Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page

Ignorance is bliss: General and robust cancellation of decoherence via no-knowledge quantum feedback

A "no-knowledge" measurement of an open quantum system yields no information about any system observable; it only returns noise input from the environment. Surprisingly, performing such a no-knowledge measurement can be advantageous. We prove that a system undergoing no-knowledge monitoring has reversible noise, which can be cancelled by directly feeding back the measurement signal. We show how no-knowledge feedback control can be used to cancel decoherence in an arbitrary quantum system coupled to a Markovian reservoir that is being monitored. Since no-knowledge feedback does not depend on the system state or Hamiltonian, such decoherence cancellation is guaranteed to be general, robust and can operate in conjunction with any other quantum control protocol. As an application, we show that no-knowledge feedback could be used to improve the performance of dissipative quantum computers subjected to local loss.Comment: 6 pages + 2 pages supplemental material, 3 figure

Control and Filtering for Discrete Linear Repetitive Processes with H infty and ell 2--ell infty Performance

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass to pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws for the sub-class of so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control. The main contribution is to show how control law design can be undertaken within the framework of a general robust filtering problem with guaranteed levels of performance. In particular, we develop algorithms for the design of an H? and $\ell_{2}–\ell_{\infty}$ dynamic output feedback controller and filter which guarantees that the resulting controlled (filtering error) process, respectively, is stable along the pass and has prescribed disturbance attenuation performance as measured by $H_{\infty}$ and $\ell_{2}$–$\ell_{\infty}$ norms

Tiny Codes for Guaranteeable Delay

Future 5G systems will need to support ultra-reliable low-latency communications scenarios. From a latency-reliability viewpoint, it is inefficient to rely on average utility-based system design. Therefore, we introduce the notion of guaranteeable delay which is the average delay plus three standard deviations of the mean. We investigate the trade-off between guaranteeable delay and throughput for point-to-point wireless erasure links with unreliable and delayed feedback, by bringing together signal flow techniques to the area of coding. We use tiny codes, i.e. sliding window by coding with just 2 packets, and design three variations of selective-repeat ARQ protocols, by building on the baseline scheme, i.e. uncoded ARQ, developed by Ausavapattanakun and Nosratinia: (i) Hybrid ARQ with soft combining at the receiver; (ii) cumulative feedback-based ARQ without rate adaptation; and (iii) Coded ARQ with rate adaptation based on the cumulative feedback. Contrasting the performance of these protocols with uncoded ARQ, we demonstrate that HARQ performs only slightly better, cumulative feedback-based ARQ does not provide significant throughput while it has better average delay, and Coded ARQ can provide gains up to about 40% in terms of throughput. Coded ARQ also provides delay guarantees, and is robust to various challenges such as imperfect and delayed feedback, burst erasures, and round-trip time fluctuations. This feature may be preferable for meeting the strict end-to-end latency and reliability requirements of future use cases of ultra-reliable low-latency communications in 5G, such as mission-critical communications and industrial control for critical control messaging.Comment: to appear in IEEE JSAC Special Issue on URLLC in Wireless Network

Bit Allocation Law for Multi-Antenna Channel Feedback Quantization: Single-User Case

This paper studies the design and optimization of a limited feedback single-user system with multiple-antenna transmitter and single-antenna receiver. The design problem is cast in form of the minimizing the average transmission power at the base station subject to the user's outage probability constraint. The optimization is over the user's channel quantization codebook and the transmission power control function at the base station. Our approach is based on fixing the outage scenarios in advance and transforming the design problem into a robust system design problem. We start by showing that uniformly quantizing the channel magnitude in dB scale is asymptotically optimal, regardless of the magnitude distribution function. We derive the optimal uniform (in dB) channel magnitude codebook and combine it with a spatially uniform channel direction codebook to arrive at a product channel quantization codebook. We then optimize such a product structure in the asymptotic regime of $B\rightarrow \infty$, where $B$ is the total number of quantization feedback bits. The paper shows that for channels in the real space, the asymptotically optimal number of direction quantization bits should be ${(M{-}1)}/{2}$ times the number of magnitude quantization bits, where $M$ is the number of base station antennas. We also show that the performance of the designed system approaches the performance of the perfect channel state information system as $2^{-\frac{2B}{M+1}}$. For complex channels, the number of magnitude and direction quantization bits are related by a factor of $(M{-}1)$ and the system performance scales as $2^{-\frac{B}{M}}$ as $B\rightarrow\infty$.Comment: Submitted to IEEE Transactions on Signal Processing, March 201

Wasserstein Distributionally Robust Regret-Optimal Control under Partial Observability

This paper presents a framework for Wasserstein distributionally robust (DR) regret-optimal (RO) control in the context of partially observable systems. DR-RO control considers the regret in LQR cost between a causal and non-causal controller and aims to minimize the worst-case regret over all disturbances whose probability distribution is within a certain Wasserstein-2 ball of a nominal distribution. Our work builds upon the full-information DR-RO problem that was introduced and solved in Yan et al., 2023, and extends it to handle partial observability and measurement-feedback (MF). We solve the finite horizon partially observable DR-RO and show that it reduces to a tractable semi-definite program whose size is proportional to the time horizon. Through simulations, the effectiveness and performance of the framework are demonstrated, showcasing its practical relevance to real-world control systems. The proposed approach enables robust control decisions, enhances system performance in uncertain and partially observable environments, and provides resilience against measurement noise and model discrepancies

Modern And Decentralized Control For Multivariable Processes

Control methodologies to cope with multivariable process systems are studied in this thesis. Topics on both modern and conventional decentralized control strategies are covered with the major focus on the latter.;In the modern control aspect, the two most common approaches--the LQ optimal control and the eigenvalue assignment design are discussed. Emphasis is placed on investigation of LQG applications to complex real-time processes, and eigenvalue assignment design for improved steady state and robust performance. By careful consideration of practical issues and innovative use of model identification techniques, a strongly interactive and non-linear multivariable pressure tank system is satisfactorily controlled by the LQG scheme. A PI state feedback controller is proposed, and an eigenvalue assignment design for robust performance is discussed.;With respect to decentralized control, various issues including interaction measurement, variable pairing, stability and stability robustness, robust performance, controller design and integrity, are systematically addressed. Major results include: (1) A new interaction measure capable of measuring the absolute interaction and the nature of interaction is developed. (2) A new comprehensive variable pairing criterion, based on the Niederlinski Index, is presented. (3) The use of the RGA as a direct measure of integrity is expanded. (4) A series of stability conditions for decentralized control under independent design and variable pairing are established. (5) A new stability robustness measure to evaluate the effects of model error on process gains is developed. (6) New disturbance directionality indices and robust performance criteria with respect to model uncertainty associated with manipulated variables are developed, and robust design procedures for general multivariable controllers are provided

A novel robust predictive control system over imperfect networks

This paper aims to study on feedback control for a networked system with both uncertain delays, packet dropouts and disturbances. Here, a so-called robust predictive control (RPC) approach is designed as follows: 1- delays and packet dropouts are accurately detected online by a network problem detector (NPD); 2- a so-called PI-based neural network grey model (PINNGM) is developed in a general form for a capable of forecasting accurately in advance the network problems and the effects of disturbances on the system performance; 3- using the PINNGM outputs, a small adaptive buffer (SAB) is optimally generated on the remote side to deal with the large delays and/or packet dropouts and, therefore, simplify the control design; 4- based on the PINNGM and SAB, an adaptive sampling-based integral state feedback controller (ASISFC) is simply constructed to compensate the small delays and disturbances. Thus, the steady-state control performance is achieved with fast response, high adaptability and robustness. Case studies are finally provided to evaluate the effectiveness of the proposed approach