Input Energy Constraint Research Articles

Energy-Limited Joint Source-Channel Coding of Gaussian Sources over Gaussian Channels with Unknown Noise Level.

We consider the problem of transmitting a Gaussian source with minimum mean square error distortion over an infinite-bandwidth additive white Gaussian noise channel with an unknown noise level and under an input energy constraint. We construct a universal joint source-channel coding scheme with respect to the noise level, that uses modulo-lattice modulation with multiple layers. For each layer, we employ either analog linear modulation or analog pulse-position modulation (PPM). We show that the designed scheme with linear layers requires less energy compared to existing solutions to achieve the same quadratically increasing distortion profile with the noise level; replacing the linear layers with PPM layers offers an additional improvement.

Optimal regulation performance of discrete time‐delay systems based on quantization and input energy constraints

AbstractIn this paper, we study the optimal regulation problem of networked control systems and propose a new performance index for a given discrete time‐delay system. The regulation performance of the controlled plant is investigated by considering the effects of various constraints on the communication channel such as quantization, bandwidth, and packet dropouts using frequency domain methods and two‐degree‐of‐freedom control techniques. The results show that the regulation performance is not only related to the location and direction of the non‐minimum phase zeros and unstable poles of a given system but also related to the internal time delay of the controlled plant. Packet dropouts, quantization, and bandwidth limitations can also negatively affect the optimal performance. In addition, the trade‐off of the input energy constraint can also make the optimal regulation performance suffer. Finally, the reliability of this innovative result is illustrated by some simulation examples.

Probabilistic fault recoverability analysis of flight control process

Probabilistic Fault Recoverability (FR) property reveals the capability of a system to accommodate faults under admissible input energy constraints in the sense of satisfactory probability. Motivated by the idea of probabilistic control methods, a class of admissible probability density functions is designed for detailed description of fault parameters, under which several probabilistic FR conditions are established. This significantly enlarges the range of recoverable faults obtained from the deterministic FR analysis. The tradeoffs between the risk of performance degradation and this increased recoverability margin are exactly achieved by allowing a small risk of FR violation. This paper analyzes the probability FR of dynamic systems with switching and interconnection characteristics, and applies the new results to several aircraft models including single longitudinal aircraft dynamic, Highly Maneuverable Technology (HiMAT) vehicle and meta aircraft. Simulation results show the efficiency of the proposed methods based on the comparison between deterministic and probabilistic cases.

An off‐policy approach for model‐free stabilization of linear systems subject to input energy constraint and its application to spacecraft rendezvous

SummaryThis note is concerned with the problem of stabilizing a class of linear continuous‐time systems with completely unknown system dynamics subject to input energy constraint. To deal with this problem, a model‐based low gain feedback law is designed firstly by establishing a special algebraic Riccati equation. Such a low gain feedback law can semiglobally stabilize the linear systems subject to input energy constraint with the exact system model. In order to relax the assumption that the system model is exactly known, an off‐policy reinforcement learning approach is designed to solve the same problem without requiring the completely knowledge of the system dynamics. Finally, in order to verify the effectiveness of the proposed model‐free approach, simulation result on the spacecraft rendezvous problem is introduced.

Fault recoverability analysis of interconnected systems

Fault recoverability (FR) property reflects the capability of the system to accommodate faults through control reconfiguration under admissible input energy constraints. This study analyses the FR of interconnected non-linear and linear systems. Several explicit bounds of the amount of control energy required to drive the initial states of the interconnected system to the origin are computed. This helps to evaluate the FR under both centralised and distributed control schemes. The new results are further applied to meta aircraft configuration to verify the effectiveness.

Free Final Time Input Design Problem for Robust Entropy-Like System Parameter Estimation.

In this paper, a novel method is proposed to design a free final time input signal, which is then used in the robust system identification process. The solution of the constrained optimal input design problem is based on the minimization of an extra state variable representing the free final time scaling factor, formulated in the Bolza functional form, subject to the D-efficiency constraint as well as the input energy constraint. The objective function used for the model of the system identification provides robustness regarding the outlying data and was constructed using the so-called Entropy-like estimator. The perturbation time interval has a significant impact on the cost of the real-life system identification experiment. The contribution of this work is to examine the economic aspects between the imposed constraints on the input signal design, and the experiment duration while undertaking an identification experiment in the real operating conditions. The methodology is applicable to the general class of systems and was supported by numerical examples. Illustrative examples of the Least Squares, and the Entropy-Like estimators for the system parameter data validation where measurements include additive white noise are compared using ellipsoidal confidence regions.

Adaptation of the Alicki—Fannes—Winter method for the set of states with bounded energy and its use

We describe a modification of the Alicki-Fannes-Winter method which allows to prove uniform continuity on the set of quantum states with bounded energy of any locally almost affine function having limited growth with increasing energy. Some applications in quantum information theory are considered. The asymptotic continuity of the relative entropy of entanglement and of its regularization under the energy constraint on one subsystem is proved. Channel-independent continuity bounds for the quantum mutual information at the output of a local channel and for the output Holevo quantity under the input energy constraint are obtained.

Informative input design for Kernel-Based system identification

This paper discusses the design of input sequence for Kernel-Based system identification. From the Bayesian point of view, the kernel reflects a priori information about the target system, which implies that the information obtained from I/O data differs over kernels. This paper focuses on finding an input sequence which maximizes the information obtained through an observation according to the kernel which is given in advance. As an appropriate measure of such information, the mutual information is adopted. For the given kernel, a concrete procedure is proposed to find the input sequence maximizing the mutual information subject to the input energy constraints. Numerical examples are given to illustrate the effectiveness of the proposed input design. Furthermore, it is shown analytically that the impulse input is optimal for a special class of kernels.

Minimum output entropy of a non-Gaussian quantum channel

We introduce a model of non-Gaussian quantum channel that stems from the combination of two physically relevant processes occurring in open quantum systems, namely amplitude damping and dephasing. For it we find input states approaching zero output entropy, while respecting the input energy constraint. These states fully exploit the infinite dimensionality of the Hilbert space. Upon truncation of the latter, the minimum output entropy remains finite and optimal input states for such a case are conjectured thanks to numerical evidences.

On the constrained classical capacity of infinite-dimensional covariant quantum channels

The additivity of the minimal output entropy and that of the χ-capacity are known to be equivalent for finite-dimensional irreducibly covariant quantum channels. In this paper, we formulate a list of conditions allowing to establish similar equivalence for infinite-dimensional covariant channels with constrained input. This is then applied to bosonic Gaussian channels with quadratic input constraint to extend the classical capacity results of the recent paper [Giovannetti et al., Commun. Math. Phys. 334(3), 1553-1571 (2015)] to the case where the complex structures associated with the channel and with the constraint operator need not commute. In particular, this implies a multimode generalization of the “threshold condition,” obtained for single mode in Schäfer et al. [Phys. Rev. Lett. 111, 030503 (2013)], and the proof of the fact that under this condition the classical “Gaussian capacity” resulting from optimization over only Gaussian inputs is equal to the full classical capacity. Complex structures correspond to different squeezings, each with its own normal modes, vacuum and coherent states, and the gauge. Thus our results apply, e.g., to multimode channels with a squeezed Gaussian noise under the standard input energy constraint, provided the squeezing is not too large as to violate the generalized threshold condition. We also investigate the restrictiveness of the gauge-covariance condition for single- and multimode bosonic Gaussian channels.

Tracking Performance Bound with Finite Control Energy and Erasure Channel Energy Constraint

AbstractThis paper studies the tracking performance of the single‐input single‐output (SISO), finite dimensional, linear and time‐invariant (LTI) system under the channel input energy constraint over the Erasure channel. A new performance index is proposed which is minimized over all two‐degree‐of‐freedom stabilizing controllers. The explicit expressions of the lower bound of the performance index and the minimum of the signal‐to‐noise ratio are obtained. The results show that the performance bound is correlated to unstable poles, non‐minimum phase zeros and the packet loss probability. Finally, examples are given to validate the conclusions derived.

A Solution of Gaussian Optimizer Conjecture for Quantum Channels

The long-standing conjectures of the optimality of Gaussian inputs for Gaussian channel and Gaussian additivity are solved for a broad class of covariant or contravariant Bosonic Gaussian channels (which includes in particular thermal, additive classical noise, and amplifier channels) restricting to the class of states with finite second moments. We show that the vacuum is the input state which minimizes the entropy at the output of such channels. This allows us to show also that the classical capacity of these channels (under the input energy constraint) is additive and is achieved by Gaussian encodings.

On the effect of additional input channels on the achievable performance of discrete-time control systems

This paper deals with the quantification of performance bounds in multiple-input multiple-output (MIMO) control systems when energy-constrained input channels are added to the plant. We focus on stable, discrete-time, linear time-invariant (LTI), and right-invertible MIMO systems. The performance is quantified using the 2-norm and assuming step references, whilst the control input energy constraint is on the increments of the additional input signals. Our main result is a closed form expression that quantifies the improvement in performance that results as a consequence of the additional input channels.

Lower bound of tracking performance with finite control energy and channel energy constraint

This paper studies the tracking performance of the single-input single-output (SISO), finite dimensional, linear and time-invariant (LTI) system over an additive white Gaussian noise (AWGN) channel with finite control energy and channel input energy constraint. A new performance index is proposed which is minimized over all stabilizing two-degree-of-freedom controllers. The explicit expressions of the lower bound of the tracking performance and the minimum of signal-to-noise required are obtained. The results show that the lower bound is correlated to the unstable pole, non-minimum phase zero and the channel scaling factor. Finally, one example is given to validate the conclusions by adopting the special inner-outer factorization.

Semi-Global Stabilization of Linear Time-Delay Systems with Input Energy Constraint

AbstractThis paper is concerned with semi-global stabilization of linear systems with actuator delay and energy constraints. Under the condition of null controllability by vanishing energy, the parametric Lyapunov equation based L2 low gain feedback is adopted to solve the problem. If the delay in the system is exactly known, a delay-dependent controller is designed and if the delay in the system is either time-varying or not exactly known, a delay-independent controller is established. The proposed approach is used in the linearized model of the relative motion in the orbit plane of a spacecraft with respect to another in a circular orbit around the Earth to validate its effectiveness.

Capacity of a bosonic memory channel with Gauss-Markov noise

We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a ``quantum water-filling'' solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit of an infinite number of modes. The method can also be applied to a more general noise environment which is constructed by a stationary Gauss process. The extension of our results to the case of broadband bosonic channels with colored Gaussian noise should also be straightforward.

Physiological flexibility in the Andean lizard Liolaemus bellii: seasonal changes in energy acquisition, storage and expenditure

According to the "barrel model", an organism may be represented by a container, with input energy constraints (foraging, digestion, and absorption) symbolized by funnels connected in tandem, and energy outputs (maintenance, growth, and reproduction) symbolized by a series of spouts arranged in parallel. Animals can respond to changes in environmental conditions, through adjustments in the size of the funnels, the fluid stored inside the barrel, or the output flow through the spouts. In the present study, we investigate the interplay among these processes through the analysis of seasonal changes in organ size and metabolic rate in a lizard species (Liolaemus bellii) that inhabits extremely seasonal environments in the Andes range. We found that digestive organ size showed the greatest values during spring and summer, that is, during the foraging seasons. Energy reserves were larger during summer and autumn, and then decreased through winter and spring, which was correlated with overwintering maintenance and reproductive costs. Standard metabolic rate was greater during the high-activity seasons (spring and summer), but this increase was only noticeable at higher environmental temperatures. The ability of many lizard species to reduce their maintenance cost during the cold months of the year, beyond what is expected from temperature decrease, is probably related to their success in coping with highly fluctuating environments. Here, we demonstrate that this ability is correlated with high physiological flexibility, which allows animals to adjust energy acquisition, storing and expenditure processes according to current environmental conditions.

Sequences that maximize the symmetric capacity under the requirement of quasi-scalability

We examine the symmetric capacity of quasi-scalable systems under the equal average input energy constraint. It turns out that the maximum achievable symmetric capacity is equal to the maximum achievable sum capacity. Moreover, the multiple-OCDMA signature sets, which are known to maximize the sum capacity under the constraint of quasi-scalability, actually achieve this maximum symmetric capacity.

Sequences that maximize the symmetric capacity under the requirement of quasi-scalability

We examine the symmetric capacity of quasi-scalable systems under the equal average input energy constraint. It turns out that the maximum achievable symmetric capacity is equal to the maximum achievable sum capacity. Moreover, the multiple-OCDMA signature sets, which are known to maximize the sum capacity under the constraint of quasi-scalability, actually achieve this maximum symmetric capacity.

Fuzzy control with input energy and state variance constraints for perturbed ship steering systems

In this paper, a fuzzy controller design problem is considered for nonlinear perturbed ship steering systems. The nonlinear perturbed ship steering system is transformed into a Takagi-Sugeno (T-S) fuzzy model, which has similar dynamics to the original nonlinear system. By using linear feedback controller design technology, a nonlinear fuzzy controller is developed for the perturbed T-S type ship steering model. Building on the nonlinear fuzzy controller, a number of most important performance constraints in fuzzy control systems are addressed. These include stability conditions, minimum control input energy, and individual state variance constraints. Finally, a numerical simulation is given to show the effects of the proposed fuzzy control methodology.