through simulations of challenging example problems based on the recently proposed Miniaturized Distributed Occulter/Telescope small satellite mission, which demonstrate that the proposed algorithm converges several times faster than comparable algorithms in literature.
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