ℋ∞ optimization with spatial constraints

A generalized ℋ∞ synthesis problem where non-euclidian spatial norms on the disturbances and output error are used is posed and solved. The solution takes the form of a linear matrix inequality. Some problems which fall into this class are presented. In particular, solutions are presented to two problems: a variant of ℋ∞ synthesis where norm constraints on each component of the disturbance can be imposed, and synthesis for a certain class of robust performance problems

Linear Control Theory with an ℋ∞ Optimality Criterion

This expository paper sets out the principal results in ℋ∞ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods

Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview

Disturbance Observer has been one of the most widely used robust control tools since it was proposed in 1983. This paper introduces the origins of Disturbance Observer and presents a survey of the major results on Disturbance Observer-based robust control in the last thirty-five years. Furthermore, it explains the analysis and synthesis techniques of Disturbance Observer-based robust control for linear and nonlinear systems by using a unified framework. In the last section, this paper presents concluding remarks on Disturbance Observer-based robust control and its engineering applications.Comment: 12 pages, 4 figure

Worst-case analysis of identification - BIBO robustness for closed loop data

This paper deals with the worst-case analysis of identification of linear shift-invariant (possibly) infinite-dimensional systems. A necessary and sufficient input richness condition for the existence of robustly convergent identification algorithms in l1 is given. A closed-loop identification setting is studied to cover both stable and unstable (but BIBO stabilizable) systems. Identification (or modeling) error is then measured by distance functions which lead to the weakest convergence notions for systems such that closed-loop stability, in the sense of BIBO stability, is a robust property. Worst-case modeling error bounds in several distance functions are include

Signal Reconstruction via H-infinity Sampled-Data Control Theory: Beyond the Shannon Paradigm

This paper presents a new method for signal reconstruction by leveraging sampled-data control theory. We formulate the signal reconstruction problem in terms of an analog performance optimization problem using a stable discrete-time filter. The proposed H-infinity performance criterion naturally takes intersample behavior into account, reflecting the energy distributions of the signal. We present methods for computing optimal solutions which are guaranteed to be stable and causal. Detailed comparisons to alternative methods are provided. We discuss some applications in sound and image reconstruction

Resource Allocation for Energy-Efficient 3-Way Relay Channels

Throughput and energy efficiency in 3-way relay channels are studied in this paper. Unlike previous contributions, we consider a circular message exchange. First, an outer bound and achievable sum rate expressions for different relaying protocols are derived for 3-way relay channels. The sum capacity is characterized for certain SNR regimes. Next, leveraging the derived achievable sum rate expressions, cooperative and competitive maximization of the energy efficiency are considered. For the cooperative case, both low-complexity and globally optimal algorithms for joint power allocation at the users and at the relay are designed so as to maximize the system global energy efficiency. For the competitive case, a game theoretic approach is taken, and it is shown that the best response dynamics is guaranteed to converge to a Nash equilibrium. A power consumption model for mmWave board-to-board communications is developed, and numerical results are provided to corroborate and provide insight on the theoretical findings.Comment: Submitted to IEEE Transactions on Wireless Communication

Optimal control of the state statistics for a linear stochastic system

We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from LQG as well as from formulations that bound the probability of violating state constraints. We develop results for optimal state-feedback control in the two cases where i) steering of the state distribution is to take place over a finite window of time with minimum energy, and ii) the goal is to maintain the state at a stationary distribution over an infinite horizon with minimum power. For both problems the distribution of noise and state are Gaussian. In the first case, we show that provided the system is controllable, the state can be steered to any terminal Gaussian distribution over any specified finite time-interval. In the second case, we characterize explicitly the covariance of admissible stationary state distributions that can be maintained with constant state-feedback control. The conditions for optimality are expressed in terms of a system of dynamically coupled Riccati equations in the finite horizon case and in terms of algebraic conditions for the stationary case. In the case where the noise and control share identical input channels, the Riccati equations for finite-horizon steering become homogeneous and can be solved in closed form. The present paper is largely based on our recent work in arxiv.org/abs/1408.2222, arxiv.org/abs/1410.3447 and presents an overview of certain key results.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1410.344