A general framework to solve both the continuous and discrete-time LQ and Hpreview control algorithms is presented in this paper. The obtained preview control form consists of a fill-state fwdback term which is identical to well known LQ and Hresults. The preview terms utilizes previewable disturbance signals to improve tracking or regulation performance. Simulation results of the tracking cont...

In this paper, optimal Lp − Lq estimates are obtained for operators which average functions over polynomial submanifolds, generalizing the k-plane transform. An important advance over previous work (e.g., [9]) is that full Lp − Lq estimates are obtained by methods which have traditionally yielded only restricted weak-type estimates. In the process, one is lead to make coercivity estimates for c...

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(R,X),Lq(R,X)). We show that the admissibility of the pair (Lp(R,X),Lq(R,X)) is equivalent to the uniform exponential dichotomy of an evolution family if and only if p ≥ q. As applications we obtain characterizations for uniform exponential dichotomy o...

The linear quadratic (LQ) optimal control problem is studied for a partial differential equation model of a time-varying plug flow tubular reactor. First some properties of the linearized model around a specific equilibrium profile are studied. Next, an LQ-control feedback is computed by using the corresponding operator Riccati differential equation, whose solution can be obtained via a related...

This paper is concerned with a stochastic linear–quadratic (LQ) control problem over a finite time horizon with Markovian jumps in the problem parameters. The problem is indefinite in that the cost weighting matrices for the state and control are allowed to be indefinite. A system of coupled generalized (differential) Riccati equations (CGREs) is introduced to cope with the indefiniteness of th...

The cross section for production of R-parity violating squarks (q̃) or leptoquarks (LQ) with masses above 200 GeV by positron-proton scattering at HERA can be substantially increased by a moderate increase of the beam energies. If, for example, the positron energy is raised from 27.5 to 32.5 GeV and the proton energy from 820 to 1000 GeV, the q̃/LQ production cross section for masses of 200 – 230...

We consider the exploration-exploitation tradeoff in linear quadratic (LQ) control problems, where the state dynamics is linear and the cost function is quadratic in states and controls. We analyze the regret of Thompson sampling (TS) (a.k.a. posterior-sampling for reinforcement learning) in the frequentist setting, i.e., when the parameters characterizing the LQ dynamics are fixed. Despite the...

We investigate the small deviation problem for weighted fractional Brownian motions in Lq–norm, 1 ≤ q ≤ ∞. Let BH be a fractional Brownian motion with Hurst index 0 < H < 1. If 1/r := H + 1/q, then our main result asserts lim ε→0 ε log P (∥∥∥ρBH∥∥∥ Lq(0,∞) < ε ) = −c(H, q) · ‖ρ‖ Lr(0,∞) , provided the weight function ρ satisfies a condition slightly stronger than the r– integrability. Thus we e...

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